AFalkenroth Diss
INAUGURAL - DISSERTATION
zur
Erlangung der Doktorwürde
der
Naturwissenschaftlich-Mathematischen Gesamtfakultät
der
Ruprecht-Karls-Universität
Heidelberg
vorgelegt von
Achim Falkenroth
aus Müllheim
Tag der mündlichen Prüfung:
27. Juli 2007
Visualisierung von
Sauerstoff-Profilen
in der wasserseitigen Grenzschicht
Gutachter:
Prof. Dr. Jürgen Wolfrum
Prof. Dr. Bernd Jähne
Dissertation
submitted for the degree of Doctor of Natural Sciences to
the Combined Faculties for Natural Sciences and for Mathematics
of the
Ruperto–Carola
University of Heidelberg
Germany
Visualisation of Oxygen Concentration Profiles
in the Aqueous Boundary Layer
presented by
Dipl. Chem. Achim Falkenroth
born in Müllheim
Institute of Environmental Physics
Group: Digital Image Processing and Waves
Referees:
Prof. Dr. Jürgen Wolfrum
Prof. Dr. Bernd Jähne
day of oral exam: 27. July 2007
Abstract
In environment studies as well as for technical application, the study of air–water gas
exchange is crucial. For process studies, a novel visualisation technique of oxygen concentrations in water was realised with high spatial resolution. To resolve turbulent processes
in water, also the temporal resolution was pushed to the limit of a imaging frame rate of
185 Hz. For this purpose, the well-established method of laser-induced fluorescence (LIF)
was extended introducing in this type of studies a new phosphorescent ruthenium dye that
is more than 15 times more sensitive to oxygen than the previously used indicator dye.
The chemical synthesis of this metal–ligand complex MLC was adapted to a preparation
without intermediate steps.
The challenge of this imaging technique for small-scale interactions was to resolve a
very thin boundary layer extending less than a millimetre below the water surface. An
image processing algorithm was developed that allow the automatic detection of the exact
location of the air–water phase boundary within the resolution of 25 µm/pixel. Only by
this step, an accurate direct determination of an important parameter for gas-exchange
studies, the boundary-layer thickness, is feasible.
The developed methods were applied to systematic gas-transfer measurements mostly
with surfactants, conducted in a range of wind speeds between 0.8–7 m/s in a circular wind–
wave facility. The measured gas-transfer velocities compared extremely well to exchange
rates derived from mass-balance methods. The novel visualisation technique drastically
increased the poor signal quality inherent to standard LIF techniques. This enabled accurate measurements of gas-transfer velocities from aqueous concentration profiles for the
first time.
Kurzfassung (German)
In den Umweltwissenschaften ebenso wie in technischen Anwendungen ist die Untersuchung des Gasaustausches grundlegend. Für mechanistische Studien wurde eine neuartige Visualisierungstechnik für Sauerstoffkonzentrationen in Wasser mit einer hohen räumlichen Auflösung realisiert. Um turbulente Prozesse im Wasser sichtbar zu machen, wurde
eine Bildrate am Limit der zeitliche Auflösung von 185 Hz verwendet. Für diesen Zweck,
wurde die bereits etablierte Methode der Laser induzierten Fluoreszenz (LIF) erweitert und
ein neuer phosphoreszenter Farbstoff verwendet, der eine mehr als 15-fach stärkere Sauerstoffempfindlichkeit aufwies verglichen mit dem zuvor verwendeten Farbstoff. Die chemische Synthese des Farbstoffs wurde auf eine Darstellung ohne Aufarbeitung angepasst.
Die Herausforderung dieses bildgebenden Verfahrens für kleinskalige Wechselwirkungen ist, eine sehr dünne Grenzschicht aufzulösen, die sich weniger als einen Millimeter
unter die Wasseroberfläche erstreckt. Ein Bildverarbeitungsalgorithmus wurde entwickelt,
der eine automatische Erkennung der exakten Position der Luft–Wasser-Phasengrenze innerhalb der Auflösung von 25 µm/Pixel erlaubt. Dieser Schritt ermöglicht die genaue
Bestimmung eines wichtigen Parameters von Gasaustauschstudien, die Grenzschichtdicke.
Die entwickelten Methoden wurden auf gezielte Gasaustauschmessungen vornehmlich mit einem Oberflächenfilm angewendet, die mit Windstärken zwischen 0.8–7 m/s
in einem zirkulären Wind–Wellen-Kanal durchgeführt wurden. Die gemessenen GasTransfergeschwindigkeiten stimmten äußerst gut mit Austauschraten überein, die aus
Massenbilanzverfahren bestimmt wurden. Die neue Visualisierungstechnik erhöhte die
Signalqualität von Standard-LIF-Techniken drastisch. Dies ermöglichte erstmals genaue
Messungen der Gas-Transfergeschwindigkeiten aus wasserseitigen Konzentrationsfeldern.
Table of Contents
I
1
Introduction and Theory
1 Introducing the Topic
1.1 Motivation: Fields of Application . . . . . . . . . . . . . . . . . . .
1.2 Aims and Corresponding Methods . . . . . . . . . . . . . . . . . .
1.3 Outline of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
6
8
2 Theory and Literature Review: Gas Exchange on Small Scales
2.1 Characteristic Quantities of Gas Exchange . . . . . . . . . . . . . .
2.2 Conceptual Description of Gas Exchange . . . . . . . . . . . . . . .
2.2.1 Stagnant Film Model . . . . . . . . . . . . . . . . . . . . .
2.2.2 K -Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Surface-Renewal Model . . . . . . . . . . . . . . . . . . . .
2.3 Gas-Exchange Parameters from Depth Profiles . . . . . . . . . . .
2.4 Review: Gas Exchange with LIF in the Literature . . . . . . . . .
11
11
15
16
16
19
22
23
II
Experimentals
25
3 Characterisation: Phosphorescence Dye and Quenching
3.1 Luminescence and Quenching . . . . . . . . . . . . . . . .
3.2 Beer–Lambert’s Law of Absorption . . . . . . . . . . . . .
3.3 Ruthenium Complex as a Luminescent Dye . . . . . . . .
3.4 Chemical Synthesis of the Ruthenium Complex . . . . . .
3.5 Absorption Spectra of the Dye . . . . . . . . . . . . . . .
3.6 Phosphorescence Emission Spectra . . . . . . . . . . . . .
3.7 Comparison of the Ruthenium Complex with PBA . . . .
4 Set-up: the Wind–Water Facility
4.1 Set-up at the Circular Wind–Wave Channel
4.2 Optics for Imaging . . . . . . . . . . . . . .
4.3 Spatial Calibration and Blurring . . . . . .
4.4 Varying the Bulk Concentration . . . . . . .
4.5 Controlling the Wind Speed . . . . . . . . .
ix
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27
27
30
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41
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47
48
5 Methods: Evaluation of Image Series
5.1 Pre-processing: Sensor Corrections . . . . . . . . . . .
5.2 Detection of the Surface . . . . . . . . . . . . . . . . .
5.3 Consideration of Absorption . . . . . . . . . . . . . . .
5.4 Calculate Concentrations from Luminescence Intensity
5.5 Effect of Blurring . . . . . . . . . . . . . . . . . . . . .
5.6 Fitting a Model to Measured Profiles . . . . . . . . . .
5.7 Polynomial Fit as Alternative . . . . . . . . . . . . . .
III
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Results and Discussions
51
52
52
57
58
60
60
62
65
6 Results: Gas-Transfer Velocities and Depth Profiles
6.1 Smooth Surface Under Wind Stress . . . . . . . . . . . . . . . . . .
6.1.1 Analysis of Concentration Fields in the Boundary Layer . .
6.1.2 Concentration Profiles and Turbulence Models . . . . . . .
6.1.3 Comparison of Transfer Velocities from LIF-Measurements
6.1.4 Transfer Velocity from the Bulk Concentration . . . . . . .
6.1.5 Comparison with Transfer Velocities of Other Gases . . . .
6.2 Bulk Turbulences Generated with a Mixing Pump . . . . . . . . .
6.3 Turbulence Structures with Wind Waves . . . . . . . . . . . . . . .
6.4 Fluctuation Profiles of the Concentration . . . . . . . . . . . . . .
6.4.1 Fluctuations in Bulk Turbulences . . . . . . . . . . . . . . .
6.4.2 Fluctuations in Wavy Conditions . . . . . . . . . . . . . . .
6.4.3 Fluctuations with Wind Stress at Smooth Surface . . . . .
67
67
68
71
74
76
78
79
82
88
89
90
91
7 Conclusions: Discussion of the Findings
95
8 Summary and Outlook
99
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.2 Outlook: Possible Improvements and New Concepts . . . . . . . . 101
IV
Appendix
103
A Wavy Conditions with Unsuccessful Image Registration
105
B Mathematica Script for Boundary-Layer Mathematics
111
C Software Tools
C.1 Data Acquisition with Heurisko Software .
C.2 Retrieving Oxygen Probe Data . . . . . .
C.3 Evaluation Scripting in MatLab Language
C.4 Type-Setting . . . . . . . . . . . . . . . .
117
117
117
117
118
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List of Figures
119
Index
121
Bibliography
125
Part I
Introduction and Theory
1
Chapter 1
Introducing the Topic
1.1
Motivation: Fields of Application
Exchange processes between air and water play an important role in natural
environments and technical applications. Their study can deepen our understanding of fundamental physics of turbulent processes in fluid dynamics.
The efficient transfer of chemical species between a gas phase and a liquid
phase is optimised in industrial plants using falling films, spray chambers or
bubble columns. Substances are absorbed by solvents or stripped from them.
Facilities extract H2 S from water to improve the quality of drinking water.
The treatment of water form sources near the soil surface include the stripping of carbonic acid in gas-exchange installations. The aeration of waste
water is essential in the biological treatment where micro-organisms decompose undesired contents in sewage. The re-aeration of lakes and rivers across
the water surface is a critical process for the ecology of these environments,
especially if they show high biological activity.
Gas transfer between the atmosphere and the oceans is an important actor
in the theatre of global climate change. Due to the use of fossil hydrocarbons
as a source of energy, the concentration of the important greenhouse gas in
the atmosphere carbon dioxide CO2 increased from a pre-industrial value of
about 280 ppm to 383 ppm in 2007 as seen in Fig. 1.1. The actual annual
increase is about 1.9 ppm as a mean of the last decade.
The International Panel on Climate Change (IPCC [2007]) reports that
the present atmospheric concentration of carbon dioxide exceeds by far the
natural range over the last 650,000 years (180–300 ppm) as determined from
ice cores. Nobody seriously doubts that the increase of carbon dioxide in the
atmosphere is caused by anthropogenic fossil fuel consumption.
The oceans are capable of storing atmospheric gases. A considerable sink
of these gases are deep water formations. An estimation by Siegenthaler
3
4
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Figure 1.1: Measured concentration increase of CO2 in the atmosphere during
the last 50 years. This curve is named after C.D. Keeling. The
mean concentration increases continuously. The periodical variation
of the concentration is due to seasonal biological activity (Courtesy
of Dr. P. Tans, NOAA/ESRL, www.esrl.noaa.gov/gmd/ccgg/trends)
and Sarmiento [1993] assumes that the uptake of CO2 by the oceans is
about a third of the anthropogenic emission.
Oxygen can be used as an environment tracer to determine the extend
of the role of the ocean as a sink. The burning of hydrocarbons consumes
atmospheric oxygen. When carbon dioxide is transformed into biomass, oxygen is released again. By taking the difference of the expected atmospheric
N2 /O2 ratio after the consumption of the known amount of fossil fuels in the
last years and the actual oxygen concentration found in the atmosphere, the
part that ended up in the oceans can be calculated to be approximately 30%
as documented by the IPCC [2001]. Sensitive measurements were carried
out by Keeling et al. [1996] and Manning [2001] and taken as a basis for
global gas-exchange modelling by e.g. Keeling et al. [1998].
The enhancement of air–water gas exchange by waves is striking. Several
authors (Wanninkhof [1992], Naegler et al. [2006], Ho et al. [2006b] to
cite only a few) introduced different parametrisation of the gas-transfer velocity with the wind speed with significant uncertainties regarding the measured
data and the underlying theoretical assumptions.
1 Introducing the Topic
5
Takahashi et al. [2002] assembled a world map of approximate local
CO2 fluxes through the ocean surface. A version that was included in the
IPCC report [2007] is shown in Fig. 1.2. In the annual mean, the warm
tropospheric regions of the ocean act as a source of CO2 whereas sinks are
found in polar regions. This is because the solubility of this gas decreases
with higher water temperature. The locally resolved information for this
map are temperature informations and the estimation of the wind speed
computed from satellite microwave backscattering. The latter is a measure
of the sea-surface roughness. On his web site referenced in the bibliography,
Takahashi et al. states that estimated fluxes change by 30% when the wind
speed is computed from two different parametrisations. Similar uncertainties
are expected when the assumed dependence of the gas-exchange rate from
wind is changed.
The IPCC [2007] comments Fig. 1.2: “The annual flux of CO2 for 1995
with 10 m winds is –1.6 GtC/yr, with an approximate uncertainty of ±1
GtC/yr, mainly due to uncertainty in the gas-exchange velocity and limited
data coverage.” The quadratic relation between wind speed and gas-transfer
velocity proposed by Wanninkhof [1992] was taken to calculate the exchange rate. The factor of proportionality in this parametrisation is not
well known. Moreover, also a cubic [Wanninkhof and McGillis, 1999] or
linear [Krakauer et al., 2006] dependence has been proposed.
Figure 1.2: World map of global mean sea-to-air flux of CO2 . A significant part
of the large error in this modelling is due to the uncertain behaviour
of the gas-exchange velocity (From IPCC [2007])
6
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Wanninkhof [2007] demonstrated that the gas transfer from the atmosphere into the ocean is one bottleneck besides the slow transport of gases
into deep water. He demonstrated that the influence of gas exchange variables is decisive for the results of global climate models. The improvement
of the reliability of these models is important to convince policy makers of
the need to change the employment of energy.
The interaction between ocean and the atmosphere is complex as summarised graphically in Fig. 1.3. Besides the exchange of heat and momentum,
the transfer of chemical species takes a central part in this system. A profound knowledge of mechanisms in this system and its interdependencies is
the basis of understanding influences on effects such as climate change. The
surface ocean lower atmosphere study (SOLAS) tries to link the different
aspects of air–sea interaction.
Waves amplify the gas exchange but they can be generated by light winds
only if the surface is clean and free of any kind of surface active substances.
A special case in the system shown in Fig. 1.3 is the gas transfer through the
air–sea interface covered by a surface film. Surfactants decrease the surface
tension and the different parts of the surface are hindered in their mobility.
This has a strong impact on the hydro dynamics in the boundary layer,
effectively damping waves and suppressing turbulences close to the interface.
This leads the focus on natural surfactants having a considerable influence
on air–sea interactions [Frew et al., 1990].
All these uncertainties demonstrate the need for a more substantial knowledge about small-scale processes. The gas exchange between the atmosphere
and the ocean is controlled by a thin sub-millimetre aqueous boundary layer.
Because of limited experimental techniques, the details of the mechanisms
and the structure of the turbulence near the phase boundary are not studied enough. Meanwhile some new well-engineered imaging techniques are
matured that give direct insight into the transfer processes and promise fundamental progress. Some of these techniques will be documented in the
following.
1.2
Aims and Corresponding Methods
The objectives of this study are:
• Visualisation of concentrations in water. Concentration fields are visualised
in water by applying the idea of laser-induced fluorescence LIF. Indicator
dyes are sensitive to dissolved gases and the intensity of luminescent emission
varies with the concentration. A fast digital camera with 640×480 pixel and
a resolution of 25 µm/pixel looks at a laser-light sheet with a frame rate of
1 Introducing the Topic
7
Figure 1.3: The forms of interaction between the ocean and the atmosphere are
manifold. The SOLAS programme coordinates research on these
very different topics that are depicted in the chart (From [SOLAS])
185 Hz. A high imaging rate is important to resolve the turbulence processes.
After calibration the concentration is calculated from the light emitted by
the luminescent dye at every location.
• LIF with a novel class of phosphorescent dyes. The established oxygen
indicator, a pyrene derivative, has some drawbacks, e.g. the low sensitivity
and small quantum yield. These lead to a poor signal-to-noise ratio. A type
of ruthenium metal–ligand complexes MLC shows better properties regarding
the requirements of LIF applications in water. Oxygen quenches efficiently
the phosphorescence of this dye. As the quenching process is fast compared
to mass fluxes, the concentration of the quencher O2 is evaluated reliably at
any point.
• Study of concentration fields in gas-exchange experiments. In laboratory
experiments the gas exchange is studied under a range of different reproducible conditions. In a wind–wave facility of the Aeolotron laboratory at
the University of Heidelberg, these conditions are fully controllable. The
wind speed can be varied accurately in the range between 0.8–7 m/s. A surfactant film on the water surface suppresses the generation of wind waves
even at high shear stress. A disequilibrium of concentration induces a invasion flux of oxygen from ambient air into the degassed water bulk across the
8
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
air–water interface.
• Extraction of concentration profiles. The difficulty in studying the mechanisms of air–water gas exchange is due to the small thickness (30–800 µm)
of the aqueous mass-boundary layer at a free interface. This thin skin of the
water body dominates the gas exchange through the surface. Accurate measurements of the intensity profile near the phase boundary are a premise for a
further analysis. By image processing steps the surface position is detected in
every image row for image registration. Further evaluations produce a mean
concentration profile for the determination of the boundary-layer thickness.
• Comparison of calculated transfer velocities with reference measurements.
The boundary-layer thickness of every concentration profile depends on the
gas flux at this position. The computed transfer velocity is compared with
mean gas-exchange rates of trace gases at the same wind conditions. They
are measured simultaneously with a mass-balance method during the evasion
of these gases.
• Comparison of the profile shape with model predictions. Theoretical models predict the concentration profile based on hydrodynamic assumptions
for certain conditions. They express the physical mechanism of turbulent
transport across the diffusive boundary layer. Different gas-exchange concepts introduced in Sec. 2.2 cohabit in the literature. Classical mass-balance
methods can not distinguish between the different theoretical concepts considering that they measure the mean flux averaged over the whole interface.
Only techniques that visualise localised concentration fields of the dissolved
gases give direct insight into the turbulence close to the phase boundary
because the descriptions differ significantly only in the concentration distribution within this thin layer. The comparison of the shape of the theoretical
profiles with the measured data reveal the dominant mechanism for the selected condition.
1.3
Outline of this Thesis
In a first part, the characteristic quantities are defined and the fundamental
concepts of gas exchange are discussed in Chap. 2. Here the theoretical
description of the mean concentration profile in the mass-boundary layer are
developed.
For laser-induced fluorescence, a suitable dye is needed and thus a ruthenium complex is presented and characterised in the next part in Chap. 3.
Fundamentals of luminescence and its quenching are introduced aside specific absorption and emission spectra of the phosphorescent luminophore.
Also the chemical synthesis of the organo-metallic compound is described.
1 Introducing the Topic
9
Gas-exchange experiments were carried out in a water flume under a range
of different wind speed conditions. The equipment is illustrated in Chap. 4.
The properties of the instrumentation and of the optical set-up are explained.
The need of resolving areas in the scale of 100 µm in the water leads to an
optical blurring of the images. The influence of this blurring on the final
measurement is detailed in this chapter.
To extract concentration profiles and measurable gas-exchange parameters from grey-value image sequences, some steps of image processing are
needed that are the subject of Chap. 5. For the calculation of the boundarylayer thickness, two approaches will be described, a commonly used method
of extrapolation of the highest gradient and a newly developed method considering the blurring in a model function.
In Chap. 6 the results are exposed and the good performance of the novel
imaging technique is demonstrated. Concentration profiles are compared to
the theoretical ones, and gas transfer velocities are shown together with reference measurements from a mass-balance method. The behaviour of the
concentration field in different gas-exchange experiments with varying conditions is presented. The findings in experiments with a smooth surface are
analysed. A side product was the generation of bulk turbulence that could
be analysed with the same techniques as the data measured under wind
stress.
Finally the results are evaluated and summarised in Chap. 7. At the end,
a summary of this work is found in Chap. 8 where also an outlook on further
studies and future research is suggested.
Chapter 2
Theory and Literature Review:
Gas Exchange on Small Scales
In this chapter the basic relationships of physical parameters and properties
are presented that describe the gas transfer through the interface between
air and water. In general, the transfer between two phases is driven by a
difference of any transportable physical quantity such as gases, momentum
or heat. Nonetheless, the description will be limited here to the exchange
processes of gases.
2.1
Characteristic Quantities of Gas Exchange
When gases are transferred from the air into the water or vice versa, the
mass flux through the surface area A defines a flux density j that can be
determined by monitoring the development of the concentration with time
in a water volume V assuming that the concentration change is only due to
gas exchange and not to chemical reaction:
j=
1 dm
V dc
=
A dt
A dt
(2.1)
In the case of equilibrium the mass flux from one phase into the other is
as high as in the inverse direction so that the net flux and the concentration
gradient is zero. Thus, Eq. 2.1 defines the net flux j. Generally a flux of gases
in both directions is characterised by the transfer velocity k. The transfer
velocity is defined as the constant of proportionality between the mass flux
density j and the difference in concentration ∆c across the aqueous boundary
layer.
j = k∆c
11
(2.2)
12
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
The transfer velocity k is also called the piston velocity. This quantity
can be taken as the velocity of an imaginary syringe piston that presses the
concentration into the water.
The solubility of a substance is usually not the same in both phases.
Thus, the concentrations reach an equilibrium with a certain concentration
difference at the interface. To correct for this, one of the concentrations
can be scaled by the Ostwald solubility α. With this the flux through an
interface is:
j = k(cbulk − αcair )
with the dimensionless solubility
α = ceq,bulk /ceq,air
One way to determine αcair in an experiment where cair = ceq,air is kept
constant is to measure the concentration in the water bulk cbulk in the state of
equilibrium. It is advantageous to use the same measurement technique for
determining cbulk and αcair because some errors of the measurement cancel
out and an additional uncertainty from the value of solubility is avoided.
The underlying assumption is that the water concentration directly at
the surface is always in equilibrium with the air concentration. This is to say
that the solving process for the transition between the phases is sufficiently
fast compared to the mass transport near the interface by mere diffusion to
neglect the influence on these equations. This implies also that there is no
resistance to mass transfer in the air.
Combining Eq. 2.1 with Eq. 2.2 yields the mass-balance method for
measuring the transfer velocity k with the knowledge of the mixing height
h = V /A:
h
dc
= k∆c
dt
(2.3)
The flux density ~j due to diffusion can be calculated from the gradient
of concentration by Fick’s law and is caused by random thermal motion of
the particles:
~
~j = −D∇c
(2.4)
The factor D is called diffusivity and has the common units of [cm/s2 ].
This diffusion constant is a specific quantity of a substance in a given medium.
For all gases the diffusivity is much higher in air than in water. This is
also a reason why for most gases the resistance to mass transfer in air can
2 Theory and Literature Review: Gas Exchange on Small Scales
13
be neglected compared to the resistance in water. For our application the
diffusivity of oxygen in water is important. The temperature dependence is
given by Mayer [1995] from data in Jähne [1980].
The minus sign in Eq. 2.4 reflects the observation that mass flux is in the
direction towards lower concentration. At the interface this relation holds
also in presence of turbulence, given that here the vertical mass flux is only
due to diffusion because the surface can not be penetrated by flows or eddies.
Thus, jz can be taken from the gradient of concentration at the surface that
forces the gas into the bulk of the water. In this text the coordinate z is the
depth from the water surface.
The gradient of the concentration c can change in time t due to the mass
transport by diffusion or by transport in streams with the velocity ~u of the
fluid. The resulting relation is called Fick’s 2nd law:
dc
∂c
~ = −∇
~ ~j = D∇
~ 2c
=
+ ~u ∇c
(2.5)
dt
∂t
Therefore, also the transfer velocity k depends on the diffusivity D of the
transported species. If the transfer velocities of different gases A and B are
compared under the same conditions, a relation between them is revealed
[e.g. in Jähne, 1980]:
k ∝ D+n ⇒
kA
DA +n
ScA −n
ν
=
=
+n
−n with Sci =
kB
Di
DB
ScB
(2.6)
The Schmidt number Sc was introduced in the literature to describe the
relation of diffusivity to the momentum transport expressed in the quantity
of the kinematic viscosity of water ν = µ/% where µ is the dynamic viscosity
and % is the density of the medium. For gases dissolved in water the dimensionless Schmidt-number ranges between 100–2000. The Schmidt-number
exponent n depends on the forcing conditions of the gas exchange. For wind
driven gas exchange it was shown that the exponent is 2 /3 for a smooth
rigid interface and 1 /2 for the free surface [Jähne and Haußecker, 1998;
Degreif, 2006].
In field studies the development of the single concentrations are not as
easily accessible as other quantities. A parametrisation for the gas exchange
with these parameters is needed. In most ocean gas-exchange studies the
wind speed u10 in the height of 10 m above the water surface is used as a
parameter [Wanninkhof, 1992; Naegler et al., 2006]. The relation adopts
the following form:
k=
Sc−n
u10 χ
β
(2.7)
The coefficient β is estimated empirically with a high variability by measuring tracer gases like He and SF6 [Ho et al., 2006a; McGillis et al., 2001;
14
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Nightingale et al., 2000]. Mostly a quadratic dependence (χ = 2) from
wind speed is assumed but also cubic [Wanninkhof and McGillis, 1999]
or linear [Krakauer et al., 2006] dependencies are found.
A parameter, that takes the condition like surfactants or roughness of
the water surface into account, is the mean wave slope σ̄w [Jähne, 1985;
Degreif, 2006]. In global modelling the wind fields are taken as a parameter
and they are computed from a measure of the surface roughness determined
by satellites via radar backscattering. The friction velocity u? as a measurable
quantity includes more influences on momentum transfer from wind into
water.
To characterise the gas exchange, some other quantities are important in
this work. Dividing the diffusivity D by the transfer velocity k, a quantity
z? with the unity of a distance is calculated that is called boundary-layer
thickness. Using Eq. 2.2 and Eq. 2.4 this spatial scale is geometrically given
as the interception of the vertical gradient of the concentration at the surface
with the bulk concentration level as seen in Fig. 2.1:
z? =
Normalised depth z+ from surface
0
c bulk
D
∆c
∆c
=D
= ∂c k
jz
− ∂z z=0
Concentration c
(2.8)
c surface
water surface
1 <−− z
*
2
3
4
5
6
Figure 2.1: Definition of the boundary-layer thickness z? in a concentration profile c(z+ ) (solid line) derived from the gradient of the concentration
∂c/∂z+ at the surface z+ = 0 (broken line) with z+ = z/z?
2 Theory and Literature Review: Gas Exchange on Small Scales
15
The sole assumption for this is that at the water surface the molecular
diffusion is the only process driving the balancing of the gas concentrations
towards the equilibrium. All the transport by flows and eddies is dumped by
viscosity and buoyancy near the interface.
Another quantity is derived by the ratio of z? and k giving the time scale
t? of the gas-exchange process. This is the time that is needed for a particle
to pass through a distance z? driven by molecular diffusion. Using Eq. 2.8
makes clear that only one of the three parameters t? , z? or k is needed to
characterise the gas exchange:
t? =
D
z?
= 2
k
k
(2.9)
The value of this number can be given by taking typical values of the
transfer velocity k = 3.6 cm/h = 10−3 cm/s and the diffusion coefficient of
oxygen in water D = 2.4 10−5 cm2 /s at 25°C.
D
= 0.24 mm
k
z?
= 24 s
t? =
k
z? =
In this work the boundary-layer thickness z? is the key parameter to
measure. Even with the knowledge of the profile close to the surface, the
value of z? can not be measured as a distance for all cases because it depends
on the transport process below the surface and thus from the turbulence
structure.
Diffusion is dominating only near the surface. In the case that no mean
flow exists close to the surface, only turbulence adds to the diffusion. The
character of the turbulence alters the form of the vertical concentration profile and with this the level of concentration where z? is reached. In the
next section different models are summarised describing the mechanism of
transport that add to the diffusion.
2.2
Conceptual Description of Gas Exchange
With increasing distance from the surface, turbulence adds to the molecular diffusion as a mass-transport mechanism. There are different theories
about the description of the turbulence processes. They all yield in different
concentration profiles in the boundary layer that can be visualised with the
presented LIF technique.
16
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
2.2.1
Stagnant Film Model
A very simplistic model is the model that assumes only diffusion up to a
certain distance from the surface and at a certain point the turbulence is
the only gas transporting force. To adapt this stagnant film model, first
published by Lewis and Whitman [1924], to a given transfer velocity, the
diffusion layer thickness can be adjusted and is the same as z? . For the
concentration profile this model predicts a linear line like the broken line in
Fig. 2.1. In this model, the Schmidt-number exponent is n = 1.
k ∝ Sc−1
(2.10)
The idea of a sudden change from diffusion to turbulence at a certain
depth is not physically reasonable and the implication of the dependence
of the gas exchange rate from the Schmidt-number exponent of n = 1 is
not found in gas-exchange experiments. As it underestimates the transfer
velocity k, the value calculated using this simple model can be taken as a
lower limit.
2.2.2
K -Model
Turbulence eddies can not penetrate the surface and only diffusion is present
exactly at the surface. In this picture the eddy size has to decrease towards
the surface. This is why the model is also called small-eddy model. This
effect happens everywhere and is statistically independent from time. This
means that a turbulence effect is simply added to the molecular diffusion
but increases with depth from zero to get dominant beyond the boundary
layer. The diffusivity is now the sum of the molecular diffusion coefficient D
and a turbulent diffusion coefficient Kt that gave this concept also the name
K-model. Considering the turbulence in Eq. 2.5 with Eq. 2.4 yields:
∂
∂c̄(t, z)
∂c̄(t, z)
=
(D + Kt (z))
(2.11)
∂t
∂z
∂z
The characterisation of the turbulence structure by a turbulent diffusivity Kt includes some temporal or spatial averaging and describes the mean
concentration profiles c̄(t, z).
Coantic [1986] deduces a cubic relationship between the turbulent diffusivity and the depth for a smooth rigid wall using some assumptions about a
limited mobility of the surface water. For a free surface he yielded an increase
as a square of the distance to the interface and Coantic cited some authors
[Davies, 1972; Brutsaert and Jirka, 1984] that observed this increase.
2 Theory and Literature Review: Gas Exchange on Small Scales
17
The concentration depth profile can be computed from the differential
equation if the depth dependence of the turbulent diffusivity Kt is expressed
according to a power law in the way Jähne et al. [1989] did:
Kt (z) = αm z m with m > 2
(2.12)
In the case of stationary conditions the concentration does not change
with time t, and the partial derivatives of Eq. 2.11 become an ordinary differential quotient:
d
m dc̄(z+ )
0 =
(1 + αm+ z+ )
(2.13)
dz+
dz+
In the latter equation a transition to dimensionless variables was made
where the variables are scaled by constants describing the flux:
z+ =
z
αm z? m
and αm+ =
z?
D
(2.14)
The second-order ordinary differential equation in Eq. 2.13 can be solved
by substitution of dc̄/dz+ := y. The resulting first order differential equation
is solved by separation of the variable and integration:
αm+ m z+ m−1
dy(z+ )
= −
y(z+ )
dz+
1 + αm+ z+ m
Z
Z
1
αm+ m z+ m−1
dz+
dy = −
y
1 + αm+ z+ m
ln(y(z+ )) = − ln(1 + αm+ z+ m ) + č2
c2
⇒ y(z+ ) =
1 + αm+ z+ m
(2.15)
(2.16)
The function ln denominates the natural logarithm. The integration constant c2 = exp(č2) = −1 can be given under consideration of the boundary
condition y(0) = dc̄/dz+ |z+ =0 = −1 what is the one dimensional Fick’s law
of Eq. 2.4 in the dimensionless version with the assumption that molecular
diffusion is the only transport process at the surface.
Inverting the substitution, the depth dependent function of the concentration c̄(z+ ) is found:
Z
Z z+
1
c̄(z+ ) =
y(z+ ) dz+ = c1 −
dž+
(2.17)
1 + αm+ ž+ m
0
with m > 0
Again the integration constant c1 = 1 is determined by a boundary condition: c̄(0) = 1. According to the definition of the relative concentration c̄
18
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
between 0–1, this concentration has to vanish at large distances. Using this
boundary condition, an expression for αm+ can be given:
Z ∞
1
(2.18)
lim c̄(z+ ) = 1 −
dž+ = 0
z+ →∞
1 + αm+ ž+ m
Z ∞0
m
m 1
π
⇒ αm+ =
(2.19)
=
m dž+
1 + ž+
m sin(π/m)
0
with m ∈ N > 1
For the special cases of a free surface (m = 2) and a smooth rigid wall
(m = 3 or 4), specific functions can be written as:
π π
π π
z+ = arccot
z+
(2.20)
m = 2 ⇒ c̄(z+ ) = 1 − arctan
2
2
2
2
π2
with α2+ =
4
√
√
3
1
4π
3
3 +
arctan √ −
z+ −
ln 9 + 2 3πz+
m = 3 ⇒ c̄(z+ ) =
4 2π
9
2π
3
√
√
3
2
2
+
ln 81 − 18 3πz+ + 12π z+
(2.21)
4π
8π 3
with α3+ = √
81 3
π 1
π 1
(2.22)
m = 4 ⇒ c̄(z+ ) = 1 + arctan 1 − z+ − arctan 1 + z+
π
2
π
2
1
1
+ ln 8 − 4πz+ + π 2 z+ 2 −
ln 8 + 4πz+ + π 2 z+ 2
2π
2π
π4
with α4+ =
64
For m = 2 or 3 this is a similar result as found by Münsterer [1996].
A detailed derivation of these equations using the algebra programme Mathematica can be found in Appendix B. The transformation in Eq. 2.20 from
arctan(x) to arccot(x) has to be treated with caution because different definition ranges for x are encountered leading to different results for x 6 0.
The corresponding graphs are shown in Fig. 2.2 where the normalised concentration c+ is defined between the concentration at the surface csurface and
the bulk concentration cbulk .
c+ =
c − cbulk
csurface − cbulk
(2.23)
With increasing m, Kt decreases for values lower than z = z? or z+ = 1,
and Kt gets more and more dominant for values z > z? . Hence, with increasing m, the curves approach the linear curve predicted by the stagnant
film model. The Schmidt-number exponent n was derived theoretically by
2 Theory and Literature Review: Gas Exchange on Small Scales
19
Normalised concentration c
+
0
0
Normalised depth z
+
1
0.5
1
water surface
−− boundary−layer thickness z*: z+= 1 −−
2
3
m = 4 ( n = 3/4) smooth surface K−model
4
m = 3 ( n = 2/3) smooth surface K−model
m = 2 ( n = 1/2) free surface K−model
5
p = 1 ( n = 2/3) smooth surface renewal model
p = 0 ( n = 1/2) free surface renewal model
6
Figure 2.2: Model functions for the cases of a free surface and a smooth rigid
surface assuming the K-model (= small-eddy model) or the surfacerenewal model
Coantic [1986] as n = 32 and 12 for a smooth rigid surface (m = 3) and a
free surface (m = 2) respectively. This leads to the relation with m of the
power law of Eq. 2.12 as:
n=1−
1
m
(2.24)
The third mentioned possibility in Eq. 2.22 is m = 4 what makes n = 34 .
There are experiments like in a convection tank in Jähne [1980] that suggest
such a Schimdt number dependence.
2.2.3
Surface-Renewal Model
Danckwerts [1951, 1970] proposed an event based model in which large
eddies dominate the transport. These eddies reach the phase boundary replacing the surface water with bulk water. Simultaneously they drag the
surface water with concentrations that are in equilibrium with the air phase,
deeper in the water bulk. A modelling parameter here is the time constant
of the renewal rate. Danckwerts used the mathematical formulation that
Higbie [1935] developed to describe the gas exchange in a stage column. In
this film column a periodicity was given by the distance of the stages. In
20
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Higbie’s set-up it was not turbulence that renewed a surface but the water
was exposed only for a certain time to the air.
In analogy, Danckwerts claimed that the different patches of the surface are exposed to the air for a certain time before they are renewed statistically in events with a renewal rate λ characteristic for the gas-exchange
conditions. These events are called sometimes large eddies giving this name
also to the model. Using this assumption, Eq. 2.5 can be extended by a
renewal term in the following form:
∂2
∂c̄(t, z)
= D 2 c̄(t, z) − λ(z) c̄
∂t
∂z
(2.25)
Again, for stationary conditions this equation can be solved as an ordinary
differential equation. In the dimensionless form the solution is quite obvious
considering the boundary conditions:
d2
c̄(z+ ) − λ+ c̄(z+ ) with λ+ = λ t?
(2.26)
dz+ 2
dc̄(z+ ) c̄(0) = 1 and
= −1 and lim c̄(z+ ) = 0 ⇒ λ+ = 1
z+ →∞
dz+ z+ =0
0
=
⇒ c̄(z+ )
=
e−z+
(2.27)
So the boundary condition limz+ →∞ c̄(z+ ) = 0 confines the renewal rate λ
to be the inverse of the time constant t? −1 defined in Eq. 2.9. For comparison
the exponential function is also plotted in Fig. 2.2.
Harriott [1962] stated that the eddies can not reach the surface but
they can come very close to it. This satisfies the hydrodynamic condition
that only molecular diffusion is present at the surface. This is especially the
case for smooth rigid surfaces. In this penetration model the distance of the
eddies from the surface is another parameter for the gas transfer velocity.
The closer the surface gets the fewer eddies reach that distance. Gulliver
[1991] framed this concept in a conceptual sketch of the size of z? depending
on the renewal eddies as displayed in Fig. 2.3.
In analogy to Eq. 2.12 the depth dependence of λ is assumed as a general
power law as it was done by Jähne et al. [1989]:
λ = γp z p with p > 0
(2.28)
In this equation the classical view of Danckwerts [1970] is represented
by the case of p = 0 where the renewal is only at the surface and not depth
dependent. With the power law for the renewal rate, Eq. 2.25 turns into the
following form:
0 =
d2
c̄(z+ ) − γ+p z+ p c̄(z+ ) with γp+ = γp z? p t?
dz+ 2
(2.29)
2 Theory and Literature Review: Gas Exchange on Small Scales
21
Figure 2.3: Variation of the boundary-layer thickness due to surface-renewal
events. N.B.: δ is identical to z? of Eq. 2.8 (Adapted from Gulliver [1991])
For p = 1 this equation is the Airy differential equation and the solution
for c̄(z+ ) is an Airy function:
d2
c̄(z+ )
dz+ 2
=
γ+1 z+ c̄(z+ )
(2.30)
dc̄(z+ ) = −1 and lim c̄(z+ ) = 0 ⇒ γ+1 ≈ 2.58
c̄(0) = 1 and
z+ →∞
dz+ z+ =0
1
Ai(0)
Ai − 0
z+ ≈ 2.82 Ai (1.37 z+ )
(2.31)
⇒ c̄(z+ ) =
Ai(0)
Ai (0)
In Fig. 2.2 the form of this function is compared to the results of the
other models.
For the surface-renewal model, Csanady [1990] calculated the dependence of the Schmidt-number exponent to be the same as in the K-model
with 32 and 12 for a smooth rigid surface (p = 1) and a free surface (p = 0)
respectively yielding the following relation:
n=1−
1
p+2
(2.32)
This means that at a free surface it is assumed that every renewal event
reaches the phase boundary. Thus, when a mean concentration profile follows
the prediction of the surface-renewal model, a concentration fluctuation at
the phase boundary is expected while the other presented models do not
predict fluctuations directly at the surface.
22
2.3
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Gas-Exchange Parameters from Depth Profiles
From the form of the depth profile like in Fig. 2.1 there are two ways of
accessing the transfer velocity k: one is the calculation of the gradient at
the surface using Eq. 2.8. This method is independent of the structure of
turbulence because turbulence can be neglected at the surface:
∂c −D ∂z
z=0
k=
(2.33)
∆c
The other method measures a depth dependent on the assumed turbulence structure in the aqueous boundary layer. One criterion for the turbulence is the surface condition: is it wavy or flat. Another one is the form of
the mean profile following the theory discussed in Sec. 2.2.
Knowing the functional description of the concentration, the boundarylayer thickness z? can be found at the depth z+ = 1. As can be seen in
Fig. 2.2, this is for the K-model from Eq. 2.20 and Eq. 2.21 c̄(1) = 0.361
and c̄(1) = 0.235 for m = 2 and m = 3 respectively. In the surface-renewal
model the values from Eq. 2.29 and Eq. 2.31 are c̄(1) = 1/e = 0.368 and
c̄(1) = 0.240 for p = 0 and p = 1 respectively.
As this is only valid for the mean profile, a statistical problem arises
that is mentioned recently in Jähne et al. [2007]. For this technique, taking
the mean of the concentration is equivalent to averaging the boundary-layer
thickness z? what is after Eq. 2.8 proportional to the inverse of the transfer
velocity k:
1
D
hz? i = D
6=
(2.34)
k
hki
The determination of k via a thickness z? in a mean profile is only admissible if the variation of the concentration-profile form is not very high. This
is especially not the case in the surface-renewal model with a free surface
where the transport is dominated by statistical processes in which the form
of the profile changes completely. In LIF experiments sometimes injection
events are visible what is also reported by several other authors [Herlina
and Jirka, 2004; Takehara and Etoh, 2002]. Variano and Cowen
[2007] cited also Nagaosa [1999] and Magnaudet and Calmet [2006]
that show similar phenomena in simulations.
For this case Jähne et al. [2007] proposed a bimodal evaluation calculating two different values of k, one for surface-renewal events and another
for the time in between. The difficulty for the implementation is to find a
unique criterion in every instant for this decision.
2 Theory and Literature Review: Gas Exchange on Small Scales
23
In LIF experiments that visualised the water boundary layer, the correct
gradient of the oxygen concentration at the surface could not be determined
directly because of optical blurring and high noise level. To reduce the noise,
either smoothing of the data was done or averaging over a number of depth
profiles, or both [Duke and Hanratty, 1995; Münsterer, 1996; Herlina, 2005].
To handle the blurring, some authors applied the method of taking the
highest gradient of the smoothed data in some depth near the surface as the
gradient at the surface defining the mass flux j. The data near the surface,
where the blurring was obvious, was corrected by extrapolation. Assuming
an exponential function, the boundary-layer thickness z? was measured at a
depth where the concentration decreased to 1/e.
1
c+ (z) = e−z/z? ⇒ c+ (z? ) =
(2.35)
e
In an exponential function this distance is the same as the inverse of the
normalised concentration gradient at the surface or the distance from the
surface at the extrapolation of this gradient to the bulk concentration level
cbulk .
1
∂c+ =−
−
(2.36)
∂z z=0
z?
The highest gradient of smoothed measured data is often far from the
surface and so the distances are not the same.
In this work both aspects, blurring and noise, were considered by fitting
a model function that consists of a convolution of a function describing the
concentration increase near the surface and a Gaussian smoothing function
assumed as the point spread function (PSF) expressing the blurring explained
in detail in Sec. 5.6. This fitting procedure is stable enough to determine
the boundary-layer thickness of the noisy single depth profiles that were
measured when no surface-renewal events are seen. With surface-renewal
events the theoretical profiles are applicable only to mean profiles where the
noise level is low. The different steps will be described in detail in Chap. 5
about the image processing methods. The results of fitting single profiles will
be compared to the fits of mean profiles in Sec. 6.1.3.
2.4
Review: Gas Exchange with LIF in the
Literature
In the literature two different kinds of visualisation techniques for gases dissolved in water are reported: first the pH-indicator technique and later the
oxygen-quenching technique with the pH-indicator technique.
24
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
The key point of the pH-indicator technique is the conversion of the
flux of an acid or alkaline gas from the air to the water surface into a
flux of fluorescence intensity by a chemical reaction with a dye. 40 years
ago this technique was used to investigate the gas-transport mechanisms in
falling films (Fahlenkamp [1979]; Hiby et al. [1967]; Hiby [1968, 1983]).
In 1989, the pH-indicator technique was first used in a grid-stirred tank
by Asher and Pankow [1989]. The authors measured time series of the
CO2 concentration fluctuations close to a gas-liquid interface at a fixed position using dichloro fluorescein. The first successful measurements of vertical
concentration-profiles within the aqueous mass-boundary layer at a free interface in a wind–wave facility were reported by Jähne [1991] using HCl gas.
More detailed studies using fluorescein followed later (Münsterer [1996];
Münsterer and Jähne [1997]; Schladow et al. [2002]; Variano and
Cowen [2007]).
In the same year, the first successful measurements from wind–wave
flumes using the oxygen-quenching technique were reported by Wolff et al.
[1991]. Pyrene butyric acid PBA was used, a dye known from measurements of dissolved oxygen concentrations in cells (cf. Vaughan and Weber
[1970]). PBA luminescence was stimulated by a N2 laser in the UV at 337 nm.
Later other authors used the same dye in wind–waves flumes (Münsterer
[1996]; Münsterer et al. [1995]; Woodrow and Duke [2002]) and gridstirred tanks (Herlina and Jirka [2004, 2007]) for oxygen exchange studies.
The rather qualitative character of the previously published results indicates that the currently used fluorescent dyes still show significant disadvantages. The use of PBA to measure oxygen dissolved in water gives rise
to several problems. Firstly, the quenching effect is rather weak causing a
poor signal-to-noise ratio of the concentration measurements. Secondly, it is
difficult to solve PBA in water. Thirdly, PBA is a surface active chemical
species. This means that the hydrodynamic boundary conditions at the air–
water interface (surface tension and surface elasticity) are altered by PBA.
Thus, the search for a more suitable fluorescent dye seemed promising, and
a better luminescent dye for the oxygen-quenching technique could be found
that will be presented in the next chapter.
Part II
Experimentals
25
Chapter 3
Characterisation:
Phosphorescence Dye and
Quenching
The currently applied dye in oxygen visualisation techniques, pyrene butyric
acid PBA, showed disadvantages like weak susceptibility to quenching, low
solubility and surface activity. Hence, the search for a more suitable alternative seems promising. Castellano and Lakowicz [1998] proposed a
ruthenium complex as a soluble phosphorescent dye for the analysis of oxygen concentrations in water.
This class of the luminescent dye, that is used in this work, has little
application in other fields because this type of chemical species does not
behave well in living cells and most application need to fix an insoluble dye
in a medium such as membranes. Consequently, this chemical is not easily
available. The synthesis of the metallo-organic complex is described before
it is characterised by its spectra of absorption and emission.
3.1
Luminescence and Quenching
There are different processes inducing a substance to emit light. Energy
sources other than light are present in chemiluminescence (chemical reaction), incandescence (heat), electroluminescence (electrical current), crystalloluminescence (crystallisation), fractoluminescence (fracture of a crystal),
piezoluminescence (pressure) or radioluminescence (ionising radiation).
In light induced photo-luminescence the energy comes from the absorption
of UV or visible light exciting an electron from its singlet ground state S0 to a
vibrational state of the first excited singlet state S1 . These energy transitions
are depicted in the so-called Jablonski diagram in Fig. 3.1.
27
28
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Figure 3.1: Jablonski diagram describing the energy transitions and typical
lifetimes in a molecule relevant for fluorescence and phosphorescence
After the absorption the vibronic energy is dissipated into heat and the
particle ends up in the vibronic ground state of the excited state S1 . From
here there are different relaxation paths. In fluorescence a photon is emitted
and a vibrational state of the ground state S0 is reached. Then the lifetime
of the excited state is of the order of 10−8 s. Fluorescence is observed only
in the case that the faster process of internal conversion (IC) is suppressed,
which leads to a transition from one singlet state into another. Here the
energy would be dissipated by a non-radiative relaxation.
In some cases the excited energy states of the triplet and the singlet
interact allowing a intersystem crossing (ISC) into the triplet state T1 . The
ground state of the excited triplet state has a long lifetime because the photon
emission relaxing to a singlet state is not allowed and thus shows lifetimes τ
usually longer than 10−7 s. This emission is called phosphorescence.
Absorption leads to an excited state of the molecule. The probability for
an electronic excitation to cause an emission of a photon is called quantum
yield φ of the luminescence. In addition, the presence of certain substances
may decrease the luminescence further. This quenching of the luminescence
intensity I depends on the concentration of the quencher [Q]. When a luminescent dye is excited continuously the absorption rate a and the relaxation
rate ã are of the same magnitude. The relaxation is proportional to the concentration of the dye in the excited state [D? ]0 . In absence of any quencher
3 Characterisation: Phosphorescence Dye and Quenching
29
the relaxation can be non-radiative energy dissipation with a rate knr or the
emission of a photon with the luminescence rate Γrad .
a = ã = (knr + Γrad ) [D? ]0 = γ [D? ]0
(3.1)
The constant of proportionality γ is the inverse of the lifetime τ0 of the
excited state in absence of the quencher. In the presence of a quencher but
keeping the excitation a the same, there is an additional relaxation rate kQ .
With higher concentrations [Q] of the quencher, a higher quenching effect is
observed:
a = γ [D? ] + kQ [Q][D? ]
(3.2)
Taking the ratio of Eq. 3.1 and Eq. 3.2 simplifies the relation. The number
of photon emissions and thus of luminescence intensity I is correlated directly
with the number of molecules in the excited state [D? ]:
γ [D? ]0
(γ + kQ [Q]) [D? ]
1
1
γ
=
with τ0 =
=
γ + kQ [Q]
1 + kQ τ0 [Q]
γ
1
=
with KSV = kQ τ0
1 + KSV [Q]
1 =
⇒
[D? ]
I
=
?
[D ]0
I0
I
I0
(3.3)
The Eq. 3.3 is called Stern–Volmer equation [1919]. With high values
of the quenching constant KSV , the luminescence is very sensible to the presence of oxygen. The dependence on the quenching concentration is evident
when the luminescence is plotted versus the quencher concentration as it is
done in Fig. 3.2.
There are different mechanisms of quenching. It may occur after the
formation of a temporal complex between the quencher and the dye. In
this static quenching the concentration of the active luminophore is reduced
and the absorption spectrum may be changed due to the absorption of the
complex. The luminescence lifetime is independent of the concentration of
the quencher.
In dynamical quenching the decrease of luminescence is induced by collisions between the dye and the quencher. Here the quantum yield φ is reduced
and also the lifetime of the excited state is shorter. By measuring the decrease of luminescence with time after a very short excitation pulse as it
is done in fluorescence lifetime imaging FLIM, dynamical quenching can be
distinguished from static quenching.
In the case of the triplet, molecule oxygen the mechanism seems to be
a spin–spin interaction leading to intersystem crossing with non-radiative
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Mean intensity I/I0 (%)
30
Stern Volmer fit
Ru complex
PBA
100
80
60
40
20
0
0
5
10
15
O concentration (mg/L)
2
Figure 3.2: Relation between the quencher concentration and the luminescence
of the ruthenium complex described in Sec. 3.3 (KSV =11300) and
the often used dye PBA (KSV =645, Vaughan and Weber [1970],
dash-dotted line). The values for the ruthenium complex are taken
from Vogel [2004]. The solid line is a fit of the Stern–Volmer
relation to the data. More dense data points are found in Fig. 5.8
relaxation. Lakowicz [2006, Chap. 9.2] cites some authors [Evans, 1957;
Kawaoka et al., 1967; Kearns and Stone, 1971] that have studied oxygen
quenching but the correct mechanism is still discussed.
3.2
Beer–Lambert’s Law of Absorption
In the beginning of photo-luminescence processes, the energy is transferred
to the molecule by absorption of light. When electro-magnetic radiation
passes a medium, it can interact with the matter inducing absorption that
in general depends on the wavelength λ of the radiation. The attenuation of
the light intensity dI 0 (λ) is proportional to the incident intensity I 0 in this
area.
dI 0 (λ)
= −α(λ)I 0
(3.4)
dx
The absorption coefficient1 α is characteristic for the passed medium and
h
i
1
adopts the unit length
. By integrating, the light attenuation between the
1
The so-called attenuation coefficient (formerly extinction coefficient) accounts also
for scattering and luminescence (cf. International Union of Pure and Applied Chemistry
IUPAC [1997]).
3 Characterisation: Phosphorescence Dye and Quenching
31
points x = 0 and x = l can be calculated where the intensity decreases from
I0 to I:
ZI
I0
Rl
1
0
−α(λ) dx =
dI
=
I0
0
I
− [ln I 0 ]I0 =
[α(λ) x]l0
=
− ln I + ln I0 = +α(λ) l − 0 =
I0
ln =
α(λ) l
I
(3.5)
The inverse of α is called penetration depth lp and denominates the distance in which the radiation decreases to 1/e. Disregarding luminescence
and scattering, the transmittance T decreases exponentially with the length
of the optical path l in the matter.
T =
I
= e−α(λ) l
I0
(3.6)
When a chemical substance in the medium causes the absorption, the
absorption coefficient α can be expressed using the number concentration
n = number
of the substance: α = n σA , where σA (λ) has the area unit [m2 ]
volume
and thus describes the absorption cross section.
The fraction of the absorber can also be given by the amount concentrah
i
tion of the molecules cA = NnA in units of mol
with the Avogadro number
L
23 1
NA = 6, 022 10 mol . This yields the molar absorption coefficient2 κA in units
h 2i
of cm
: α(λ) = cA κA (λ).
mol
Taking the decadic logarithm of Eq. 3.6 leads to a form of the Beer–
Lambert’s law.3 Here the absorbance (or absorbancy) A is proportional to
the length of the optical path l in the medium and to the concentration of the
absorber cA with the decadic molar absorption coefficient εA as a material
property constant of the solved substance.
A = − lg
I
= cA εA (λ) l
I0
(3.7)
This absorbance A is frequently found in spectroscopy characterising the
spectroscopic property of a substance at the wavelength of highest absorption. While the absorbance depends on the length of the optical path in the
2
The symbol κ is preferred by the IUPAC [1997] for the natural logarithmic absorption
coefficient.
3
Often called Beer–Bouguer–Lambert or simply Beer’s law. In German the
chronological order of the names is followed. This exponential relation was found independently in similar forms by the two scientists: Pierre Bouguer 1729, Johann
Heinrich Lambert 1760. It was extended to the concentration in liquids by August
Beer 1852.
32
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
medium and the concentration of the absorber, the extinction coefficient at a
certain wavelength is specific for any substance. Analogously, the expression
ln II0 is called Napier absorbance4 Ae . The different factors can be converted
with this relation: κ = σA NA = ε ln 10.
3.3
Ruthenium Complex as a Luminescent
Dye
Oxygen has been known a long time as a substance that reduces quantum
yields of luminophores [Kautsky, 1939]. As O2 is abundant in the atmosphere, this is a problem for most applications in fluorescence spectroscopy.
To use this phenomenon fruitfully for the measurement of oxygen concentrations, some luminescent dyes with long lifetimes show the suitable quenching
properties.
Vaughan and Weber [1970] presented pyrene butyric acid PBA as a
quenchable dye. The water solubility and favourable properties made of it a
versatile oxygen indicator in cell biology as well as in visualising gas-exchange
processes. Its structure is shown in Fig. 3.3.b. A disadvantage of the dye is
that it lowers the surface tension like a tenside in a soap. Then the molecules
accumulate at the surface because the energy is lower when the ionic part
is solved in the water and the hydrophobic organic part has less contact
with water. The same low energy condition can be established when these
molecules gather to form micelles in the water.
Surface activity of a dye for visualising the gas exchange with different
wind conditions is not desired because it lowers the concentration in the
bulk but foremost because surfactants alter the surface tension and reduce
the waves (cf. Frew et al. [1995]; Frew [1997]). Other disadvantages of
this dye will be analysed in detail in Sec. 3.7.
Phosphorescence in aqueous solutions is observed rarely (cf. Chap. 8.18
in Lakowicz [2006]) because the luminescence of long lifetime states are
quenched quickly by oxygen or other quenchers like amino acids, CS2 or even
water itself. It occurs only where the chromophoric centre is well protected
like inside a protein or a screening organic ligand. This is the case for example
in platinum or palladium porphin derivates and also for diimine complexes
4
After a posthumous publication of Napier of 1619 about the logarithm with the base e
but also the term optical density OD(λ) or extinction is common, what is used more in
general as the sum of absorption, luminescence, reflection and dispersion. The IUPAC
[1997] dissuades from the use of these terms because they were not clearly defined. The
implicating logarithms are not always with the same base leading to misunderstandings
because in the physical literature the work with the natural logarithm is more usual.
3 Characterisation: Phosphorescence Dye and Quenching
33
OH
O
(a)
(b)
Figure 3.3: Chemical structure of luminescent dyes. (a) The ruthenium complex
Ru(dpp ds)3 . (b) The organic molecule pyrene butyric acid PBA
of ruthenium, osmium and rhenium (cf. Chap. 20.3 in Lakowicz [2006]).
Zelelow et al. [2003] applied a platium(II) porphyrin complex for oxygen measurement diffused in a membrane. Barlow et al. [1998] used the
quenching of a phosphorescent palladium(II) porphin complex to measure
the concentration of oxygen in the heart organ with an imaging technique.
The system for measuring oxygen water concentrations proposed by
Castellano and Lakowicz [1998] is based on another soluble phosphorescent metal complex. The structure shown in Fig. 3.3 is a chemical compound consisting of three diimine ligands and a ruthenium central
ion. Its systematic name is sodium tris(4,7-diphenyl-1,10-phenanthroline
disulfonic acid)ruthenate(II) (Na4 [RuII (dpp ds)3 ]) and the sum formula is
Na4 [Ru(C24 H14 N2 O6 S2 )3 ] with a molecular weight of M = 1710.6 g/mol and
the Chemical Abstracts Service Registry Number (CAS) 23316-7-5.
The literature knows the ligand also with the names disodium
batho-phenanthroline-disulfonate BPS, 4,7-diphenyl-1,10-phenanthrolinium di(sodiosulphonate) or (1,10-phenanthroline-4,7-diyl)bis-benzenesulfonic
acid disodium salt and it has the specific weight of M = 536.5 g/mol. The
ligand is sold as a hydrate of the disodium salt (CAS: 52746-49-3 or 5374442-6). The position of the sulfonate groups is often given as 4,4’ (para) but
in most synthesis this position is not controlled.
The ionic sulfonate groups turn the molecule into a water-soluble substance. The 3-D structure is symmetric and thus shows no surface activity.
A related compound without the sulfonic acid groups, so that it is not
soluble in water, is the tris(4,7-diphenyl-1,10-phenanthroline)ruthenium(II)
dichloride (Ru(dpp)3 ) (CAS 36309-88-3). Fixed in a membrane the dye is
34
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
used in sensors to measure oxygen concentrations with a optical method
described by Lakowicz [2006, Chap. 19.4].
A new application for oxygen indicating dyes is the use in optodes, i.e.
membrane tips at the end of light conducting glass fibres [Narayanaswamy
and Wolfbeis, 2004; Schröder, 2006; Schröder et al., 2007]. These
can measure the oxygen concentration in environments as small as a single
biological cell.
3.4
Chemical Synthesis of the Ruthenium Complex
In the literature [see overview of Krause, 1987] various reactants were employed for the synthesis of this class of compounds. No objections to the
use of ruthenium chloride, RuCl3 , were found. Other educts like potassium
pentachloro ruthenate K2 RuCl5 seemed to be more expensive related to the
content of ruthenium.
Only the complex with a reduced Ru2+ ion as a centre atom shows the
characteristic colour and phosphorescence. As a reductive reactant, ascorbic
acid (AscA) was chosen because of its availability.
Other reducing agents mentioned by Krause [1987] are hypophosphite
(NaH2 PO2 ) or tartrate (Na2 (HCOHCOO)2 ). Rose and Wilkinson [1970]
proposed to reduce first the ruthenium with hydrogen gas H2 . This avoids the
creation of side products but the intermediate solution of blue ruthenium(II)
is prone to oxidation and can be handled only in inert atmosphere, e.g. by
employing standard Schlenk techniques. Anderson and Seddon [1979]
urged workers to adopt this method where trace impurities may be critical
in spite of the grater intricacy and lower yields involved. The synthesis of
Ru(dpp ds)3 via the blue solution is described by Anderson et al. [1985].
A variant of the applied synthesis of the η 2 -chalate complex is described
in Rabilloud et al. [2001] without any purification. In the publication the
solution of the dye can be stored in the refrigerator for several months. It
was applied for staining proteins in electrophoresis.
Chemical reaction:
AscA
RuIII Cl3 + 3 Na2 (dpp ds) −−−→ Na4 [RuII (dpp ds)3 ] + 2 NaCl + HCl (3.8)
T
100 mg (0.45 µmol) ruthenium(III) chloride hydrate, RuCl3 · x H2 O (alfa
aesar, Karlsruhe), were solved in 20 ml deionised water and heated to boiling
temperature. The use of a reflux condenser is advisable. 800 mg (1.5 µmol)
of the ligand 4,7-diphenyl-1,10-phenanthroline disulfonic acid disodium salt
3 Characterisation: Phosphorescence Dye and Quenching
35
(98%, alfa-aesar, Karlsruhe) was added in little excess and the solution was
kept boiling for 20 min. The solution turned in deep greenish brown.
An excess of 1 g (5.7 µmol) ascorbic acid sodium salt (AscA, here vitamin C L-ascorbic acid) was added and boiled further 20 min. The solution
changed colour instantly to orange–brown. The filtering of the hot product
solution was skipped. After cooling down to room temperature, the pH was
adjusted to 7 with diluted sodium hydroxide solution. The solution showed
now the characteristic red luminescence when illuminated with blue light.
The solution can be evaporated and dried in a exsiccator over phosphorus
pentoxide P4 O10 in vacuum what gives a orange–brown solid. As the ruthenium complex is not soluble in other solvents than water, the substance was
cleaned with ethanol. With this, most of the excess of educts and other salts
are taken away.
For further purification the chemical compound can be recrystallised from
ethanol–water solution. After solution in little amount of water the substance
can be chromatographed with water as eluant as described by Anderson
et al. [1985].
3.5
Absorption Spectra of the Dye
The absorbance A of the ruthenium dye following the definition of Eq. 3.7 was
measured with a commercial HP 8453 UV–Vis spectrometer. The spectrum
is shown in Fig. 3.4.
4
Absorbance A (rel.u.)
3.5
3
2.5
2
1.5
1
0.5
0
200
300
400
500
600
Wavelength (nm)
700
800
Figure 3.4: Absorption spectra of the ruthenium complex: absorbance of a UV–
Vis spectrometer (broken line) and absorption measured via the
emission at 617 nm in a fluorescence spectrometer (solid line)
36
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
There are several high absorption bands in the UV range of the wavelength spectrum below 350 nm and a broad distinct absorption band in the
blue between 400–500 nm. The absorption maximum in the blue is 462 nm.
The relation between absorption and emission can be measured in a fluorescence spectrometer. The emission at a fixed wavelength is measured
while the exciting light energy is changed continuously. This is done with a
Fabry–Pérot interferometer (often called etalon) as a adjustable band-pass
filter in the path of the white exciting light. The intensity of the detected
luminescence must be normalised with the spectrum of the white exciting
light to compensate its effect.
In Fig. 3.4 also the spectrum of such a measurement is shown. The
wavelength of the detected luminescence was fixed at 617 nm so that the best
dynamic range of the signal could be used. The differences in the spectra
may be explained by a better resolution of the fluorescence spectrometer.
The thin band width of the light passed through the etalon seems to be
better than the resolution of the UV-Vis spectrometer determined by the slit
function and the discretisation in pixels in the line detector. The differences
in the UV range of the spectrum can be caused also by absorptions of the
dye that do not induce phosphorescence at the fixed emission wavelength.
Here the absorptions result in higher electronic states that have different
probabilities for transitions into the triplet state T1 in Fig. 3.1.
3.6
Phosphorescence Emission Spectra
The luminescent emission spectra were obtained with two methods. One was
the excitement with a blue LED with a central wavelength of 445 nm. The
emission was analysed with the Ocean Optics spectrometer USB2000. A glass
fibre was positioned 90° to the LED in front of a small cuvette with a solution
of the dye. The scattered blue light from the LED was filtered with an edge
filter that cuts off any light above 470 nm. The fibre was mounted at the
case of the spectrometer. Two spectra with different oxygen concentrations
in the solution are displayed in Fig. 3.5.b. The amount of oxygen dissolfe in
the water did not change the shape of the spectrum but only the intensity.
A second method is to measure the emission in a fluorescence spectrometer also shown in Fig. 3.5.b. Here the excitation wavelength was fixed to
473 nm (solid line) and 279 nm (broken line) and the wavelength of the emission was scanned with the same etalon filter as for the absorption spectrum
in Fig. 3.4.
There is no characteristic difference in the emission between 550–750 nm
but there is an additional luminescence between 350–450 nm when the ruthe-
3 Characterisation: Phosphorescence Dye and Quenching
37
50
Linear intensity (a.u.)
40
30
20
10
0
300
400
500
600
700
Wavelength (nm)
800
900
400
500
600
700
Wavelength (nm)
800
900
(a)
50
Linear intensity (a.u.)
40
30
20
10
0
300
(b)
Figure 3.5: Emission spectra of the ruthenium complex observed at different oxygen concentrations and excitation wavelengths. (a) Oxygen concentration of 8 mg/mol (solid line) and 1 mg/mol (broken line) exciting
with a blue LED showed the identical shape. (b) Spectra from a fluorescent spectrometer with excitation 279 nm (broken line) gives the
same emission in the red as excited with at 473 nm (solid line) but
has an additional emission in the UV
38
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
nium complex is illuminated with UV light. This can be fluorescence or
phosphorescence of the second excited triplet state T2 . It was not studied if absorptions of wavelengths below 350 nm lead to the same quenching
properties like the excitation with longer wavelengths.
For comparison with the linear emission spectrum, the logarithmic absorbance spectrum of Fig. 3.4 was transformed into a linear intensity spectrum IA by doing the following calculation:
IA = 10A − 1
(3.9)
The large Stokes shift between the absorption and the emission with
little overlap of the spectra in Fig. 3.6 demonstrate that there is very little
self-absorption. This is an advantage for a dye in the application as an
indicator.
70
absorption
phosphorescence emission
Linear intensity (a.u.)
60
50
40
30
20
10
0
400
500
600
700
Wavelength (nm)
800
900
Figure 3.6: Absorption and emission spectra of the Ru complex: absorbance of
a UV–Vis spectrometer (broken line) and phosphorescence emission
after the excitation with the wavelength of 473 nm in a fluorescence
spectrometer (solid line)
3 Characterisation: Phosphorescence Dye and Quenching
3.7
39
Comparison of the Ruthenium Complex
with PBA
For the measurement of oxygen concentrations, the luminescent dye has to
fulfil some requirements of very different aspects. An ideal oxygen indicator
as a water soluble dye for the herein described type of application should
comply the following list:
Desired properties:
High quenching constant
High absorbance
Good quantum yield
High photo-stability
Large Stokes shift
Good solubility
Low surface activity
Compatibility with available light sources
Regarding this list of desirable characteristics, the advantages of the
ruthenium complex can be compared to pyrene butyric acid PBA of Fig. 3.3
that has been widely used in other oxygen–LIF studies of gas exchange (for
literature see Sec. 2.4).
ˆ A high quenching constant, and thus, high sensitivity according to the
Stern–Volmer equation in Eq. 3.3, requires a long lifetime of the
excited state in the order of at least some µs. Ru(dpp ds)3 shows a
unquenched lifetime of 3.7 µs and a quenching constant KSV defined
by Eq. 3.3 of 11 300 L/mol (0.35 L/mg) as reported by Castellano
and Lakowicz [1998] and confirmed by own measurements shown in
Fig. 5.8. This graph shows that the intensity of luminescence in air saturated water with a oxygen concentration of 8.3 mg/mol is only about
10% of the intensity in absence of oxygen. Hence, 90% of the phosphorescence was quenched. The indicator is especially sensitive at low oxygen concentrations. This represents a much higher sensitivity to oxygen
than the quenching constant of PBA (645 ±79 L/mol in Vaughan and
Weber [1970] or 683 ±70 L/mol in Münsterer [1996]). The luminescence in air saturated water is still 87% (cf. Fig. 3.2).
ˆ PBA needs a UV laser as a light source (e.g. a N2 laser at 337 nm).
This excitation wavelength of high energy leads to some additional
bleaching. The ruthenium complex shows better photo-stability and
absorbs in the visible blue between 400–500 nm where cheap and handy
light sources like LEDs or diode pumped solid state dpss lasers for the
stimulation of the luminescence are available. Fig. 3.4 shows 462 nm as
a maximum of absorption in the visible.
40
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
ˆ The Stokes shift of Ru(dpp ds)3 between a stimulation with 473 nm
and an emission maximum of 618 nm (cf. Fig. 3.6) is 145 nm. Above
530 nm, absorption is low enough to have no significant self-absorption
of the fluorescent light. This is a much larger Stokes shift than
for PBA when employing a N2 laser with a stimulation at 337 nm,
an emission maximum at 375 nm and a Stokes shift of 38 nm (cf.
Vaughan and Weber [1970]) resulting in self-absorption. Using an
other laser like a twice frequency-doubled yttrium–aluminium garnet
YAG with the wavelength of 266 nm [Schladow et al., 2002; Lee and
Schladow, 2000] changes the excitation wavelength but the problem
of the self-absorption is the same.
ˆ The six sulfonic groups make Ru(dpp ds)3 excellently soluble in water,
and the dye shows no surface activity (cf. Sec. 3.3). In contrast, PBA is
almost insoluble in water. It can only be solved in NaOH before mixing
with water resulting in a much lower maximum of concentration.
Chapter 4
Set-up: the Wind–Water
Facility
Gas-exchange studies are of interest in oceanography and limnology. To
dissolve luminescent dyes in such environments seems to be quite unrealistic.
Even though there are experiments of using fluorescein as a tracer for water
mixing [Ho et al., 2006b].
To study the mechanism in small scales like a air–water boundary layer,
it appears to be more appropriate to simulate some of the natural conditions
in the laboratory because a luminescent dye can be solved homogeneously
in the water and examined with a stable optical set-up under controllable
conditions.
The experiments were conducted in a small circular wind–wave channel.
In such a facility the wind field over the water surface reaches an equilibrium
after some minutes. The optical set-up and the generation of the various
wind speeds will be documented in this chapter as well as the methods for
changing and measuring the oxygen concentration in the water.
4.1
Set-up at the Circular Wind–Wave Channel
The small circular wind–wave flume in Heidelberg featured a diameter of
1.2 m and a channel width of 20 cm. A sketch of it is shown in Fig. 4.1. The
water height in the presented studies were between 10–13 cm. The tank was
filled with approximately 70 L of distilled water. The concentration of the
added phosphorescent dye was about 10−5 mol/L. The channel was equipped
with temperature sensors in the air and the water and some pipe connections
for probing water and air samples.
The facility had four rotating paddles to generate the wind. The speed
41
42
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Flat mirror
Laser
Cylindrical mirror
Oxygen probe
Laser light sheet
Tube pump
12 cm
Optical adaptor
paddle
Cuvette
Total height 45 cm
Wind
Water depth
20 cm: Channel width
Camera
Diameter: 120 cm
Gas-ex pump
Gas exchanger module
Mixing pump
Figure 4.1: Schematic drawing of the small wind–wave facility and the optical
set-up
was controlled by adjusting the current of the rotor depending on the actual wind speed. When a propeller sensor reported a lower wind speed the
controlling PC raised the current and vice versa.
A commercial Clark-type electrode oxygen sensor was used to gather
informations about the value and the changing rate of the oxygen concentration in the water bulk. The amperometric electrodes have their name
from Clark [1956]. The method of analysing reducible and oxidisable substances is also called polarography. In modern sensors, oxygen penetrates a
membrane of the sensor and is reduced at a cathode, creating a measurable
electrical current. This current is proportional to the O2 concentration in the
environment of the device. This technique works in air as well as in water.
The reaction of the oxygen is irreversible so that small amounts of oxygen
4 Set-up: the Wind–Water Facility
43
are consumed during the measuring process. This produces a drift of the signal over time in a stagnant medium. In order to assure stirring, a constant
water flux was pumped out of the channel, passed the oxygen sensor in a
small cuvette and re-entered the channel.
4.2
Optics for Imaging
A laser sheet was generated with a cylindrical mirror in the path of the
laser light. The direction of the sheet was adjusted orthogonal to the wind
direction as seen in Fig. 4.1.
Using a scanning flat mirror instead of the cylindrical mirror to generate the laser sheet gave rise to triggering problems with the camera. The
homogeneity of the light sheet was slightly better. But the dominant influence on the light-sheet structuring arose from the poor optical properties
of the scratched channel cover. In this work only the results with the laser
sheet generated by the cylindrical mirror are described. An example of the
captured image is shown in Fig. 4.2.
Depth from surface z (mm)
−5
0
5
10
0
5
Width (mm)
10
Figure 4.2: Typical image of the laser sheet taken with the measurement camera.
The darkening is caused by the quenching of the oxygen penetrating
the surface towards the degassed water bulk. The upper part of the
image is a total reflection at the surface
The laser was a commercial diode-pumped solid-state dpss laser (from
Roithner, Vienna). The output power was adjustable with the current to a
maximum of about 50 mW. The output wavelength was fixed at blue 473 nm
44
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
with a spectral width much less than the resolution of the available spectrometers of 0.3 nm.
The laser-line expansion to 2 cm was small relative to the distance of 50 cm
between the water surface and the expanding mirror so that the assumption
of parallel light in the first 10 mm below the surface is justified. The diameter
of the laser beam was about 1 mm what was also the thickness of the resulting
light sheet.
The camera was a CCD-camera with 1/3” Kodak sensor (monochrome,
progressive scan) with a resolution of 640×480 pixel (Dragonfly Express from
Point Grey Research, Canada). The maximal frame rate was 200 frames per
second. But when taking a long series of images, there was a delay for the
image acquisition so that the effective frame rate in the described experiments
was 185 Hz.
The distance of the camera from the light sheet was about 50 cm, and
most of the optical path was in the water. To minimise the distortion of the
optical path, a water filled optical adapter was glued on the channel wall.
This corrected for some of the distortion reducing the blurring and permitted
the camera to look through a plane window.
The camera was tilted horizontally to reduce occlusion effects from waves.
This angle was 5–10°. Thus, the upper part of the captured image is a total
reflection on the surface. If the surface is not distorted by waves and is flat,
the reflection is a mirror image of what is seen below the surface. An example
of this is shown in Fig. 4.2. At z = 0 a dark horizontal line indicates the
surface because here oxygen penetrates the surface and a higher concentration
in the boundary layer lowers the luminescence intensity by quenching.
The presented method is most powerful without waves. Waves lead to
occlusions of the surface when observed from the side. Higher waves would
also move the surface out of the frame that is pictured by the measurement
camera. And enlarging the imaged area decreases the resolution. Between
these two factors an optimum has to be found.
Surfactants suppress the generation of waves with wind speed up to several meters per second. They also effect the gas exchange between air and
water. Biological surfactants as from phytoplankton are important in a natural environment [Frew et al., 1990] and the effect of surface films have been
of interest in several studies [Frew et al., 1995; Frew, 1997].
In most experiments in the circular channel, one or two drops of stearic
acid with the systematic name of octadecanoic acid were applied on the water
surface as a surfactant to generate a stagnant film.
4 Set-up: the Wind–Water Facility
45
−4
−2
−− Surface −−
Depth (pixel)
200
300
400
500
Depth from surface (mm)
100
2
4
6
8
10
600
100
(a)
0
200 300 400
Width (pixel)
70
75 80 85 90
Grey value (a.u.)
95
(b)
Figure 4.3: Image for spatial calibration of a millimetre scale. (a) Above the
surface at pixel 158 the total reflection is seen. A pixel resolution of
25.2±0.2 µm/pixel can be read off. (b) Mean of the 10 profile lines
marked in (a) to determine the pixel resolution
4.3
Spatial Calibration and Blurring
For the spatial pixel resolution a millimetre scale positioned at the laser sheet
in the water was captured with the camera in the experimental set-up. The
image is shown in Fig. 4.3.a.
The left side of the image shows a white area of saturation because of the
laser line illuminating the scale. This assures that the millimetre scale was
positioned in the plane of the laser sheet which is in the focal plane of the
camera optics.
To determine the pixel resolution, the distance of 437 pixel of 11 scale
marks with a distance of 1 mm was taken. With this the distance from one
pixel to the next is 25.2±0.2 µm/pixel. To visualise the scale marks, a mean
grey value of 10 lines, that are highlighted in Fig. 4.3.a, is shown in Fig. 4.3.b.
The surface in Fig. 4.3 is the middle between the longer scale marks. The
reflection of the water surface in the upper part of the image is bent near the
phase boundary by the scale dipping into the water. Because of this effect,
the marks near the surface appear distorted.
The edges of the marks are not sharp. This is a property of the optical
path quality that can be explained by the oblique course of the light passing
different materials and by the high magnification. During the evaluation of
46
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
the data the importance of knowing the extend of blurring became apparent.
To assess the extend of blurring, an edge in the image of Fig. 4.3.a was
selected. It is the the area marked with a box at the right bottom in the
image. In Fig. 4.4.a this area is zoomed. In Fig. 4.4.b a model function was
fitted to a mean of the 16 rows. The model consisted of a box function with
the mean values of the darker part and of the brighter part. To consider the
blurring, a convolution of this function with a blurring function was done
that was assumed to be the one-dimensional point spread function (PSF) of
the optical system.
For this blurring, a Gauss normal probability curve (Gaussian) fb was
2
was taken as a measure of the extend of the
assumed and the variance σblurr
blurring:
x2
exp −
2σblur 2
fb (x) = NNorm
(4.1)
The normalisation factor NNorm was chosen as the sum of all values so
that a convolution with this function does not change the mean grey value.
555
560
560
570
570
575
580
−5 0 5 10
580
Grey value (rel.u.)
Depth (pixel)
565
585
590
590
595
465 470 475
Width (pixel)
(a)
55
60
65
Grey value (a.u.)
(b)
1
0.9
0.8
−5 0 5 10
Distance (pixel)
(c)
Figure 4.4: Estimating the extend of blurring in the optical path. (a) A detail of
the image in Fig. 4.3.a. Taking the mean of all 16 rows reduces the
noise. (b) The mean row (dots) can be compared to a a box model
(dash–dotted line) convoluted with different blurring functions. The
2
convolution with a Gaussian of σblur
= 7 (solid line) fits best. (c) Effect of the blurring on the grey value: two lines with the distance of
8 pixel before and after convolution with the blurring function
4 Set-up: the Wind–Water Facility
47
The resulting function from convolution of the box model with the Gaus2
sian was fitted to the averaged measured rows and σblur
was varied. The
2
fit with σblur = 7 yields the lowest residual difference between the measured
points and the model function. This means that after 4 pixel the intensity
goes down to less than 1/e. In Fig. 4.4.b also convoluted functions with
2
σblur
= 4 and 20 are plotted with broken lines for comparison.
2
The value σblur
= 7 is the upper limit of the blurring because not all
the assumptions will be fulfilled that the black mark on the scale is printed
with a sharp edge, that this edge is ideally projected in the middle between
two pixels and that the camera is perfectly parallel to this edge excluding
smoothing by averaging.
In Fig. 4.4.c the effect of the blurring is demonstrated. A measure of
the optical resolution is the minimum of the distance where two lines can be
2
distinguished. After convolution with a Gaussian with σblur
= 7 this distance
is 8 pixels. With the pixel resolution of 25.2 µm, this results in a effective
optical resolution of about 200 µm. But with noise the distance can grow.
Figure 4.5: Photograph of the ”Jostra Quadrox” gas-exchanger module from Maquet. It was used to lower the concentration of oxygen in the water
bulk
4.4
Varying the Bulk Concentration
In order to strip dissolved oxygen from the water, a ”Jostra Quadrox” gasexchanger module from Maquet is installed (see Fig. 4.5) in a volume of
20 × 20 × 5 cm2 . It contains membrane capillaries with a total membrane
48
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
surface of 1.8 m2 and a water volume of 250 ml. These small capillaries have
micro perforations that are permeable only for gas molecules while liquids
are held back. The device is normally used in cardio–pulmonary machines
to load blood with oxygen and extract carbon dioxide. The gas exchanger
can be used for other gases as well [Vogel, 2006].
Oxygen concentration cbulk (mg/L)
10
9
8
7
6
5
4
3
2
1
0
−0.5
0
0.5
1
1.5
Time (h)
2
2.5
3
3.5
Figure 4.6: Decrease of oxygen concentration during degassing with the gasexchanger module.
In the work described herein the gas exchanger was employed with a
vacuum of 60 mbar to degas the water to oxygen concentrations lower than
0.8 mg/L as it is seen in Fig. 4.6.
Water was pumped through the module with a flux of 14 L/min, so that
the concentration in the wind–wave flume decreased from approximately
8.8 mg/L to 0.83 mg/L after 3 hours as is seen in Fig. 4.6. The starting
concentration was higher than the equilibrium concentration of 8.3 mg/L because at the beginning of this measurement the gas-exchanger module worked
with a sightly elevated pressure from a gas generator. At higher pressure the
partial pressure of oxygen in water is higher than at ambient pressure. The
gas generator stripped CO2 and H2 O from ambient air and was used to assure
a sufficient air flux in the gas exchanger.
4.5
Controlling the Wind Speed
In the experiments with wind, the speed of the wind paddles was varied by
controlling a power supply with a PC. The computer gathered information
on the wind speed and raised the current if the mean wind speed was too
4 Set-up: the Wind–Water Facility
49
low and lowered it if the wind speed was too high. Wind measurements are
shown in Fig. 4.7.a.
In experiments with parallel measurements of gas-exchange rates of trace
gases, the wind speed was increased after 30 min. When only oxygen was
measured, the wind speed was changed after 20 min. Shortening the exchange
times increases the contrast in the boundary layer because with time the
oxygen concentration in the water bulk increases and so the intensity of
phosphorescence decreases.
10
Wind speed v (m/s)
8
6
4
2
0
0
0.5
1
1.5
2
(a)
2.5
Time (h)
3
3.5
4
4.5
O2 concentration cbulk (mg/L)
10
8
6
4
2
0
0
(b)
0.5
1
1.5
2
2.5
Time (h)
3
3.5
4
4.5
Figure 4.7: Typical development of the wind speed in an experiment. (a) The
wind changed after a fixed time of 30 min. (b) Correlated to the
wind speed was the increase of bulk oxygen concentration
50
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
In this experiment a surfactant forced a smooth surface. At wind speed
higher than 7 m/s the surface film breaks what can be seen in the plot after
4 hours. In a first moment the wind energy is transformed into wave energy
and the speed slowed down. It takes some time to adjust the current to
achieve the maximum wind speed of almost 8 m/s.
In Fig. 4.7.b the parallel development of the oxygen concentration with
the wind speed is displayed. With increasing wind speed the slope of the
oxygen curve rises. When the surface film breaks, waves are generated and
the gas exchange is enhanced dramatically.
Chapter 5
Methods: Evaluation of Image
Series
Pre-processing:
Sensor correction
Feature extraction:
Surface detection
Image registration
Shifting of the single profiles
Normalisation:
Consideration of the absorption
Calibration:
From intensities to concentrations
Modelling:
Effect of blurring
Averaging:
Mean conc. profile
Model fitting:
Theoretical
profiles
Alternative fitting:
Polynomial fit
Parameter extraction:
Boundary-layer
thickness
Figure 5.1: Flow chart of the image processing steps: from raw image data of
luminescence intensity to concentration profiles and the boundarylayer thickness
51
52
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
5.1
Pre-processing: Sensor Corrections
Grey value
The data acquired by the CCD chip of a digital camera has little offset for
that negative values are not possible. To account for this offset, a dark image
has to be subtracted from the acquired images.
Before any experiment a dark sequence of 5000 images was captured under
the same conditions as during the experiment but without the laser light.
This was done by blocking the laser beam. Averaging one column in time
results in a noisy dark image line like the one shown in Fig. 5.2. The influence
of surrounding light was low because of the small integration time at a frame
rate of 185 Hz.
2
1
0
0
100
200
300
400
Pixel number (z direction)
500
600
Figure 5.2: A mean column of a sequence of dark images. The two different parts
of the chip show a little different offset. The z-direction is the depth
The built-in CCD chip in the Dragonfly-Express camera, that was used
for all measurements, consisted of two independent fields that showed a little
shift between these areas, and at the interface additional intensity differences
were seen. Especially in low light conditions it was important to correct for
this effect. Thus, the first step of the evaluation was to subtract the dark line
from every measured line. The dynamic sensitivity of the chip shows a similar
structure originating from the two parts but it was not corrected. Is has an
observable effect when luminescence is low at high oxygen bulk concentrations
as in Fig. 6.3 at high measurement numbers where the luminescent signal is
low.
5.2
Detection of the Surface
The position of the free water surface in a depth profile moves between images
and in most cases also from line to line. The motion is caused by waves,
vibrations or agitation. For the evaluation of luminescence intensity profiles
the shift of the surface position has to be taken into account.
A helpful feature in the images is that in invasion experiments of oxygen
the luminescence in the boundary layer decreases and that this structure is
5 Methods: Evaluation of Image Series
53
mirrored by total reflection at the surface what is seen in the example image
of Fig. 4.2. This feature and its symmetry is used for the automatic surface
detection in this thesis.
Difficulties in estimating the position of the surface arise from other factors than the concentration that can alter the light intensity. For high frame
rates the signal-to-noise ratios get low. Another factor is that reflections on
the surface may be disturbed by a rough surface and show very low intensity
far from the surface. Or passing waves lead to occlusions and no surface can
be seen at all. Also, in surface-renewal events the lowest concentration can
be found below the surface.
In the literature some solutions of the problem of surface detection were
developed. Variano and Cowen [2007] decided by eye where the surface
in every image was. The surface appeared brighter because of the reflection
of floating particles. A drawback of this tedious work is that some bigger
particles give some reflections also when they are only near the laser sheet.
Also a second camera looking at the surface from a position slightly above
the interface level can be used. The method was presented by Banner and
Peirson [1998] and applied for some LIF measurements by Variano and
Cowen [2007]. In the upper camera the surface is clearly seen as the end
of the light sheet because there are no interfering reflections. The images of
the two cameras have to be spatially correlated and synchronised in time.
Another method uses the fact that the highest concentration of oxygen is
normally found at the surface and the luminescence shows a local minimum
at the surface. But the intensity drops also with the depth because of the
absorption by the dye and because of some other effects mentioned above.
Münsterer [1996] compared this local minimum method to other methods regarding their sensibility to noise as shown in Fig. 5.3. He modelled a
depth profile and added different levels of random noise resulting in ratios of
the surface signal to the noise. Then the different methods of surface detection were applied and the difference between the detected surface position
and the input of the model was computed as a standard deviation σerr . The
deviations are all relatively small because the symmetry is not very sensitive
to noise.
Different convolution kernels are studied for the use as symmetry filters in
order to find the feature of the symmetry produced by a total reflection. The
simplest point symmetric filter consists of a constant positive value on one
side and a constant negative value of the same magnitude on the other side.
For filtering a convolution of the filter mask and the measured depth profile
is done. Near a point of high symmetry the filtered signal passes through a
region of large local asymmetry and gives a large value. At a point of high
symmetry the filter has a zero crossing. This box-symmetry filter may have
54
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
120
grey value
S/N = 50
110
S/N = 16
100
S/N = 5
90
100
150
200
250
300
350
400
pixel
(a)
standard deviation σ [pixels]
symmetry filter ( σ = 12)
(b)
2,5
symmetry filter ( σ = 8)
2,0
symmetry distance
local minimum
1,5
2 nd derivative
(Canny) ( α = 0.2)
1,0
0,5
0,0
0
5
10
15
20
25
30
35
40
45
50
signal-to-noise ratio
Figure 5.3: Effect of noise for different symmetry filters (a) Three modelled profiles with different signal-to-noise ratios. (b) Deviations from the
correct symmetry point for different methods depending on the noise
(From Münsterer [1996])
5 Methods: Evaluation of Image Series
55
(a)
Grey value (a.u.)
a similar negative behaviour to noise as a box filter. The reception of noise
is shown in Fig. 5.3.b.
In the same figure also a measure of the symmetry distance is found. This
computation intensive method is based on the distance of the measured data
points to a perfectly symmetric curve. The accuracy at high noise levels is
not very good.
Münsterer [1996] stated that a symmetry filter that consists of a binomial filter (also Gaussian filter, further reading in Jähne [2005]) that is
inverted at the centre worked better as the box-like symmetry filter. The binomial filter has the same form as was used as a blurring function in Eq. 4.1.
The shape of the binomial symmetry filter and of the box-symmetry filter is
found in Fig. 5.4.c.
50
40
30
20
0
100
200
300
400
500
600
0
100
200
300
400
500
600
1
0
−1
(c)
Grey value (rel.u.)
(b)
1
0
box point sym.(σ2=12)
−1
0
10
20
Depth z (pixel)
30
binomial sym. (σ2=15)
40
50
60
smoothed grad. (σ2=13)
Figure 5.4: Effect of three different filters on the surface detection. (a) Example
of a measured profile. Left side is the reflection of the right side.
(b) Filtered profile. The effects of the filter masks on the example are
very similar. (c) Different masks for filtering. (For the box-symmetry
filter, σfilt 2 is quarter of the length.) The mask was convoluted twice
with the profile. The maximum gives the surface
The binomial symmetry filter is compared to two similar filters. Because
of the symmetry the gradient of the intensity should change the sign at the
surface. The convolution of the simplest gradient filter ([−1 0 1 ]) would
detect no edges but only noise. Making the mask larger corresponds to the
56
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
symmetry filter discussed above. Another possibility is to suppress the noise
first by a binomial filter and then apply the small gradient filter. The shape
of a combined binomial smoothing and the tree-element gradient mask is
shown in Fig. 5.4 with the name smoothed gradient filter.
To detect the correct zero crossing, the symmetry filter or the gradient
filter was applied twice detecting the surface at the maximum of the filtered
signal. For the gradient filter this corresponds to the second derivative. By
spline interpolation of five pixels around the maximum even a sub-pixel accuracy of the surface detection can be achieved. But considering the accuracy
of the detection and also the difficulty in shifting the noisy profiles by less
than a pixel, only rounded integers were allowed for shifting.
The size of the mask can be optimised for the specific task of finding the
symmetry in a measured profile by looking at the signal-to-noise ratio after
applying the filter. Here the signal is the global maximum of the second
derivative and the noise is every local maximum that is not the surface. The
optimisation is demonstrated in Fig. 5.5 for three filter types.
Signal−to−noise ratio SNR
10
box point symmetry
binomial symmetry
smoothed gradient
8
6
4
2
0
0
5
10
15
20
25
2
Measure of filter width σ
30
35
Figure 5.5: Filter optimisation: selection of the suitable filter width for surface
detection shown in Fig. 5.4. N.B.: The signal of SNR is the maximum
of the filtered signal at the right surface position while the noise is
the a secondary peak leading to wrong detections
When the filter is too narrow the noise creates local maxima that are not
desired. For wide filters, the characteristic feature, that is to be detected, is
2
smeared out. The optimum for this task was around σfilt
= 13. The name
2
of σfilt is used for analogy to the filters using a Gaussian also for the box-
5 Methods: Evaluation of Image Series
57
symmetry filter but it is simply the quarter of the total length of the mask.
2
The optimum length of σfilt
= 12 of the box-symmetry filter was used for the
further evaluation. This length worked best for the critical detection with
thin boundary layers.
In Fig. 5.4.b the effect of the convolution of a measured profile with the
three different convolution kernels is shown. After optimising the length of
every filter, no preference for a certain filter type was found.
A measured depth profile is shown in Fig. 5.6.a. Taking the mean of the
lines without any surface detection leads to an additional blurring. After
the surface is detected, the lines can be arranged to put the surface at the
same pixel position and then the lines can be averaged. This is shown in
Fig. 5.6.b. After this image registration and averaging, also a little dip is
visible at the surface originating from particles floating on the surface giving
high reflection intensities. This shows that the optical resolution is good
enough to see effects of the surface.
Grey value
45
40
35
30
25
(a)
Grey value (a.u.)
220
(b)
240
260
280
300
320
340
360
380
280
300
320
340
Pixel number (z direction)
360
380
45
40
35
30
<−− surface
25
220
240
260
Figure 5.6: (a) Profile. Left side is the reflection of the right side. (b) Mean
after surface detection and image registration. N.B.: no smoothing
was done on the displayed profiles
5.3
Consideration of Absorption
After the surface is found, the profile of light intensity can be corrected for
the absorption of the dye. If the exciting laser light is coming from above
the surface, the laser-light intensity in a certain depth is lower because it has
58
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
been absorbed partially by the dye in the water layer above. Consequently,
also the luminescent emission gets lower.
The effect of this decrease is seen in the right of Fig. 5.6.b and it can be
calculated with the Beer–Lambert’s law of Eq. 3.4. In the evaluation an
empirical exponential was fitted to the profile disregarding the first 100 pixel
from the detected surface where the oxygen quenching occurs.
z
I = aA exp(− ) + bA
(5.1)
lp
Grey value (rel.u.)
The penetration depth lp was established as 900 pixel. With the scaling
factor fsc = 25.2 µm/pixel this is 22.7 mm. This was taken for all measurements with the same dye concentration. The other two parameters, the factor
aA and an offset bA , were fitted for every line because the absolute intensity
was fluctuating and some scattered light was not affected by absorption.
For a measured profile this normalisation takes the form as shown in
Fig. 5.7. The relative intensity of phosphorescence is one for gas concentrations that are the same as the oxygen concentration in the bulk. Near the
surface the intensity decreases because a higher concentration of the quenching oxygen that penetrates the water surface. A measure of quality of this
normalisation step is a constant baseline in some distance from the water
surface where no turbulence structures are expected.
1
0.8
0.6
220
240
260
280
300
320
340
Pixel number (z direction)
360
380
Figure 5.7: Mean profile normalised to Beer–Lambert absorption shows a constant baseline far from the water surface (on the right)
5.4
Calculate Concentrations from Luminescence Intensity
The relation between concentration of a quencher like oxygen and the intensity of luminescence is described by the Stern–Volmer equation of Eq. 3.3:
I
1
=
I0
1 + KSV [O2 ]
5 Methods: Evaluation of Image Series
59
For small differences in concentration, a linear approximation of this relation is justified. In this case, the normalised intensities can be taken directly
to compute normalised concentrations as it was done in Falkenroth et al.
[2007].
To establish a more accurate relation between intensity and local oxygen
concentration over a wide range of concentrations from 0.8–8 mg/L, several
calibration curves were measured. A typical graph is shown in Fig. 5.8.
1
I / I0
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
O concentration (mg/L)
7
8
2
Figure 5.8: Calibration curve: effect of quenching for different O2 concentrations.
1
The quenching constant was measured to be 11 000 M
The sole parameter of the fitted curve is the quenching constant KSV and
is was calculated to be 11 000 ± 2000 L/mol = 0.345 ± 0.063 L/mg.
The calibration loses accuracy for a fluctuating laser light because of effects like occlusions by the spinning wind paddles or reflection and refraction
at the free water surface. Also the calibration of the oxygen probe was not
stable between different measuring days. In addition, renewal events altered
the intensity of the luminescence in the reference depth during the calibration
measurement. They were caused by the bulk turbulence generated by the
pump of the gas exchanger. However, using the curvature of the calibration
function is nevertheless appropriate.
The calibration procedure can be omitted when using other dyes like the
ones that were used previously for the visualisation of the water-boundary
layer. The quenching constant of PBA is much smaller and so the curvature
of the calibration curve can be neglected. Using pH-indicators, a pH range
is selected where the intensity of the fluorescence is linear with the pH value.
But to get to the molecular concentration of the acid or base, the logarithmic
scale of the pH must be considered.
Applying the above calibration on the measured data, the problem of
the fluctuating laser intensity in the water emerges. This can be handled
60
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
by normalising the intensity far from the surface to the intensity that is
expected at the concentration that is measured at the same time with the
oxygen probe sensor. The assumption here is that in the mean of several
pixel and far from the surface, the concentration is equivalent to the bulk
concentration. The resulting mean concentration profile is shown in Fig. 5.10.
After this calibration procedure the effect of fluctuating incident light has no
influence on the signal any more.
5.5
Effect of Blurring
Grey value (a.u.)
The surface is not imaged as a sharp discontinuity because of the limited
quality of the optical path of the luminescence reaching the camera. The
image is blurred. This effect is a problem for the determination of surface
concentration and its gradient and also the boundary-layer thickness.
A homogeneous blurring can be described as a convolution of the real
profile with a blurring function. In digital image processing this function is
called the point spread function (PSF).
2
In this work a Gaussian as described in Eq. 4.1 with a variance σblur
=7
was assumed for the blurring function (for the determination of the extend
of blurring, see Sec. 4.3). As the optical path for the described experimental
set-up was kept stable, the same function was used for the evaluation of all
images taken. The effect on a modelled profile is shown in Fig. 5.9.
40
30
20
220
240
<−− surface
260
280
300
320
340
Pixel number ( z direction)
360
380
Figure 5.9: Effect of blurring on a model function: the smoothing of a modelled
curve is evident at the sharp edge of the surface
5.6
Fitting a Model to Measured Profiles
The increase of the oxygen concentration near the surface can be described
with the appropriate model following the theoretical profile as illustrated in
Sec. 2.2. Considering the mirror effect at the surface and with the convolution
5 Methods: Evaluation of Image Series
61
with the blurring function, a model function is designed that depends on only
two parameters: an depth scaling parameter z?m describing the boundarylayer thickness and the concentration difference ∆cm between the surface
csurface,m and the water bulk cbulk,m that is used to calculate the normalised
concentration c+ . In invasion experiments the surface concentration can be
lower than the concentration of the equilibrium with air because of a thin airside boundary layer. The reference bulk concentration cbulk,m is the baseline
of the concentration profile.
c+ =
cm − cbulk,m
∆cm
(5.2)
This smoothed model function can be fitted to every single concentration
profile from Sec. 5.4 to determine the parameters as demonstrated in Fig. 5.10
with the profile p = 1 of Eq. 2.31. In this procedure the residual difference
between the measured data and the modelled function was minimised. The
non linear least square algorithm implemented in the MatLab software made
use of a subspace trust region method and the software documentation cites
Coleman and Li [1996, 1994] for reference.
240
Pixel number (z direction)
260
<− Surface
280
300
320
340
measured concentration profile
BLFunction
BLMFunction
extrapolation of surface gradient
360
2.5
3
3.5
4
4.5
5
O2 concentration (mg/L)
5.5
6
6.5
Figure 5.10: Extracting the boundary-layer thickness z? with fitting method.
BLFunction is the theoretical concentration profile without blurring. BLMFunction is the model function that was fitted to the
data. The extrapolation of the concentration gradient at the surface yields z?
62
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Fitting is possible also with noisy data. Thus, no smoothing of this data
is needed before this evaluation step. A smoother depth profile is obtained by
averaging several lines. Both computations were carried out and compared.
The consideration of the blurring in the fitted model is especially important in cases when the extend of blurring is large.
Multiplying the parameter z?m in the units of pixels with the scaling
factor fsc = 25.2 µm/pixel of the pixel resolution determined in Sec. 4.3 gives
directly the boundary-layer thickness z? . According to Eq. 2.36, it is the
inverse of the gradient of the normalised concentration c+ at the surface
determined by the flux that is present in the boundary layer in that moment
derived in Sec. 2.2.
∂c+ 1
−
= −
∂z z=0
z?
From the slope of the concentration profile at the surface, the flux and
thus the transfer velocity k can be calculated directly from Eq. 2.33 by knowing the diffusivity Dox of oxygen at the measured temperature.
5.7
Polynomial Fit as Alternative
Fitting the model function to the measured data is a computationally expensive method for the evaluation. A much faster way to extract boundary-layer
thickness z? is to measure a thickness of the depth profile where the concentration reached a certain level.
The first unknown is the surface concentration. Because of the blurring
the concentration is higher than directly calculated from the luminescence
intensity in invasion experiments. If the extend of blurring is much smaller
than the boundary-layer thickness, then the extrapolation of the maximal
slope to the surface is a good guess. To estimate the value of the highest
gradient a polynomial of order three was fitted to the measured values around
the surface as seen in Fig. 5.11.
Now different distances from the surface can be extracted with corresponding levels of concentration. In the case of a smooth surface that behaves like a rigid wall, the concentration falls to a fraction of 0.24 of the
surface concentration at the distance of the boundary-layer thickness z? as
shown in Sec. 2.3.
For a free surface, the concentration falls to 1/e of the surface concentration within the boundary-layer thickness assuming the classical surfacerenewal model (cf. Eq. 2.35). When the profile follows an exponential function as claimed by the model, another way to extract the same distance from
5 Methods: Evaluation of Image Series
63
Pixel number (z direction)
240
260
280
<−− extrapolated maximum
<−−−−− highest gradient
<−−−−− 1/e of maximum
<−−−−− 0.24 of maximum
<−−−−−−−− extrapolated to baseline
300
320
2.5
3
3.5
4
4.5
5
O2 concentration (mg/L)
5.5
6
6.5
Figure 5.11: Extracting the boundary-layer thickness z? with polynomial fit
(solid line) to a measured depth profile (circles). The extrapolation (broken line) of the maximum slope of a polynomial fit function
gives the extrapolated surface concentration. Depending on the assumed theoretical profile, the boundary-layer thickness z? can be
measured at different concentration levels
the surface is to extrapolate the slope at the surface to the baseline of the
normalised bulk concentration level.
In Fig. 5.11 as in all evaluated profiles, the highest gradient of the concentration profile is near the 1/e concentration. Consequently, the distance
at the extrapolation to the baseline is always higher than the distance at 1/e
level.
Part III
Results and Discussions
65
Chapter 6
Results: Gas-Transfer
Velocities and Depth Profiles
The image processing algorithm extracted the properties of gas exchange
from the images in the boundary layer. Now, these parameters will be presented and discussed. Criteria for their quality will be developed and analysed. Systematic gas-exchange measurements with a smooth surface and
different wind speeds are analysed. The assignment to one of the theories of
turbulence introduced in Sec. 2.2 is the subject of the first part. Additionally,
the developed tools were found to be applicable also to the study of turbulence structures generated by a mixing pump. Furthermore, few examples of
concentration fields below a wavy surface revealed some interesting details.
Finally, concentration fluctuations calculated for all three different external
conditions are documented.
6.1
Smooth Surface Under Wind Stress
A main objective of this part is to find the correct theoretical model that describes best the measured concentration profile in the boundary layer during
gas-exchange experiments with different wind speeds. First the concentration
field is analysed. Because of the blurring, the concentration and its gradient
can not be determined directly at the surface. In a second step, the model
profile is fitted to the data with the method described in Sec. 5.6 and the
error of the fit is analysed. The results suggest two candidates for the model
to be the appropriate description of the measured mean profiles.
In the fitting procedure, the boundary-layer thickness is calculated in
the mean profile and in every single profile. Both results are compared in
Sec. 6.1.3 to the values calculated with the alternative method presented in
Sec. 5.7 where a polynomial is fitted to the measured mean profile and the
67
68
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
data near the surface is reconstructed by extrapolation.
To decide about the actual transfer velocity, the values of the two model
candidates are compared to mass-balance methods of oxygen bulk concentrations Sec. 6.1.4 and other gases in Sec. 6.1.5 determined in parallel measurements as a ground truth.
6.1.1
Analysis of Concentration Fields in the Boundary Layer
Measurements with a smooth surface were performed with a surfactant that
suppressed the generation of wind waves. Augmenting the wind force, the
gas-exchange rates increase without the generation of visible turbulence structures. The image processing steps described in Chap. 5 yield mean concentration profiles. 12 sequences of 5000 frames were taken for a single wind
speed. After raising the wind speed, the imaging was stopped for more than
7 min to assure stabilisation of the wind field before taking the next series of
images.
During the experiment the oxygen concentration increased in the way
shown before in Fig. 4.7. It was not possible to keep the bulk concentration
low with a working gas-exchanger module because its pump generated visible
bulk turbulences that significantly increased the gas transfer at the surface.
The influence of these turbulences and their structure will be studied in
Sec. 6.2. With increasing bulk concentration the contrast of luminescence
decreased what had a negative effect on the signal-to-noise ratio.
Fig. 6.1 shows time series of one vertical image line in the laser sheet
observed with 185 Hz for 27 s giving 5000 frames. A typical image of the
camera is seen in Fig. 4.2. The images shown here are taken after a constant
wind speed was established for half an hour. The distance from the surface
to the bottom of the image is approximately 10 mm. In the images the
boundary layer is visible as a horizontal darkening and gets thinner with
increasing wind speeds. Especially in Fig. 6.1.b periodic dark vertical lines
are occlusions by the four wind paddles.
6 Results: Gas-Transfer Velocities and Depth Profiles
69
Frame number
1000
2000
5.4
10.8
3000
4000
5000
16.2
21.6
27
(a)
(b)
(c)
(d)
0
Time (s)
Figure 6.1: Raw time series of one vertical line (640 pixel) of the laser sheet.
(a) 20 min after stopping the O2 -stripping pump and without wind.
(b) Wind speed of 0.8 m/s. (c) 3 m/s. (d) 6 m/s. N.B: Above the
dark surface a total reflection is seen in the images
70
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
From image series similar to the examples shown in Fig. 6.1, arbitrary
single intensity profiles are shown in Fig. 6.2. The intensity decreases with
increasing oxygen concentration what is seen as low intensity near the surface.
Here oxygen penetrates the phase boundary. High oxygen concentrations
are also seen as a lower signal at higher wind speeds because during the
experiment with step wise increasing wind speeds, more and more oxygen
gets solved in the water. This leads to a low contrast near the surface at
high wind speeds.
0
0.8 m/s
4.0 m/s
8.0 m/s
100
Depth (pixel)
200
300
400
500
600
10
15
20
25
30
35
Intensity of phosphorescence (grey value)
40
45
Figure 6.2: Single intensity profiles before image processing show the signal quality at the different wind speeds. The contrast at the surface at the
position around 300 pixel decreases with higher bulk concentrations
From 5000 grames, a mean concentration profile is computed. The depth
is displayed in Fig. 6.3 up to pixel number 256 including 50 pixel of the total
reflection at the surface at negative depth. The bulk concentration increased
stepwise because of the waiting time between the sequences.
The increase in concentration near the phase boundary is observed with a
high spatial resolution of 25.2 µm/pixel. In this experiment the concentration
at the surface is increasing with time. It may be explained by a thinner air–
side boundary layer if this is not an artefact of the oxygen calibration.
A step in the bulk concentration level at the depth of about 1.6 mm
originates from an artefact of the camera chip described in Sec. 5.1. But
in general the baseline of the concentration is stable what means that the
correction for the Beer-Lambert absorption from Sec. 3.2 works fine.
6 Results: Gas-Transfer Velocities and Depth Profiles
71
Figure 6.3: Mean concentration profiles of one measurement series with stepwise
increased wind speed. The maximum of concentration is not the
concentration at the surface because of the optical blurring
6.1.2
Concentration Profiles and Turbulence Models
With different assumptions about the turbulence structure, different concentration profiles in the boundary layer can be deduced from the theory
discussed in Sec. 2.2. To decide which description has the dominant influence on the depth profiles seen in Fig. 6.3, the theoretical profiles were fitted
to the normalised measured concentrations.
In Fig. 6.4.a the surface-renewal model with a smooth interface and p = 1
was assumed as the depth dependence of the turbulent diffusion. For comparison the other profiles discussed in Fig. 2.2 are plotted in the same graph
with the normalisation from the fit with p = 1. It is clearly seen that the
models with m = 2 or 3 and p = 0 are distant from the measured data. But
the line with m = 4 from the K-model is also near the measured data.
This shows that in the case of a smooth surface it is very difficult to distinguish between the conceptual models by just analysing the depth profiles.
To document the dangers of fitting the profiles, in Fig. 6.4.b the fit of the
identical data was done to the model with m = 4. This graph suggests that
this is the best fit to the model. A definite decision on the suitable model can
72
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
0
0.2
0.4
0.6
Normalised O concentration
0.8
1
(a)
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
(b)
2
Figure 6.4: Analysing the form of a measured concentration profile () with
two different models. The wind speed was 1 m/s and the boundarylayer thickness was 585 µm. (a) The best model seems to be the
surface renewal with the rigid-wall-assumption (p = 1, solid line).
The other models of Fig. 2.2 are plotted for comparison (broken lines,
m2, p0, m3, p1, m4). The K-model m = 4 has a very similar form.
(b) The same measured profile can be analysed by fitting the Kmodel (m = 4, solid line) to the data. Here it appears that only this
model is the best description of the profile. (m2, p0, m3, p1, m4)
The shape of a measured profile alone can not distinguish between
the models at a smooth interface
6 Results: Gas-Transfer Velocities and Depth Profiles
73
not be on the basis of a single mean profile. After fitting the other models
with m = 2 or 3 and p = 0, they could be excluded clearly as adequate
descriptions of the measured profile.
A better criterion for the decision of the best theoretical description than
looking at only one fit could be to analyse the residual difference between
the data and the fitted model for different conditions. Such a study is shown
in the graph in Fig. 6.5.
A low value of standard deviation of error σerr between the fitted model
and the data signifies a good accordance. The best accordance between the
fit and the data is seen for the model with m = 4, but the difference to p = 1
is not significant. For all models, the value of σerr first decreases with higher
wind speed. This is because the boundary layer gets thinner and the share of
the fitted region is larger where the bulk concentration is a constant baseline.
In this region the difference between a model and the data is naturally small
without any information about the quality of the fit. But it is possible that
secondary currents that are present in the water of circular wind–wave flumes
at small turbulence states are also responsible for this tendency.
Standard deviation of fit σerr
1.5
m2
m3
m4
p0
p1
1
0.5
0
0
2
4
Wind speed (m/s)
6
Figure 6.5: Error σerr for different model-fits varying the wind speed. The data
differs less from the model p = 1 than from m = 4, considering that
the highest wind speed is subject to a low signal-to-noise ratio. The
difference of the models is not significant enough to decide in favour
of one of it
There are some explanations for the observation that σerr increases with
wind speeds higher than 5 m/s. One is that the signal-to-noise ratio is lower
for these measurement points because of the increased oxygen concentration
in the bulk. Furthermore, due to the faster flux, a thinner boundary layer is
more difficult to detect correctly with the given optical resolution. Another
74
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
reason may be that the effect of the step in the concentration baseline seen
for z > 1 mm in Fig. 6.3 gets more influence.
A possible interpretation of the observation, that m = 3 becomes the
model with the lowest error for high winds, is that for low wind speeds and
high values of the boundary-layer thickness z? , the mechanism is different
than for high wind forces with thin boundary layers. The experiments that
were conducted may give a hint but do not allow a decision just from the
shape of the concentration profile.
6.1.3
Comparison of Transfer Velocities from LIF-Measurements
In the fits in Fig. 6.4 also an extrapolation to the baseline of the bulk concentration is seen. This intersection gives the value of the boundary-layer
thickness z? . It is the inverse of the gradient of the normalised concentration
at the surface. According to Eq. 2.8 this parameter can be used to determine
the gas-transfer velocity k:
k=
D
z?
(6.1)
In this definition the molecular diffusivity Dox has to be known. As
it is a temperature dependent quantity, the water temperature during the
experiment was kept constant and the change in the temperature range found
in the experiments was smaller than 0.1°C.
For a wind speed of 0.8 m/s the thickness of the boundary layer z? with
the fitted profile of p = 1 is 25.8 pixel corresponding to 0.65 mm. With Dox
of 2.36 10−5 cm2 /s at 25.1°C (from Mayer [1995]) the gas-transfer velocity
k was 1.3 cm/h what is the expected value for a slow gas exchange with little
turbulence at a smooth surface. The averaged values of 12 mean concentration profiles for every single wind speed are found in Fig. 6.6.
12 values are computed for every wind speed. The displayed values of the
boundary-layer thickness z? in Fig. 6.6 are always mean values. The displayed
comparison demonstrates also that there is little difference between fitting
the model and extrapolating the surface gradient, on the one side, and taking
the distance where the normalised concentration has fallen to the value of
0.24 predicted by the same model as deduced theoretically in Sec. 2.3, on
the other side. For this case of a smooth air–water interface, the alternative
methods yield the same result. In the following, the faster method of the
0.24 level will be taken to compare it to other values.
In the same Fig. 6.6, also the quantities from single profile fits are displayed. They are the average of 12×5000 extracted boundary-layer thickness
0.9
4
0.8
3.5
0.7
Transfer velocity k (cm/h)
Boundary−layer thickness z* (mm)
6 Results: Gas-Transfer Velocities and Depth Profiles
0.6
0.5
0.4
0.3
0.2
3
2.5
2
1.5
1
0.5
0.1
0
0
0
(a)
75
2
4
6
Wind speed (m/s)
0
2
4
6
Wind speed (m/s)
(b)
Figure 6.6: Correlation of boundary-layer thickness with wind speed. (a) Thicknesses derived with different methods are very similar: O: the distance at 0.24 level of concentration difference ∆c. B: thickness of
fitted boundary layer with model p = 1, C: boundary layer as mean
of a fit to single profiles; 4: result from fitting the model m = 4.
(b) Calculated transfer velocities using k = D/z?
values. This is a good example of what was stated in Sec. 2.3: this value
can differ under conditions of high turbulence but with low turbulence the
difference is negligible.
For comparison the results from fitting the model m = 4 are also shown
together with the other values. In the gas-transfer velocity k there is a
significant difference between the models that were not distinguishable in
the concentration profile fits of Fig. 6.4. To decide about the correct model,
the transfer rate has to be determined with an independent method such as
the mass-balance methods applied in the following Sec. 6.1.4 and Sec. 6.1.5.
An important question is: are the results reproducible? The same measurement as described above was conducted in another day. The results are
compared in Fig. 6.7. The triangles are the results from the luminescence
measurements in question.
In Fig. 6.7 for low wind speed, the agreement between the results from the
boundary-layer thickness z? in different measurement days is excellent. In
the compared measurement the wind speed took longer to reach the desired
velocity what increased the bulk concentration and lowered the signal-tonoise ratio. This is why the transfer velocity drops off earlier than in the
76
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
5.5
5
Transfer velocity k (cm/h)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
1
2
3
4
Wind speed (m/s)
5
6
7
Figure 6.7: Transfer velocities from different measurements of luminescence compared to values from oxygen bulk concentrations for different measurement series. O: same as in Fig. 6.6; 4: also luminescent measurement with same model on a different measurement; ♦: values
from probe measurements parallel to O. : parallel to 4. : different (3rd ) day but same conditions
other measurement of Fig. 6.6.b and could not be evaluated any more at the
wind speed of 7 m/s.
6.1.4
Transfer Velocity from the Bulk Concentration
Another question is asking for the ground truth. To give an estimate for
the quality of the achieved gas-exchange rates from the measurement of the
boundary-layer thickness in depth profiles, the quantity of the transfer velocity was measured also with another method and different devices. Parallel
measurements of dissolved oxygen concentration in the water and trace gases
in the air were performed constantly permitting the calculation of reference
transfer velocities kr .
Using an oxygen sensor, the water side increase in O2 concentration cw
was recorded during the experiment as shown in Fig. 6.8.a. It was assumed
that a temporal concentration change in the water with volume V is only due
to the gas exchange across the water surface A. This change of the oxygen
concentration in the water is the same as the net transition of oxygen from
6 Results: Gas-Transfer Velocities and Depth Profiles
77
one phase into the other by gas exchange. As the mass is constant, a mass
balance can be formulated:
dcw
= −kr A (cw − αcair )
(6.2)
dt
The factor α is the dimensionless Ostwald’s solubility. From this equation the transfer velocity kr can be calculated if we determine the temporal
derivative of the water–side concentration directly from the measured data.
The equilibrium water concentration cbulk,eq = α cair,eq can be determined
from concentration convergence after six hours in Fig. 6.8.a because the air–
side concentration did not change during the measurement.
Vw
9
50
Transfer velocity k (cm/h)
O2 concentration (mg/l)
8
7
6
5
4
3
solubility limit
probe values
40
30
20
10
0
2
0
(a)
2
4
Time(h)
6
0
1
2
3
Time (h)
4
5
(b)
Figure 6.8: Evolution of the bulk O2 concentration. a) Water bulk measurements
of O2 concentration. The O2 concentration reached equilibrium after
4.5 hours. (b) Gas-transfer velocities computed from Eq. 6.2. Mean
values for different wind speeds are indicated () and compared to
the results from phosphorescent measurements in Fig. 6.7
The resulting transfer velocity kr is shown in Fig. 6.8.b. As the temporal
resolution of this calculation method is in the order of minutes, the variance
of the calculated values is high. Averaged values are represented by circles
in the plot. The abrupt increase in the transfer velocity after four hours is
caused by the formation of waves. At this time the stability of the surfactant
film broke, as the critical wind speed was reached that lies between 7.5 and
8.0 m/s for the used circular wind–wave facility.
The gas-transfer velocities from the oxygen probe measurements are depicted in Fig. 6.7 together with the results from phosphorescence measure-
78
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
ments for comparison. The transfer rates for different measurements under
the same condition show the same scale of magnitude and the same tendency.
But the accuracy of this mass-balance method is not very impressing. The
reason for the scattering is that the gas-sensor data is noisy, on some days
much more than on others because of the unstable stirring of the oxygen
probe. The accuracy of the measurement depends on the flux condition in
the measurement cuvette as explained in Sec. 4.1.
6.1.5
Comparison with Transfer Velocities of Other
Gases
Similar mass-balance methods of other trace gases had a higher accuracy.
They were measured in the same experiment by Degreif [2006] and published in Falkenroth et al. [2007].
3.5
H2
N2O
3
Transfer velocity k600 (cm/h)
O2 boundary layer z* with m = 4
O2 boundary layer z* with p = 1
2.5
2
1.5
1
0.5
0
0
1
2
3
4
Wind speed (m/s)
5
6
7
Figure 6.9: Simultaneous measurement of transfer velocities of different gasses
scaled to Sc = 600. The comparison shows good agreement with the
model p = 1 and less for m = 4 at higher wind speeds
To compare the gas-transfer velocities k they have to be scaled with the
diffusivity D. More common is the scaling to a Schmidt number Sc = 600
what is the value of CO2 in sweet water (cf. Eq. 2.6). Also the temperature
dependence of the Schmidt number can be taken into account that was
6 Results: Gas-Transfer Velocities and Depth Profiles
79
retrieved from the thesis of Degreif [2006].
k600 = k
Sc(T )
600
−n
(6.3)
The gas-exchange rates of the trace gases in Fig. 6.9 were calculated
from air–side concentration measurements for the evading gases H2 and N2 O.
This figure shows that the transfer velocities derived from the boundary
layer are in agreement with the reference measurements. This comparison
demonstrates that the model of p = 1 is more likely to reflect the adequate
description of the turbulence structure in the boundary layer than the model
of m = 4. Especially at high wind speeds the latter is significantly lower
than the reference gas-exchange velocities.
The transfer rates calculated from the boundary-layer thickness in Falkenroth et al. [2007] were significantly higher. The data was the same but the
evaluation was done without concentration calibration and, what is more important, without surface detection because it was neglected without waves.
This led to an additional smoothing of the data so that the wrong model of
p = 0 was assumed what over estimates the gas flux.
6.2
Bulk Turbulences Generated with a Mixing Pump
Before an experiment the water in the channel was degassed and mixed using
a water pump. This pump generates bulk turbulences that reached the water
surface where the boundary layer with high oxygen concentrations is pealed
off. This type of structures are interesting in some fields of research [Brumley and Jirka, 1987; Lee and Schladow, 2000; Atmane and George,
2001; Herlina and Jirka, 2004; Variano and Cowen, 2007]. The time
series of one line with bulk turbulences are shown in Fig. 6.10.
The images demonstrates the penetration of the boundary layer by eddies. Most obvious are injection events: packages of water with high oxygen
concentrations are transported in filaments away from the surface where they
dilute in the well mixed bulk. These injection events are described also by
Variano and Cowen [2007] who cites also other authors.
The performance of the registration step can be best seen going from
Fig. 6.10.c to .d. Each profile is shifted so that the surface positions end up
at a fixed pixel number of 50 in the registrated image.
80
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Frame number
500
1000
1500
2000
2.7
5.4
8.1
10.8
2500
3000
3500
4000
4500
5000
13.5
16.2
Time (s)
18.9
21.6
24.3
27
(a)
(b)
(c)
(d)
Figure 6.10: Time series of bulk turbulence generated by a water pump. The water depth shown is approximately 6.5 mm. (a) 11 L/min pump flow
before image registration. (b) After image registration to the surface location. (c) 37 L/min before registration with visible waves.
(d) After registration
6 Results: Gas-Transfer Velocities and Depth Profiles
5
0.7
Transfer velocity k (cm/h)
Boundary−layer thickness z* (mm)
0.8
0.6
0.5
0.4
0.3
0.2
4
3
2
1
0.1
0
0
0
20
40
Additional pump rate (L/min)
(a)
81
0
20
40
Additional pump rate (L/min)
(b)
Figure 6.11: Correlation of boundary-layer thickness with additional pump flow
to the constant flow of the gas exchanger. Every measurement point
is an average of 12 mean profiles calculated of a time series like in
Fig. 6.10. (a) The correlation of the boundary-layer thickness with
pump flow. B from model fit to mean concentrations. O from model
fit to single concentrations. C from method with highest gradient
of polynomial. (b) Corresponding transfer velocities
When analysing these time series, it is always important to keep in mind
that a four dimensional flux in time is projected in the two dimensions of
these images and that the medium is not stagnant but flows through the illuminated area giving the impression of a movement of a single water parcel.
Despite the high density of turbulence structures, the mean profiles could
be evaluated with the same methods as shown before. The results are shown
in Fig. 6.11.
The changing condition in this Fig. 6.11 is an additional flux of a mixing
pump. It was varied in addition to the constant flux from the pump that was
connected to the gas-exchanger module. The working gas-exchanger kept the
concentration of oxygen in the bulk low what assured a constant and good
contrast in the boundary-layer. As a result of this high signal-to-noise ratio
also thin boundary-layer thicknesses smaller than 250 µm could be resolved.
The comparison of different model fits reveals that a different theoretical
description has the major influence on the turbulence structure as in the case
of gas-exchange with a smooth surface. In Fig. 6.12 it is evident that the
K-model with m = 3 is the closest to the measured data.
82
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Standard deviation of fit σerr
1
m3
m4
p0
p1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
Additional pump flux (L/min)
Figure 6.12: Error σerr for different model fits varying the pump rate
Here the error σerr does not increase significantly with thinner boundary
layers even though they are thinner than in the case of the wind experiments
with a surfactant. The reason for this is again the higher signal-to-noise ratio
because of the low oxygen concentrations in the bulk.
The fit of the model m = 3 is the best also in the graph of normalised
concentration c+ in Fig. 6.13. The shape of the profile is different enough
from the other theoretical descriptions to decide that this K-model is the
most appropriate description of the concentration distribution in the aqueous
boundary layer.
6.3
Turbulence Structures with Wind Waves
The difference of the model profiles for wavy conditions show a larger difference than the models for a smooth surface. Thus, the assignment to measured
profiles seem to be more promising at wind waves. With the imaging method
used in this work, no systematic measurements with wavy conditions were
feasible. Only very low elevations of wind waves are still in the framed field
of view of the camera with high magnification. Some examples of time series
with a wavy surface and the analysis are discussed the following.
With a clean surface, even slow winds generate small waves, so-called
capillary waves. In contrast to gravitational waves, the dominant force at
this small scale is the surface tension. These waves are small enough to be
imaged in the field of view of the camera with the high magnification used.
To keep the size of the wave small and exclude gravitational waves, a
skimmer was positioned at the surface as a barrier. The skimmer had the
width of the channel. It extended about 4 cm into the water what may have
caused additional turbulences near the water surface. The position of the
6 Results: Gas-Transfer Velocities and Depth Profiles
83
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
Figure 6.13: Fitting the theoretical models to the data of profiles with pump
turbulences (circles). For this condition the best model seems to
be the K-model m = 3 with the rigid-wall-assumption (solid line).
The other models of Sec. 2.2 are added in the plot for comparison
(broken lines: m2, p0, p1, m4). The additional pump flux was
11 L/min and the boundary-layer thickness was 435 µm
barrier was on the opposite side of the measurement position in the flume.
The skimming of the surface layer with wind stress assured also a clean water
surface.
Some example images with the wind speeds of 2.5 m/s and 2.6 m/s will
be discussed on the next pages because they show some interesting features.
84
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
In Fig. 6.15 a detail of the time series with a wind speed of 2.6 m/s is
seen. In the image the line of the dark surface is still recognisable. Beneath
it, a peeling event is visible. Here the boundary layer with high oxygen
concentration is peeled off and transported away from the surface visible as
dark structures.
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
Figure 6.14: Wavy surface: mean concentration profile at 2.6 m/s. Here the best
model is the K-model m = 3 showing a boundary-layer thickness
larger than expected (from right to left: m2, p0, m3, p1, m4)
The mean concentration profile of 5000 single profiles is shown in Fig. 6.14.
The boundary-layer thickness determined by the extrapolation of the surface
gradient as seen in the figure is 380 µm. This corresponds to a transfer velocity k of 2.2 cm/h what shows not the expected enhancement compared to
the value between 2.2–2.3 cm/h in Fig. 6.6 for a smooth surface.
The shape of the profile appears to correspond to the K-model. This
is somewhat surprising because in Fig. 6.15 structures are visible that are
more associated with surface-renewal events. The theory seems to be in
some contradiction to the observed structures. But in this case it may be
explained by a insufficient number or importance of the turbulent structures.
In Fig. 6.16 the performance of the image registration is demonstrated.
In the upper image the raw intensity of the luminescence is seen. The lowest
values are at the surface where the luminescence is quenched by oxygen
molecules that penetrate the surface. In some distance a maximum of the
intensity is reached. Then the intensity decreases by dye attenuation of the
incident light. The undulating surface can be seen clearly.
6 Results: Gas-Transfer Velocities and Depth Profiles
85
Depth from mean surface (mm)
−6
−4
−2
0
2
4
6
8
2335 2360 2385 2410 2435 2460 2485 2510 2535 2560
Frame number
Figure 6.15: Wavy surface: raw time series at a wind speed of 2.6 m/s with visible
surface-renewal events where high oxygen concentrations are pealed
off the surface and lower the intensity in turbulent structures
Frame number
500
1000
1500
2000
2.7
5.4
8.1
10.8
2500
3000
3500
4000
4500
5000
13.5
16.2
Time (s)
18.9
21.6
24.3
27
(a)
(b)
Figure 6.16: Wavy surface: image registration of time series at a wind speed of
2.6 m/s. (a) Before image registration. (b) After image registration
86
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Image processing including image registration yields time series of the
concentration profile shown in Fig. 6.16.b. No undulation can be seen any
more. The bulk shows low oxygen as a dark colour with some injection events
of high oxygen concentration. The high concentration near the surface is
centred at a straight line indicating a successful image registration.
For the image registration this is the limit case because the feature of a
reflecting surface is also not very pronounced with a wavy surface. But the
details of the time series show clearly that on most rows no occlusions hinder
the detection of the surface. Examples of unsuccessful image registration are
documented in Appendix A.
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
Figure 6.17: Wavy surface: mean concentration profile at 2.5 m/s. Here the best
model is the surface-renewal p = 0 showing a small boundary-layer
thickness (m2, p0, m3, p1, m4)
In Fig. 6.18, a detail of a time series with similar conditions but different observations is shown. The images were taken 40 min after the sequence
shown before with the a slightly slower wind of 2.5 m/s. In the whole sequence, no turbulence structures of surface-renewal events are visible.
In contrast to this finding, the profile shown in Fig. 6.17 suggests the
surface-renewal model p = 0. This model predicts a faster transport through
the boundary layer and, consequently, the boundary-layer thickness here was
210 µm what yields a transfer velocity of 4.0 cm/h what is an enhancement
of the gas flux that is expected in the presence of wind waves.
6 Results: Gas-Transfer Velocities and Depth Profiles
87
Depth from mean surface (mm)
−6
−4
−2
0
2
4
6
8
21
46
71
96 121 146
Frame number
171
196
221
246
Figure 6.18: Time series with small waves without turbulence structures at
2.5 m/s wind speed. The grey values are raw luminescence intensities without any treatment
Frame number
500
1000
1500
2000
2.7
5.4
8.1
10.8
2500
3000
3500
4000
4500
5000
13.5
16.2
Time (s)
18.9
21.6
24.3
27
(a)
(b)
Figure 6.19: Wavy surface: image registration of time series at a wind speed of at
2.5 m/s. (a) Before image registration. (b) After image registration
88
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
0
Relative depth z+ = z / z*
1
2
3
10.5 L/min
17.5 L/min
25.0 L/min
30.5 L/min
37.0 L/min
43.0 L/min
50.0 L/min
4
5
6
0
0.05
0.1
0.15
0.2
Fluctuation of the concentration c’ /∆ c
0.25
Figure 6.20: Fluctuation of the calculated concentration with bulk turbulence
for different additional pump rates with the transfer velocities of
Fig. 6.11.b
An unsuccessful image registration would result in a false profile but
Fig. 6.19.b shows that it worked fine. The high concentrations are all in
one straight line of a surface. In the raw data in Fig. 6.19.a some darker
rows are visible. Here the camera showed instabilities that showed up in
some sequences. The image processing handles this in the same way as
intensity fluctuations caused by the incident light. After the calibration the
fluctuations and the regions of low grey value do not appear in the time series
of the concentration profile.
6.4
Fluctuation Profiles of the Concentration
In this part, the analysis of the fluctuation of the concentration will be documented. This fluctuation is a measure of the turbulence in the boundary
layer. It was calculated as the standard deviation taking the root-meansquare of the difference between every single profile and the mean of 5000
profiles.
v
u
5000
u 1 X
0
t
c =
(ci − c̄)2
(6.4)
5000 i
6 Results: Gas-Transfer Velocities and Depth Profiles
89
Every fluctuation profile was normalised to the concentration difference
∆c between the bulk and the surface. 12 profiles were averaged and plotted
over the normalised depth z+ .
6.4.1
Fluctuations in Bulk Turbulences
In Fig. 6.20 the fluctuation with bulk turbulence is seen. The maxima of
the fluctuations are all within the boundary-layer thickness z? . In the bulk,
the concentrations should be homogeneously mixed and show less fluctuations. But the bulk turbulences show always many turbulence structures
from injection events what explains high fluctuation values even far from the
surface. Variano and Cowen [2007] describes also the transport of high
oxygen concentrations in long filaments deep into the bulk.
The fluctuation do not tend to zero at the surface as the hydrodynamical
model would suggest. Also the measurements with 60 µm probe sensors by
Atmane and George [2001] shown in Fig. 6.21 show some fluctuations at
the surface in the same order of magnitude. The concentrations of Herlina
[2005], plotted in the same graph, are calculated with the assumption of a
constant concentration at the surface and so the fluctuations are defined to
zero. In the classical surface-renewal model by Danckwerts [1951], the
renewal events reach the surface and should generate some fluctuations.
Figure 6.21: Comparison of concentration fluctuations in the literature (From
Herlina [2005])
90
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
In Fig. 6.21 both measurement techniques gave a maximum of the fluctuations around the distance of the boundary-layer thickness. But in both
methods the determination of this distance has some uncertainty.
Pump flow
10.5
17.5
25.0
30.5
37.0
43.0
50.0
L/min
L/min
L/min
L/min
L/min
L/min
L/min
∆c
cbulk
2.31
2.29
2.21
2.10
2.08
1.95
1.96
0.51
0.59
0.68
0.74
0.81
0.88
0.96
boundary-layer thickness
432
354
293
256
225
208
197
µm
µm
µm
µm
µm
µm
µm
Table 6.1: Parameters for the evaluation of fluctuations in the case of bulk turbulences assuming the model m = 3
6.4.2
Fluctuations in Wavy Conditions
As described in Sec. 6.3, the image registration worked only in some cases
with small waves. Here two examples of time series are presented. The
analysis of the concentration profile in Fig. 6.17 yields the surface renewal
model p = 0 for the case at 2.5 m/s. The fluctuation in this case displayed in
Fig. 6.22 in agreement with the model increases towards the phase boundary
and is at a higher level than for the case at wind speed of 2.6 m/s. Here
less fluctuations are seen and they decrease towards the interface. This is in
agreement with the profile that was found to follow the K-model in Fig. 6.14.
Wind speed
model
∆c
cbulk
boundary-layer thickness
2.6 m/s
2.5 m/s
m = 3 3.49
p = 0 4.49
1.77
1.05
350 µm
421 µm
Table 6.2: Parameters for the evaluation of fluctuations in the case of wavy conditions
The optical blurring hinders the fluctuation to fall too much. This smoothing effect prevents to observe the process directly at the phase boundary. But
the effect is also caused by sensor noise that adds to the fluctuations. The
noise level is higher at low luminescence intensity near the surface where
oxygen quenches the phosphorescence. In the experiment with bulk turbulence, the bulk concentration was kept low by continuous degassing with
6 Results: Gas-Transfer Velocities and Depth Profiles
91
0
Relative depth z+
1
2
3
4
5
2.5 m/s
2.6 m/s
6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Fluctuation of the concentration c’ /∆ c
0.45
0.5
Figure 6.22: Concentration fluctuation at a wavy surface. The fluctuation increases towards the surface at wind speed 2.5 m/s in agreement
with the found surface renewal for this case. The fluctuations decrease towards the interface at wind speed of 2.6 m/s to what the
K-model was assigned
the gas-exchanger module. Here the effect of noise should be very low and
should not change. In the experiment with a smooth surface and increasing
wind speeds, the bulk concentration was increasing lowering the signal-tonoise level with time and increasing wind speed. The results in terms of
concentration fluctuation is shown in Fig. 6.23 in the next section.
6.4.3
Fluctuations with Wind Stress at Smooth Surface
The fluctuations at a smooth interface in Fig. 6.23 increase towards the
interface but the magnitude of the values is lower by a factor of 2 compared
to the case of surface renewal in Fig. 6.22.
The low values and the trend of the fluctuation to higher values with
lower signal-to-noise ratio indicates that in this experiment the fluctuation
is mainly due to sensor noise. Also the discontinuity (at the step in Fig. 6.23
z+ = 1.2 for 1 m/s) is a hint at sensor noise because of the different properties
of the two parts of the sensor described in Sec. 5.1.
92
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
The small fluctuations in the bulk are in agreement with the observation
of only very few renewal events. The increase of these fluctuations is again
caused by the low signal-to-noise ratio at high oxygen concentrations in the
bulk.
0
Relative depth z+ = z / z*
1
2
3
0.8 m/s
1.0 m/s
2.0 m/s
3.0 m/s
4.0 m/s
5.0 m/s
6.0 m/s
4
5
6
0
0.05
0.1
0.15
0.2
Fluctuation of the concentration c’ /∆ c
0.25
Figure 6.23: Fluctuation at a smooth surface with different wind speeds
0.3
6 Results: Gas-Transfer Velocities and Depth Profiles
Wind speed
0.8
1.0
2.0
3.0
4.0
5.0
6.0
m/s
m/s
m/s
m/s
m/s
m/s
m/s
∆c
cbulk
2.53
2.43
2.24
1.99
1.75
1.49
1.24
2.55
2.86
3.32
3.86
4.43
5.01
5.59
93
boundary-layer thickness
648
604
421
337
284
256
243
µm
µm
µm
µm
µm
µm
µm
Table 6.3: Parameters for the evaluation of fluctuations in the case of smooth
surface assuming the model p = 1
Chapter 7
Conclusions: Discussion of the
Findings
This chapter evaluates the different aspects of the results of this thesis. This
is also an opportunity to compare the findings with the results that other
authors presented in related fields of research.
Phosphorescent Dye. The characterisation of a novel phosphorescent
metal–ligand complex (MLC) showed excellent agreement with the requirements for the application as an oxygen indicator in water. The Stokes
shift between absorption and emission was wide enough to exclude significant self-absorption (Sec. 3.6) that would falsify concentration computations. The synthesis of the organo–metal compound can be accomplished
without intermediates from commercially available educts (Sec. 3.4). The
new phosphorescent dye for the quantitative visualisation of concentration
fields within the aqueous mass-boundary layer shows significant advantages
over the previously used dyes. These include high quantum yield, prompt
solubility, strong absorbance, high photo-stability, large Stokes shift and
no surface activity. Thus, a much better signal-to-noise ratio and reliability
can be expected from this oxygen indicator compared to previous studies
[Münsterer, 1996; Herlina, 2005] (Sec. 3.7).
Set-up. The experimental set-up allowed the generation of reproducible
conditions for the study of gas-exchange processes (Sec. 4.1). Because of the
temperature dependence of the dye the experiments were conducted with a
stable water temperature. The introduction of a new experimental method
for changing gas concentrations in water with a novel gas-exchanger module
helped to reduce the preparation time compared to a technique relying on
nitrogen bubbling found in the literature [Herlina, 2005]. Moreover, the
accuracy and hence reproducibility is also significantly higher with these
95
96
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
gas-exchange modules. The lower bulk concentrations increased the contrast
at the boundary layer with an additional positive effect on the signal-to-noise
ratio (Sec. 4.4).
Transfer velocity. Direct measurement of oxygen-concentration profiles
turned out to be an accurate method for gas-exchange studies. The different
approaches for determining the transfer velocities in wind experiments with
a smooth surface are in good agreement proving the applicability of the
used techniques. There is no fundamental difference in the results for the
evasion of the trace gases N2 O and H2 that were carried out by Degreif
[2006] from the invasion of oxygen measured with a mass-balance method
and using the boundary-layer thickness to calculate the gas-exchange rate
for the same measurement day (Sec. 6.1.5). The measurement of reference
bulk concentration need simple improvements detailed in Sec. 8.2 to stabilise
the measured values in order to achieve the accuracy of the other methods
(Sec. 6.1.4).
Model prediction at smooth surface. The concentration profiles revealed the depth dependence of the turbulence. Analysing the profiles by fitting the theoretical predictions to them (Sec. 6.1.2) in combination with the
comparison of the transfer velocity (Sec. 6.1.5), showed that the gas-exchange
with a smooth water surface are best described by the surface-renewal model
p = 1. In this model, the transport is dominated by events. Remarkable
is the observation that no expected turbulence sturctures were seen in the
sequences. The remaining uncertainty in this statement is due to the limited
optical resolution that hinders to determine directly the concentration and
its gradient at the surface. The fitting approach helped to deal with these
limitations (Sec. 5.6).
Comparison with previous studies. In comparison, Münsterer [1996]
observed a behaviour between the models of p = 1 (surface-renewal model)
and m = 3 (K-model). Possibly also m = 4 (cf. Eq. 2.22), that was calculated only in the present work, would be an adequate model for the description of his profile shapes but this could not be verified because the data was
not available. His wind speeds over a smooth surface were up to 4 m/s but
are difficult to compare because the dimension of the wind–wave tank and
the position of the wind sensor relative to the surface was different. By calculating the friction velocity u? , a comparison could be done but the available
measurements in the same wind–wave facility of Degreif [2006] for a wavy
surface and Garbe et al. [2007] for a smooth surface show high uncertainties.
For wavy conditions Münsterer [1996] has visualised concentration profiles
7 Conclusions: Discussion of the Findings
97
suggesting the surface-renewal model p = 0 at wind speeds faster than 5 m/s.
However, the resolution gave only 3–4 measurement points within the boundary layer making the normalisation to the concentration difference difficult.
Alternative evaluation of profiles. The evaluation using simple extrapolation of the highest gradient (Sec. 5.7) yielded similar results for the
transfer velocity as the fitting procedure (Sec. 6.1.3). When the boundarylayer thickness is comparable to the blurring, the prediction of the adequate
profile was only possible by modelling the function with the theoretical profile
after convolution with the blurring function (Sec. 6.1.2). This method had
also advantages when, instead of the mean, the single profiles with a high
noise level were analysed because no smoothing of the data was necessary.
In the presence of shear, induced by wind speeds up to 7 m/s over a smooth
surface, only few turbulent structures could be observed. This is reflected
by the fact that no bimodal evaluation was needed for correct transfer rates
as suggested by Jähne et al. [2007] recently and in this case the statistical
effect described in Eq. 2.34 can be neglected. Thus, the values of the gastransfer velocity from both, mean and single profile evaluations (Sec. 6.1.3)
show no significant difference.
Bulk turbulence. A side product, that seemed to be worthy to analyse,
was the turbulence generated by a mixing pump. Hence, the concentration
profiles behave like the K-model with m = 3 described in Eq. 2.21. The
decision was more definite than in the case described above The evidence
was the residual difference between the fit and the smoothed model function
(Sec. 6.2). That this profile shape is different from the form of the profile
with wind stress is expected because no shearing forces at the interface are
present. Even though the water was circulated by the pump flow and some
shear stress was generated. This may partly explain the difference to experiments by Herlina [2005] in a shear free grid steered tank where mean flows
were avoided. She described the profiles always with exponential functions
from the surface-renewal model of Eq. 2.29. Another reason may be that her
surface was cleaned while in the pump experiments herein described a surfactant film was always present and difficult to remove, once it was applied.
Concentration fluctuations near the surface To analyse concentration
fluctuations in the boundary layer a very high signal-to-noise ratio is required
to exclude effects of the sensor noise. This prerequisite was fulfilled in the
case of bulk turbulences. Here a comparison of the fluctuation profiles with
other studies showed parallels of the measurements in the water flume to
98
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
bottom-generated tanks where other authors avoid every mean flow or shear
stress.
Chapter 8
Summary and Outlook
Before an outlook on future studies is given, the work and the central results
will be summarised in this chapter.
8.1
Summary
Gas transfer across gas–liquid interfaces is of importance in natural environments and technical applications. Recently, the exchange of gases between
the two most important reservoirs in the global cycling, the atmosphere and
the oceans, has received increased attention considering that it determines
the global distribution of many gaseous and volatile chemical species. Large
uncertainties in climate modelling are mainly due to the fact that mechanisms controlling air–water gas transfer in conditions such as the presence of
surfactants or the different domains of wind speeds are not well understood.
Current parametrisations are semi-empirical exhibiting scatter in gas-transfer
velocities in the order of 200%.
The transfer of sparingly soluble gases including carbon dioxide, methane
and oxygen is controlled by the transport from the air–water interface through
the sub-millimetre aqueous boundary layer. With novel visualisation techniques applying the idea of laser-induce fluorescence (LIF), the mechanism
of the exchange processes can be visualised. This enables the analysis of
concentration profiles a few hundreds of microns beneath the surface.
LIF studies on gas exchange previously presented in the literature verified mostly qualitative effects of the turbulence and measured concentration
fluctuations in the boundary layer. In combination with particle-image velocimetry the turbulence state of the liquids was determined in image pairs.
The signal-to-noise ratio of established LIF techniques is partly limited by the
poor quantum yield of the used luminescent dyes restricting the resolution
in space and time.
99
100
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
In this study, a novel phosphorescent ruthenium–ligand complex was applied as a luminescent dye taking advantage of its favourable properties.
The dye demonstrates an increased luminescence intensity and sensitivity to
the oxygen concentration in water. This allowed improved experiments in
a circular wind–wave channel increasing significantly the frame rate of the
digital camera. This is a vital prerequisite for exchange processes which take
place on time scales of fractions of a second. Concentration profiles could
be visualised with a high spatial resolution achieving 25.2 µm/pixel. The
enhanced intensity contrast made short exposure times possible enabling a
camera frame rate of 185 m/s that is fast enough to observe some turbulence
processes in gas-exchange experiments. Experiments were run by varying
oxygen concentrations in the water body and by measuring the response
due to the exchange processes. These experiments were facilitated by novel
commercial gas-exchange modules significantly reducing experimental effort.
A challenge in the evaluation of image series from luminescence profiles
is the detection of the surface. The developed image-processing algorithm
performed well in the case of a smooth surface. It was possible to extract
the boundary-layer thickness accurately. In the experiment with winds of
0.8–7 m/s and a surfactant film on the surface, the thickness decreased from
670 µm to 250 µm which is only little more than the effective resolution of
approximate 200 µm. From the values of the boundary-layer thickness, gastransfer velocities for a smooth surface were calculated between 1.3–3.6 cm/h.
They correlated well with reference evasion measurements of N2 O and H2
conducted in parallel. This gave a ground truth for the measured quantities.
Additionally the transfer rates were calculated from bulk oxygen measurements with a similar mass-balance method as for the mentioned trace gases.
The obtained values for the transfer rates from the mass-balance technique
are similar to the results from the other methods but showed some fluctuations.
The analysed quantitative concentration distribution in the boundary
layer is a result of molecular diffusion and turbulent transport. The mathematical description of the concentration profile revealed differences for different conceptual descriptions. A new mathematical formulation was added to
the four functions that were developed previously by other authors. These
were needed to analyse the shape of the measured concentration profiles.
The systematic analysis of the concentration profile at smooth surfaces
together with the comparison of the transfer velocity made it possible to
distinguish between the different theoretical approaches. The measured data
suggests that the description using the theory of surface-renewal events is the
best representation of the concentration profile observed. But the differences
between the models are not significant enough. However, the expected tur-
8 Summary and Outlook
101
bulence structures, that the surface-renewal model predicts, were not visible
with a flat surface even at high shear stress with wind speeds of 7 m/s.
The novel visualisation technique improved significantly the resolution
of concentration imaging in the aqueous boundary layer. In fact, for the
first time systematic measurements were accurate enough to determine the
boundary-layer thickness from concentration profiles and calculate transfer
velocities with the same accuracy as measured with mass-balance methods.
With the presented procedure, new opportunities are opened to study the
mechanisms of gas exchange on a small scale of the diffusive boundary layer
where fundamental theoretical knowledge is lacking.
8.2
Outlook: Possible Improvements and New
Concepts
The presented method with the novel indicator dye is easy to apply in other
studies providing a high signal quality for oxygen measurements in water.
A possible combination with particle-imaging velocimetry PIV enables to
visualise additionally flow fields in the water. The techniques complement
one another as shown by Herlina and Jirka [2004] and Variano and
Cowen [2007].
Currently a new inert and chemically clean linear wind–wave facility is
being constructed that is specifically designed for the visualisation technique
described in this study. The air space and the water channel will be coated
with Teflon and the whole facility is gas-tight. Therefore, acid and alkaline
gases can be used in this facility. The water channel will be 4 m long, about
0.4 m wide and 0.1 m high and can be filled with ultraclean water. This
facility will provide an improved optical access allowing the imaging with a
higher optical resolution.
The measurement of the fluorescent lifetime, that is shortened by the
presence of quenching oxygen, gives concentrations independently from the
intensity of the phosphorescence. A new type of ’smart-pixel’ sensors may
approach this aim. Such a camera is able to detect modulations of light in
the frequency range of several MHz. PMDTechnologies in Siegen, Germany,
distributes camera system that use this principle to measure distances adding
to every pixel of a 2D image a depth information. When the absolute intensity
is not the measured quantity any more than the method is not suggestible to
intensity fluctuations of the exciting light or to inhomogeneous concentration
of the dye. It is imaginable to visualise the boundary layer in the field by
dropping small amounts of dye in a focused area on a lake or the ocean.
To keep a constant signal-to-noise ratio, the bulk concentrations should
102
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
be kept as low as possible. This can be achieved by starting the experiments
quickly after the degassing procedure. But this excludes the possibility of
measuring other tracers in the same experiment that need time to be solved in
the water body for evasion experiments. One solution is to develop the massbalance method further. A new technology of oxygen probes uses a similar
phosphorescent technique as in the presented work. It is now commercially
available and promises to reduce the noisy signal of the oxygen sensor without
the need of constant stirring.
Alternatively separate experiments can be restarted for every wind speed.
Shorter measurement times increase the bulk concentration and the contrast
of luminescence at the surface boundary layer. The ideal solution to the
increasing bulk concentration would be to keep the concentration low by
continuous degassing. But here the problem arises of how to avoid the turbulences generated from the flow through the gas exchanger. And then the
transfer velocity can not be computed from the simultaneous change of bulk
concentrations or of concentrations of other reference gases.
High frame rates are needed for resolving turbulent processes and resolve
the movement of the surface subject to undulations by waves. But high
frame rates limit also the signal-to-noise ratio. The photo-stability of the
novel phosphorescent dye is good enough for the employment of a brighter
light source that would increase the signal-to-noise ratio for more accurate
measurements of fluctuations.
Part IV
Appendix
103
Appendix A
Wavy Conditions with
Unsuccessful Image
Registration
In Fig. A.2 a typical time series taken with winds of 2.8 m/s is found. The
wave slope is higher than in the images shown in Sec. 6.3 what leads to
effects that make it impossible to compute concentration profiles. A light
saturation is seen because of focussing effect of a curved wave. The surface
is rarely recognisable because passing waves cause occlusion effects. The
frequent turbulence structures are difficult to distinguish from the feature of
the surface. The waves on the surface also suppress the total reflection.
105
106
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Although the image registration in Fig. A.3 failed, the profile was analysed
with the same tools as the mean profiles before. The false mean profile in
Fig. A.1 appears to follow the surface-renewal model. This means that even
without a correct image registration, the concentration profiles seem to make
sense what is misleading. Hence, every evaluation has to be done with care
paying attention to the successful image registration of the surface. A similar
case is documented in the following.
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
Figure A.1: Wavy surface: false mean concentration profile at 2.7 m/s. After
unsuccessful image registration the profile looks like the K-model
m = 3. The boundary-layer thickness is overestimated (m2, p0, m3,
p1, m4)
A Wavy Conditions with Unsuccessful Image Registration
107
Depth from mean surface (mm)
−6
−4
−2
0
2
4
6
8
1980 2005 2030 2055 2080 2105 2130 2155 2180 2205
Frame number
Figure A.2: Time series with small waves with high turbulence structures at
2.7 m/s wind speed. Surface-renewal events are visible. The surface
is not always seen hindering a successful registration
Frame number
500
1000
1500
2000
2.7
5.4
8.1
10.8
2500
3000
3500
4000
4500
5000
13.5
16.2
Time (s)
18.9
21.6
24.3
27
(a)
(b)
Figure A.3: Wavy surface: image registration of time series at a wind speed of
2.7 m/s. (a) Before registration. (b) After unsuccessful registration
108
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
The case shown before and also the case shown in Fig. A.5 and Fig. A.6
with wind speed of 2.8 m/s represents a examples beyond the possibilities of
the used image processing techniques. But they demonstrate some pitfalls in
the analysis of the mean profile shape.
Depth from the surface z (mm)
0
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
Normalised O2 concentration
0.8
1
Figure A.4: Wavy surface: false mean concentration profile at 2.8 m/s. After unsuccessful image registration the best model seem to be the surfacerenewal p = 0. The boundary-layer thickness is overestimated (m2,
p0, m3, p1, m4)
An interesting point in Fig. A.4 is that the profile shape changes again.
With similar conditions as before, here the profile of the classical surfacerenewal model p = 0 seems to be the best. Thus, profiles without a successful
image registration do not always lead to a m = 3 profile as in Fig. A.1 but
may also look like a p = 0 profile as in Fig. A.4.
In the detail of the time series in Fig. A.5, a low contrast is seen because
of a high oxygen concentration. Similar problems in the detection of the
surface are found as in Fig. A.2 and only very few surface-renewal events.
A Wavy Conditions with Unsuccessful Image Registration
109
Depth from mean surface (mm)
−6
−4
−2
0
2
4
6
8
3617 3642 3667 3692 3717 3742 3767 3792 3817 3842
Frame number
Figure A.5: Time series with small waves with few turbulence structures at
2.8 m/s wind speed. The contrast is low because of high oxygen
concentrations in the water bulk
Frame number
500
1000
1500
2000
2.7
5.4
8.1
10.8
2500
3000
3500
4000
4500
5000
13.5
16.2
Time (s)
18.9
21.6
24.3
27
(a)
(b)
Figure A.6: Wavy surface: image registration of time series at a wind speed of
2.8 m/s. (a) Before image registration. (b) After unsuccessful image
registration
Appendix B
Mathematica Script for
Boundary-Layer Mathematics
The algebra programme Mathematica®5.0 (2003) was employed for solving of the differential equation Eq. 2.11. The starting point was the power
law proposed by Jähne et al. [1989]. Some of the results are similar as in
Münsterer [1996].
In the study herein, the model for m = 4 was needed to describe the concentration profiles at a smooth surface. This model was applied in Sec. 6.1.2
for the analysis of the turbulence structure.
In the following, the complete script will be documented to give the possibility to reconstruct the deductions in Sec. 2.2.2. Maybe it is a good starting
point to refine the theory on turbulence in the boundary layer.
111
112
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Concentration Profiles in Boundary Layer
Small Eddy Kt Model from Eq. 2.10
In[1]:=
[email protected], α, c2D
In[2]:=
eq10 = [email protected] + α z ^ m L ∗ [email protected]@zD, zDL, zD
Out[2]=
m z−1+m
α c @zD + H1 + zm αL c @zD
ü Solve stationary case of Eq. 2.10
π
mÆ2; α → + ; 1 − 2π [email protected] π2 zD = π2 [email protected]π z ê
4
2
In[3]:=
[email protected]_ D =
[email protected] ê. [email protected] 0, [email protected]
1, [email protected]@zD, zD − 1 ê. z → 0<, [email protected], zD êê Simplify
Out[3]=
1
1
91 − z H1 + 0 αL Hypergeometric2F1A , 1, 1 + , − zm αE=
In[4]:=
[email protected]_D = [email protected]@zD, m
Out[4]=
1
1
91 − z Hypergeometric2F1A , 1, 1 + , − zm αE=
In[5]:=
[email protected]@zDD
Out[5]=
1
z H− zm αL−1êm [email protected]− zm α, , 0D
m
91 − =
In[6]:=
[email protected] ê. m
Out[6]=
2 D;
m
m
m
m
> 0D
m
m
→ 82, 3, 4<
è!!!
!
ArcTanAz α E
1
4
, 1, , − z3 αE,
991 − , 1 − z Hypergeometric2F1A è!!!
3
3
α!
1
5
1 − z Hypergeometric2F1A , 1, ,
4
4
− z4 αE==
ü Determine a with bounding condition c[•]==0 to yield Eq. 2.18
(* alph=Solve[Limit[generalSol[z],zض]ã0,a]
Solve::"tdep": "The equations appear to involve the variables to be solved for in an non-algebraic way." *)
(*alph=Solve[Limit[generalSol[z],zض,AssumptionsØ(m>0)]ã0,a]
Solve::"ifun": "Inverse functions are being used by Solve"*)
In[7]:=
alphM2 = [email protected]@[email protected], z
Out[7]=
π2 ==
99α → 4
→ ∞D 0 ê. m → 2, αD
B Mathematica Script for Boundary-Layer Mathematics
2
In[8]:=
113
profile_models16.nb
alphM3 = [email protected]@[email protected], z
→ ∞D 0 ê. m → 3, αD
Solve::ifun : Inverse functions are being used by Solve, so some
solutions may not be found; use Reduce for complete solution information.
More…
8π
99α → ==
è!!!!
81 3
3
Out[8]=
In[9]:=
alphM4 = [email protected]@[email protected], z
→ ∞D 0 ê. m → 4, αD
Solve::ifun : Inverse functions are being used by Solve, so some
solutions may not be found; use Reduce for complete solution information.
Out[9]=
More…
π4 ==
99α → 64
ü Solve Eq. 2.10 with subtitution y = c and boundary condition c @0D = − 1
In[10]:=
m z−1+m α
solY = c @zD == − c @zD
H1 + zm αL
Out[10]=
m z−1+m α [email protected]
y @zD − 1 + zm α
In[11]:=
solYSep = ‡
Out[11]=
[email protected]@zDD
In[12]:=
solYSep = [email protected], [email protected]
Out[12]=
[email protected] → c2
==
1 + zm α
In[13]:=
solC2 = [email protected]@[email protected] − 1 ê. [email protected]<, c2D ê. z
Out[13]=
88c2 → − 1<<
ê. 8c ' → y, c '' → y <
1
m z−1+m α
[email protected] − ‡ z + [email protected]
[email protected]
H1 + zm αL
H∗ c2 is the overall integration constant ∗L
[email protected][email protected] + zm αD
→ 0, m > 0D
ü Find [email protected] = Ÿ y z with the boundary condition [email protected] = 1 yields:
z
1
z
[email protected] = Ÿ y z = 1 − Ÿ0 1+α zm
In[14]:=
[email protected]@[email protected], zD [email protected] ê. [email protected], [email protected], zD
H∗ y=c is the same as [email protected]=Ÿ y z and gives integration constant [email protected]
1
1
Out[14]= [email protected][email protected] + c2 z Hypergeometric2F1A , 1, 1 + ,
m
m
In[15]:=
− z αE==
m
solConc = [email protected]@[email protected], zD [email protected] ê. [email protected], [email protected]
1
1
Out[15]= [email protected] → 1 + c2 z Hypergeometric2F1A , 1, 1 + ,
m
m
− z αE==
m
1<, [email protected], zD
∗L
114
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
profile_models16.nb
3
→ 82, 3, 4<
In[16]:=
solConc ê. m
Out[16]=
è!!!!
c2 ArcTanAz α E
[email protected] → 91 + , 1 + c2 z Hypergeometric2F1A 13 , 1, 43 , − z3 αE,
è!!!!
α
5
1
1 + c2 z Hypergeometric2F1A , 1, ,
4
4
ü The boundary condition [email protected]
− z4 αE===
π
∞D = 0 leads to α = I Mm with
m [email protected]πê mD
α = ijIntegrateA m , 8zS, 0, ∞<, Assumptions →
k
1 + zS
π D m
Csc
@
m
πm jji zzy
m
1
In[17]:=
Out[17]=
k
α ê. m → 82, 3, 4<
Out[18]=
π2 , π4 =
8 π3
9 , è!!!!
4
64
81 3
In[19]:=
[email protected]%D
Out[19]=
82.4674, 1.76805, 1.52202<
In[20]:=
[email protected]@zD, z
In[21]:=
Out[21]=
> 1Eyz ^ m
{
{
In[18]:=
Out[20]=
m
m e N > 1.
→ ∞, Assumptions →
m
> 1D
π D m
[email protected] 1
m
, 1, 1 + 1m , −πm zm jij 9LimitA1 − z Hypergeometric2F1A zyz E,
m
m
k
{
z → ∞, Assumptions → m > 1E=
[email protected]@zD, z → ∞D ê.
m → 82, 3, 4, 5, 90, 100, 170, 200, 2.1<H∗ Should be zero!∗L
880, 0, 0, 0, 0, 1, 0, 1, − 0.272565<<
ü Test if solution is solution to stationary case of Eq. 2.10
In[22]:=
[email protected]
0 ê. m → 2, [email protected] 1, [email protected]@zD, zD − 1 ê. z → 0<, [email protected], zD êê Simplify
π z D
2 [email protected] 2
Out[22]=
[email protected] → 1 − ==
In[23]:=
[email protected] ê. [email protected] 0 ê. m
Simplify
Out[23]=
In[24]:=
Out[24]=
π
→ 3, [email protected] 1, [email protected]@zD, zD − 1 ê. z → 0<, [email protected], zD êê
1
4πz
− 3 π + 6 ArcTanA E − 2 è!!!3! LogA9 + 2 è!!!3! π zE + è!!!3! LogA81 − 18 è!!!3! π z + 12 π2 z2 E
è!!!!
9
3
9 =
4π
[email protected] ê. [email protected] 0 ê. m
FullSimplify
→ 3, [email protected] 1, [email protected]@zD, zD − 1 ê. z → 0<, [email protected], zD êê N êê
81.40806 + 0.477465 [email protected] − 1.39626 zD −
0.275664 [email protected] + 10.8828 zD + 0.137832 [email protected] + z H− 0.826993 + 1. zLD<
B Mathematica Script for Boundary-Layer Mathematics
115
4
profile_models16.nb
In[25]:=
[email protected] ê. [email protected] 0 ê. m
Simplify
Out[25]=
π z D − 2 [email protected] + π z D + [email protected] − 4 π z + π2 z2 D − [email protected] + 4 π z + π 2 z2 D
2 π + 2 [email protected] − 2
2
9 =
2π
In[26]:=
[email protected] ê. [email protected] 0 ê. m
FullSimplify
Out[26]=
→ 4, [email protected] 1,
→ 4, [email protected] 1,
[email protected]@zD, zD
[email protected]@zD, zD
− 1 ê. z →
− 1 ê. z →
0<, [email protected], zD
0<, [email protected], zD
81. + 0.31831 [email protected] − 1.5708 zD −
0.31831 [email protected] + 1.5708 zD + 0.159155 [email protected] + z H− 1.27324 + 1. zLD −
0.159155 [email protected] + z H1.27324 + 1. zLD<
In[27]:=
eq10
Out[27]=
m πm z−1+m
In[28]:=
[email protected]; [email protected]_ D = [email protected]
Out[28]=
π D
[email protected] 1
1
m
j
z
, 1, 1 + , −πm zm i
91 − z Hypergeometric2F1A y
j z E=
m
m
m
k
{
In[29]:=
[email protected] ê. m
π D m
π D m
[email protected] [email protected] i
y
y
m m i
m
m
jij j
z c @zD
zyz c @zD + j
z
j zz
j1 + π z j
m
m
k
{
k
{z
k
{
m
Out[29]=
→ 82, 3, 4<
π z D
2 [email protected] 2
1
4
8 π 3 z3
, 1, , − è!!!
! E,
991 − , 1 − z Hypergeometric2F1A 3
3
π
81 3
1
5
1 − z Hypergeometric2F1A , 1, ,
4
4
− 1 π4 z4 E==
64
H∗ should be always ZERO ∗L
In[30]:=
eq10
Out[30]=
80<
In[31]:=
[email protected]@zD, zD ê. m
→ 82, 3, 4<
1
Out[31]=
1
1
99− , − , − ==
π2 z2
8 π3 z3
π4 z4
1 + 1 + 1 + è!!!!
4
64
81 3
In[32]:=
[email protected]@[email protected], zD, zD ê. m
Out[32]=
π2 z
8 π 3 z2
π 4 z3
, 99 , ==
è!!!
! I1 + π2 z2 M2
8 π3 z3 2
π4 z4 M2
2 I1 + 27
3
M
16
I
1
+ è!!!!
4
64
81 3
→ 82, 3, 4<
ü postition of the boundary-layer thickness blt z∗ ; [email protected]
→ 82, 3, 4< êê N
In[33]:=
[email protected] ê. m
Out[33]=
880.360907, 0.234962, 0.174894<<
êê
êê N êê
Appendix C
Software Tools
C.1
Data Acquisition with Heurisko Software
The image processing software Heurisko®5.3 distributed by Aeon-Verlag,
Hanau, did the data acquisition controlling directly the CCD-camera. In a
script the steps of acquisition were declared writing compressed png-files for
integer images, raw-files for the sequences and tiff-files for a series of mean
lines.
In another instance it automated also the synchronised data acquisition
from the different sensors and devices and controlled a power supply.
C.2
Retrieving Oxygen Probe Data
The software delivered by WTW® with their oxygen probe wrote the gathered information in a log file and could export it after the measurement manually to an ASCII-file. It delivered also additional temperature information
from the same sensor and added the date in a chosen format.
The graphical user interface was not very comfortable to handle. And
sometimes it collected only zeros instead of the concentrations what turned
to be unusable some important measurement days. The update to a new
software version was not successful.
C.3
Evaluation Scripting in MatLab Language
The evaluation was done entirely with MatLab®7.2 R2006a software. The
script was compatible with the version 7.1 but not with 6.5. It was tried
to keep the number of used additional toolboxes small. The only additional
commercial toolbox was the optimization toolbox from MathWorks that did
the non-linear least square fitting.
117
118
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Also all plots of data in this thesis were done with this software exporting
them to eps-files with the print command after setting the correct figure size
and fonts.
C.4
Type-Setting
LATEX is a standard type-setting environment based on TEX for writing
text projects with mathematical formulas and creating automated reference
lists using BibTEX. The style of the bibliography was natbib.sty that was
adapted to display the last names first of the references in the list and to set
the names in small capitals. The parsing of the type-setting code was executed by pdftex that included directly the hyperrefs and bookmarks in the
pdf-file and handled the bitmap pictures in jpeg- and png-format as desired.
For editing the free software TeXnicCenter for MS-Windows was used
that made writing more comfortable due to its high-lighting ability and a
button for the different compilation steps. Another appreciated feature was
the project handling with the organisation of all related files.
GhostScript did the conversion of eps-files to pdf-graphics with the dos
command epstopdf.exe. This command was called directly from MatLab
with the command system.
All code is freely available from the author writing to:
Achim[at]Falkenroths.de.
List of Figures
1.1 Measured concentration increase of CO2 in the atmosphere . .
1.2 World map of global mean sea-to-air flux of CO2 . . . . . . .
1.3 The forms of interaction between the ocean and the atmosphere
2.1
4
5
7
2.2
2.3
Definition of boundary-layer thickness z? in a concentration
profile c(z+ ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Model functions for the cases of free surface and smooth surface 19
Variation of the boundary-layer thickness due to surface-renewal 21
3.1
3.2
3.3
3.4
3.5
3.6
Jablonski diagram . . . . . . . . . . . . . . . . .
Measured Stern–Volmer relation . . . . . . . . .
Chemical structure of luminescent dyes . . . . . . .
Absorption spectra of the ruthenium complex . . .
Emission spectrum of the ruthenium complex . . .
Absorption and emission spectra of the Ru complex
4.1
Schematic drawing of the small wind–wave facility and the
optical set-up . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical image of the laser sheet taken with the measurement
camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Image for spatial calibration of a millimetre scale . . . . . .
Estimating the blurring . . . . . . . . . . . . . . . . . . . . .
Photograph of the ”Jostra Quadrox” gas-exchanger module .
Decrease of oxygen concentration during degassing . . . . . .
Typical development of the wind speed in an experiment . .
4.2
4.3
4.4
4.5
4.6
4.7
5.1
5.2
5.3
5.4
5.5
5.6
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Flow chart of the image processing steps . . . . . . . . .
A mean column of a sequence of dark images . . . . . . .
Effect of noise for different symmetry filters . . . . . . .
Effect of three different filters on the surface detection . .
Filter optimisation: selection of the suitable filter width
surface detection . . . . . . . . . . . . . . . . . . . . . .
Effect of the surface detection on a mean profile . . . . .
119
.
.
.
.
.
.
.
.
.
.
.
.
. .
. .
. .
. .
for
. .
. .
.
.
.
.
.
.
28
30
33
35
37
38
. 42
.
.
.
.
.
.
43
45
46
47
48
49
.
.
.
.
51
52
54
55
. 56
. 57
120
5.7
5.8
5.9
5.10
5.11
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Mean profile normalised to Beer–Lambert absorption . . . .
Calibration curve . . . . . . . . . . . . . . . . . . . . . . . . .
Effect of blurring on a model function . . . . . . . . . . . . . .
Extracting the boundary-layer thickness z? with fitting method
Extracting the boundary-layer thickness z? with polynomial fit
58
59
60
61
63
Raw time series of one vertical line of the laser sheet . . . . .
Single intensity profiles before image processing . . . . . . . .
3D plot of one measurement series with different winds . . . .
Fitting the model to normalised concentration profiles . . . . .
Error σerr for different model-fits varying the wind speed . . .
Correlation of boundary-layer thickness with wind speed . . .
Transfer velocities from different oxygen measurements . . . .
Concentration of oxygen in the water and computed k . . . . .
Transfer velocity of different gasses . . . . . . . . . . . . . . .
Time series of bulk turbulence . . . . . . . . . . . . . . . . . .
Correlation of boundary-layer thickness with pump flow . . . .
Error σerr for different model fits varying the pump rate . . . .
Fitting the theoretical models to profiles with pump turbulences
Wavy surface: mean concentration profile at 2.6 m/s . . . . . .
Wavy surface: raw time series with surface-renewal event . . .
Wavy surface: image registration of time series at 2.6 m/ . . .
Wavy surface: mean concentration profile at 2.5 m/s . . . . . .
Time series with small waves with at 2.5 m/s wind speed . . .
Wavy surface: image registration of time series at 2.5 m/s . . .
Fluctuation of the calculated concentration with bulk turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.21 Comparison of concentration fluctuations in the literature . .
6.22 Concentration fluctuation at a wavy surface . . . . . . . . . .
6.23 Fluctuation at a smooth surface with different wind speeds .
69
70
71
72
73
75
76
77
78
80
81
82
83
84
85
85
86
87
87
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
A.1
A.2
A.3
A.4
A.5
A.6
Wavy surface: false mean concentration profile at 2.7 m/s . .
Time series with small waves with high turbulence structures
Wavy surface: image registration of time series at 2.7 m/s . .
Wavy surface: false mean concentration profile at 2.8 m/s . .
Time series with small waves at 2.8 m/s wind speed . . . . .
Wavy surface: image registration of time series at 2.8 m/s . .
.
.
.
.
.
.
88
89
91
92
106
107
107
108
109
109
Index
absorbance, 31, 35, 38, 39
concentration profile, 15, 16, 22, 60,
61, 63, 68, 96, 105
absorption, 27, 30, 36, 38, 39, 53, 57,
convolution, 23, 46, 53, 60, 97
70
cylindrical mirror, 43
absorption coefficient, 30, 31
absorption cross section, 31
dark image, 52
aeration, 3
detection of the surface, 52, 57
amount concentration, 31
differential equation, 17, 20, 111
ascorbic acid, 34
diffusion constant, 12
diffusivity, 12, 14, 16, 62, 74, 78
band-pass filter, 36
digital camera, 44, 52, 70, 101
Beer–Lambert’s law, 31, 58, 70
diimine complex, 32
bimodal evaluation, 22
binomial filter, 55, 56
educts, 34
binomial symmetry filter, 55
electrophoresis, 34
bleaching, 39
emission, 28, 36, 38, 40, 58
blurring, 23, 44, 45, 57, 60, 62, 97
emission spectrum, 36, 38
blurring function, 55
equilibrium, 11, 12, 15, 19, 61
etalon, 36
boundary condition, 17
boundary-layer thickness, 8, 14, 15, evasion, 8, 96
excited state, 28, 39
22, 61, 62, 74, 81, 84, 89
box-symmetry filter, 53, 55
Fabry–Pérot, 36
BPS, 33
Fick’s law, 12, 13, 17
buoyancy, 15
fitting, 23, 58, 60, 62, 73, 74
fluctuation of the concentration, 88
calibration, 7, 45, 59, 70
fluorescein, 24, 41
camera, 44, 52, 70, 101
fluorescence, 28
CAS, 33
fluorescence spectrometer, 36
CCD chip, 44, 52
flux density j, 11
Chemical Abstracts Service, 33
frame rate, 44, 52
chemical reaction, 11, 27, 34
friction velocity, 14, 96
climate change, 3
concentration difference, 11, 61, 75
gas-exchanger module, 47, 68, 81, 91,
concentration field, 95
95
121
122
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
gas-transfer velocity, 5, 76
Gaussian, 23, 46, 60
glass fibre, 34, 36
global modelling, 14
gradient filter, 55
heart organ, 33
hydrophobic, 32
image processing, 8, 23, 60, 108
image registration, 57, 84, 86, 90
injection events, 22, 79
internal conversion, 28
intersystem crossing, 28
invasion, 7, 52, 61, 96
IUPAC, 30–32
noise, 23, 47, 53, 55, 75, 81, 90, 91
number concentration, 31
occlusion, 44, 53, 59, 105
offset, 52
optical adapter, 44
optical resolution, 47, 57, 73
optode, 34
osmium, 33
oxygen sensor, 42, 76
paddles, 41, 48, 59, 68
parametrisation, 5, 13
particle reflections, 53
PBA, 24, 32
penetration depth, 31, 58
penetration model, 20
Jablonski, 27
pH-indicator, 23, 59
K-model, 16, 19, 21, 22, 71, 81, 82, phosphorescence, 7, 28, 32, 34, 36, 39,
49, 58, 77, 90, 101
84, 90, 96
photo-luminescence, 27
large eddies, 19
photo-stability, 39, 95
laser, 39, 40, 43, 45, 52, 57, 59
photon emission, 28
laser-induced fluorescence, 6
piston velocity, 12
LED, 36, 39
pixel resolution, 45, 62
lifetime, 28, 29, 32, 39, 101
point spread function, 23, 46, 60
ligand, 32, 33, 95
porphin derivates, 32
local minimum method, 53
power law, 17, 19, 20
luminescence lifetime, 29
pyrene butyric acid PBA, 24, 27, 32,
39
mass-balance method, 8, 12, 77, 78,
96, 102
quantum yield, 28, 29, 32, 39, 95
Mathematica, 18, 111
quencher, 28, 32, 58
mechanism of quenching, 29
quenching, 7, 23, 28, 28, 44
membrane, 27, 33, 42, 47
quenching constant, 29, 39, 59
metal complex, 33
re-aeration, 3
mirror image, 44
reactants, 34
mixing height, 12
reflection, 44, 53, 57, 59, 70, 105
model function, 23, 46, 61
resolution, 45, 47, 62, 70, 73, 77
molar absorption coefficient, 31
rhenium, 33
molecular diffusion, 15, 20
molecular weight, 33
ruthenium, 33, 39
INDEX
scanning flat mirror, 43
Schmidt number Sc, 13, 78
Schmidt-number exponent n, 18, 21
secondary currents, 73
self-absorption, 38, 40, 95
sensor, 34, 41, 42, 76, 90, 91
signal-to-noise, 24, 53, 56, 68, 73, 75,
81, 95, 101
signal-to-noise ratio, 91
simulations, 22
singlet state, 27
slit function, 36
small-eddy model, 16, 16
smooth rigid wall, 16
smooth surface, 50
smoothed gradient filter, 56
smoothing, 23, 47, 90
solubility, 5, 12, 32, 33, 39, 77
spatial calibration, 45
spatial resolution, 45, 70
spectrometer, 35, 36
spectrum, 29, 36–38
stagnant film model, 16, 18
staining proteins, 34
standard deviation, 53
stationary conditions, 17
statistical processes, 22
Stern–Volmer, 29, 39, 58
Stokes shift, 38, 40, 95
subspace trust region method, 61
surface activity, 33, 39, 40
surface detection, 52
surface film, 6, 44, 50
surface renewal, 72
surface roughness, 14
surface tension, 6, 32, 82
surface-renewal, 19–22, 53, 71, 89, 96,
97
surfactant, 6, 14, 32, 44, 50, 68, 77,
82, 97
symmetry filter, 55
123
synchronisation, 53, 117
synthesis, 33, 34, 95
temperature sensors, 41
temporal resolution, 77
trace gases, 49, 76, 78, 96
tracer, 4, 13, 41, 102
transfer velocity, 11, 13, 22, 77
transmittance, 31
triggering, 43
triplet state, 28, 36
turbulence structure, 15, 16, 22, 71,
79
turbulence structures, 58, 68, 86
turbulent diffusion, 16, 71
turbulent diffusion coefficient, 16
variance, 46, 60
vibronic energy, 28
viscosity, 13, 15
vitamin C, 35
wind paddles, 41, 48, 59, 68
wind speed, 13, 48
wind–wave facility, 7, 24, 41, 73, 77,
96, 101
124
´
A. Falkenroth: Visualisation of Oxygen Concentration Profiles
Bibliography
Anderson, S.; Seddon, K. R.: -. J.Chem.Res., page 74, 1979.
Anderson, S.; Constable, E. C.; Seddon, K. R.; Turp, J. E.: Preparation
and characterisation of 2,2’-bipyridine-4,4’-disulphonic and -5-sulphonic acids
and their ruthenium(II) complexes. J.Chem.Soc.Dalton Trans, pages 2247–2261,
1985.
Asher, W. E.; Pankow, J. F.: Direct observation of concentration fluctuations
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Danksagung (acknowledgements)
Viele Menschen haben mich auf ihre Weise zum Gelingen dieser Arbeit unterstützt. Während dieser Entstehung gab es viele interessante Begegnungen, für diese ich mich an dieser
Stelle herzlich bedanken möchte.
Zunächst will ich Prof. Dr. Bernd Jähne danken, der mir die Gelegenheit zu dieser
Arbeit in seiner Arbeitsgruppe im Institut für Umweltphysik (IUP) und am Interdisziplinären Zentrum für Wissenschaftliches Rechnen (IWR) in Heidelberg gab. Viele seiner
Ideen bereicherten die Arbeit.
Des Weiteren möchte ich Prof. Dr. Wolfrum danken sowohl für seine Unterstützung
der interdisziplinären Arbeit auch im Rahmen des Graduiertenkollegs als auch für die
Übernahme des Gutachtens.
Die experimentelle Arbeit und das interaktive Lernen in täglichen Diskussionen machten die Arbeit mit den Mitgliedern der Bildverarbeitergruppe stets fruchtbar. Ich habe
gerne mit ihnen zusammen gearbeitet und werde auch die Freizeitaktivitäten in guter
Erinnerung behalten.
Besonders möchte ich mich bei Kai Degreif für die intensive Zusammenarbeit wärend
der gesamten Dauer danken. Mit ihm zusammen entstanden die Austauschmessungen, die
zum zentralen Bestandteil der Arbeit wurden. Sehr hilfreich war mir auch seine Erfahrung
bei der Auswertung für das Massenbilanzverfahren.
Stets ein offenes Ohr fand ich bei Martin Schmidt, der mir über viele Probleme gerade
bei den komplizierten Rechenmaschinchen hinweg geholfen hat. Vor allem seiner Geduld
gebührt großer Dank.
Bedanken möchte ich mich außerdem bei Roland Rocholz, Günther Balschbach und
Pavel Pavlov für ihre stete Hilfsbereitschaft und Großzügigkeit, die wesentlich zum guten
Klima in der Arbeitsgruppe beitrugen. Besonderer Dank gilt immer wieder dem Netzbeauftragten Günther, der die computeradministrativen Voraussetzungen sicherte.
Für vielfältige Hilfe aus seinem Erfahrungsschatz als auch für den konstanten Enthusiasmus möchte ich mich auch bei Christoph Garbe bedanken. Danke auch für die
gute Zusammenarbeit im Windkanallabor an Alexandra Herzog, Kerstin Richter und Uwe
Schimpf.
Auch bei den Miniforschern Felix Vogel, Michael Hayn und Peter Ziegenhein will ich
mich für ihre Beiträge bedanken. Die Messung von Felix hat auch Eingang in diese Arbeit
gefunden [Vogel, 2004].
Bei allen betreffenden Kollegen möchte ich mich bedanken für die Korrekturen, vor
allem bei Felix, Roland und Günther, dass sie mich in den arbeitsintensiven Phasen des
Zusammenschreibens unterstützten.
Bei meinen Büromitbewohnern Ronny, Jessica, Laszlo, Christoph und Selami in wechselnder Besetzung möchte ich mich für die Hilfe bei den alltäglichen Verzweiflungen und
Problemen bedanken.
Ein Großteil der finanziellen Unterstützung kam vom Graduiertenkolleg 1114 der
Deutschen Forschungs-Gemeinschaft DFG. Ein Dank auch das Institut für Physikalische Chemie, insbesondere an Pia Heinlein für die Unterstützung bei den FluoreszenzMessungen und an Stefan Hunsmann bei der Messung der Laserleistung. Auch anderen
Mitgliedern des Graduiertenkollegs sei für ihr Engagement gedankt.
Dankend soll auch die Überlassung der ersten Farbstoffproben durch Prof. Dr. Klimant vom Institut für Analytische Chemie der Universität Graz erwähnt werden sowie
die Maquet Cardiopulmonary AG, Hirrlingen, für die Überlassung des ”Jostra Quadrox”
Gasaustauschers.
Ganz wichtig war für mich die Unterstützung durch meine Frau Nicola Falkenroth, die
einige Anspannungen dieser Zeit und viele Ungewissheiten abfedern musste. Gerade im
letzten halben Jahr hat sie mir viel abgenommen. Auch meine Tochter Elisa war wichtig
in dieser Zeit. Sie gibt den Dingen einen zusätzlichen Sinn. Bedanken möchte ich mich
auch bei meinen Eltern.
Danke!
Eidesstattliche Erklärung
Hiermit erkläre ich, dass ich die vorliegende Arbeit selbst verfasst habe und
mich keiner anderen als der ausdrücklich bezeichneten Quellen und Hilfen
bedient habe.
Heidelberg, im Juni 2007
Achim Falkenroth
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