High Speed Microfluidic Doublet Flow in Open Pools Driven by Non

High Speed Microfluidic Doublet Flow in Open Pools Driven by Non
Amar S. Basu 1, and Yogesh B. Gianchandani
Department of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, USA
We report a phenomenon in which a micromachined
heat source placed less than 50 µm above the surface of a
liquid drives a high-speed doublet flow pattern with linear
velocities reaching nearly 5 mm/sec and rotational velocities
up to 1200 rpm. Tests were performed on a 50-100 µmthick layer of water containing 3 µm polystyrene beads for
flow visualization. The thermal source is a polyimide
cantilever with an integrated heater near the tip, operated
with input powers ranging from 0-32 mW. It has no moving
parts and does not contact the liquid. The speed of the
doublet flow scales with input power as well as liquid
temperature, and is inversely related to the air gap between
the heater and liquid surface. The orientation of the doublet
flow can be reversed by changing the angle of the cantilever.
A one-dimensional array of probes used in the same manner
generates a linear flow pattern.
The ability to generate high speed micro-flow patterns
plays a critical role in the mixing, pumping, and preconcentration of particles, particularly for cellular and
biomolecular manipulations. There have been several
attempts in the past to generate vortex flow in microfluidic
An opto-electrostatically driven vortex
pattern generated by a focused 50 mW laser spot in
combination with a 2 kV/cm electric field was shown to
have a maximum particle velocity of 120 µm/sec in
conductive liquids [1]. Vortices driven electrokinetically in
polymer channels with patterned surface charges [2] operate
on less electric field (100 V/cm), but produce slower
velocities and require ionic solutions. More recently, a laser
cavitation pump was shown to generate flows up to 1 mm/s
[3]. It required that an optical fiber to be immersed in the
liquid and coupled to a high-power pulsed laser. Bubbles
generated in cavitation pumps can pose challenges for a
variety of applications. Approaches using moving parts
include a 600 rpm magnetic micro-stirrer [4].
This effort reports a thermally driven phenomenon in
which a micro-scale heat source suspended above water
drives a high-speed doublet flow patterns at the liquid
surface. Particle velocities of 5 mm/sec and rotational
velocities of up to 1200 rpm have been achieved, making it
potentially useful for high speed pumping and mixing of
liquids and suspended particles.
The heat source, a
micromachined thermal probe, is separated from the liquid
surface by a small air gap and has no moving parts, thus
Air Gap
Liquid Reservoir
Fig 1: Schematic of device operation. A heated micro-cantilever
suspended above a liquid induces a high-speed doublet flow
pattern at the surface.
eliminating common problems of mechanical wear,
Furthermore, the technique does not require ionic or
conductive liquids. In addition to generating single doublet
flow patterns, a linear array of probes is shown to generate a
linear channel-like flow pattern that would be useful for
pumping applications.
A fluidic doublet is a two-dimensional flow
characterized by two adjacent vortices of opposing rotational
directions, and resulting linear streamlines between them.
The flow pattern for a single doublet located at (x0 , y0) on a
Cartesian plane is described by the following stream
function [5]:
( x, y ) =
( y y0 )
2 ( x x 0 ) 2 + ( y y 0 ) 2
where µ is a constant reflecting the strength of the doublet.
A contour plot (Fig. 2a) illustrates the streamlines resulting
from a single doublet. The direction of flow can be inferred
from the gradient of the function, which in this case is left
to right.
To determine more complex flow patterns resulting
from multiple doublets, the stream equations for each
doublet may be added up by applying the principle of
superposition. The flow pattern generated by an array of 8
doublets with 85 µm spacing is shown in Fig. 2b. This
particular geometry was chosen to model the structure of the
multiprobe array. Flow patterns resulting from single and
multiple doublets present a number of opportunities for flow
manipulation; namely, the linear streamlines can be used to
drive high speed particle flow, while the adjacent eddies can
be used for mixing or particle trapping.
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y ( m)
x ( m)
y ( m)
x ( m)
Fig. 2: Theoretical flow patterns generated by single and multiple
doublets. (a) Streamlines for a single doublet located at (200 µm,
150 µm) on a Cartesian plane. The contours of the stream function
(Eq. 1) were plotted using a value of 1 for the constant µ. (b)
Streamlines generated by an array of 8 doublets with 85 µm
spacing obtained by summing the respective stream functions.
In this effort, high-speed doublet flow at the surface of
water is driven by a micromachined heat source suspended
at varying heights and angles above the surface of a
reservoir (Fig. 1). When the source is brought close to the
surface of the water (<50 µm), the thin air gap allows
transfer of heat to the liquid surface. The mechanism of how
the heated region drives the doublet flow is not yet clear;
however, initial data suggests that localized evaporation
plays a role.
The heat source is a micromachined thermal probe
reported in [6], consisting of a joule heater integrated near
the tip of a cantilever. Thin film metal forming the heater
and leads are embedded within a 3 µm-thick polyimide
cantilever. The excellent thermal isolation provided by a
polymer-based cantilever allows the probe tips to be heated
to temperatures up to 250 ºC with <20 mW input power.
The length and width of the cantilever as well as probe
resistance vary depending on the type of probe. In this
work, two probe geometries are used: R01 (length 360 µm,
width 42 µm, resistance 25-40 ), and R02 (length 360 µm,
width 120 µm, resistance 20-35 ). In addition to the single
R2 = 0.971
Particle Velocity
( m/sec)
Probe: RO2 (25
Gap: 25 m
Angle: 15
Input Power (mW)
Fig. 3: (a) High-speed flow is illustrated in 4 sequential
micrographs taken at 1/30 second intervals. 3 µm beads are used
to visualize the flow. (e) Particle velocities scale linearly with the
input power to the heat source. Angle and air gap are fixed at 25
µm and 15°.
probes, an 8-probe array reported in [7] is also used to drive
multi-doublet flow patterns as shown in Fig. 2. In this
device, the cantilevers have 85 µm pitch and can be heated
Experiments were carried out on a 50-150 µm thick
layer of water placed on a glass slide. Polystyrene beads
with 3 µm diameter were immersed in the liquid for flow
visualization. The micromachined cantilever was held at a
fixed angle and lowered towards the surface of the liquid
using a motorized micromanipulator. Micrographs and
video were recorded using a CCD camera, and speed was
determined by measuring distance covered by sequential
frames spaced 1/30 second apart. In accordance with
doublet flow model, the velocity of a traveling particle
increases as it approaches the center of the doublet, which in
this case appears to be directly beneath the heated cantilever
tip. In all experiments, the velocities indicated are the
maximum values measured.
In order to show that the doublet flow is in fact
thermally driven, the flow and rotational velocities were
characterized as a function of input power (Fig. 3). The
cantilever was held at a fixed angle and air gap above the
liquid surface, and the input power was ramped from 0-32
Particle velocities scale approximately linearly,
Angular Velocity
Particle Velocity
( m/sec)
Particle Velocity
( m/sec)
2000 Probe: RO2 (35 )
1000 Power: 15.4 mW
Angle: 15
Air gap ( m)
Probe: RO2 (35 )
Power: 15.4 mW
Angle: 15
Air gap ( m)
Fig. 4: The doublet speed can be controlled by modulating the air
gap. For a fixed 15 mW input power to a 35 ohm probe, particle
velocities increase nearly 5000 µm/sec as the air gap is reduced to
<10 µm. Rotational rates in the adjacent vortices approach 1300
increasing 90 µm/sec for every 1 mW applied. These results
imply that the flow is proportional to tip temperature, since it
is well known that tip temperature increases linearly with
input power [6].
Reduction of the air gap permits more efficient heat
transfer, also resulting in increased velocities. A probe was
biased at a fixed input power and lowered at 10 µm intervals
until it came into contact with the liquid. Figure 4 shows
that with a 15 mW input power, particle velocities of nearly
5000 µm/sec are achieved at air gaps of <10 µm, along with
rotational velocities of 1200 rpm in the adjacent eddies.
Particle velocities decrease as 1/x with increasing air gap,
indicating that heat transmission through the gap is inversely
proportional to the gap thickness.
The dependence of particle velocities on liquid
temperature (Fig. 5) provides further evidence supporting
thermally driven flow. In this experiment, the glass slide
below the water sample was biased at 13, 27, and 41 °C
using a circulating heating/cooling plate.
At each
temperature, particle velocities were measured as a function
of air gap while holding the probe at constant power and
angle. Trends of faster velocities with smaller air gaps hold
true as before, but it can also be seen that higher liquid
temperatures shift the entire trend upwards. For example, at
a ~10 µm air gap, the particle velocity at 13 ºC is only 165
µm/sec, compared to nearly 900 µm/sec at 41 ºC. Increased
liquid temperatures, therefore, enhance the speed of doublet
flow. Overall, particle velocities in this experiment were
slower than the results shown in Fig. 4 due to lower input
powers, and possibly due to the fact that a thinner probe
(R01) was used.
Probe: R01 (27 )
Power: 10.4 mW
Angle: 30
41 C
27 C
13 C
Air gap ( m)
Fig. 5: Effect of liquid temperature on doublet flow. Particle
velocities are plotted as a function of air gap while biasing the
glass slide at 3 different temperatures.
Increased liquid
temperatures and reduced air gaps enhance the speed of the
doublet flow. A 27 ohm probe fixed at 30° angle and 10.4 mW
input power was used in this experiment.
The geometry of the heat source plays a significant role
in the doublet pattern. For example, a probe (R02)
suspended at a 15° angle with respect to the liquid plane
results in doublet flow from left to right; however, when the
probe angle is doubled to 30° (keeping all other parameters
constant), the direction of flow is reversed, and the location
of the adjacent vortices shifts to the left as shown in Fig. 6.
The flow can also be manipulated into a linear channellike pattern by generating multiple doublets with arrayed
heat sources. The 8-probe array was biased at 2.3V,
dissipating 92 mW total power in six probes (probes 1 and 4
were nonfunctional). The resulting flow pattern (Fig. 7) has
a linear flow region with adjacent rotational regions as
predicted by simulations (Fig. 2b). Distortions in flow are
observed in several regions, such as the trajectory marked
with a triangle, and can be attributed to the difference in air
gap between the various probes in the array in addition to the
fact that two probes were not operational. The noticeably
smaller velocities (190 µm/sec) compared to single probes
may be attributed to the reduced temperatues of the heaters
in the multiprobe array. These results illustrate that flow is
Fig. 6: The direction of the flow can be reversed by changing the
angle of the heater. For example, using probe R02 at a 15° tilt, 15
mW input power, and a ~15 µm air gap, the doublet flows left to
right, and the rotation in the vortices is counter-clockwise (a).
Increasing the angle to 30° while keeping all other parameters
constant reverses the direction of the flow and rotation and shifts
the location of the vortices to the left of the cantilever (b).
Fig 7: Linear flow generation using an 8-probe array, numbered 18 from the top down. The array was placed ~15-20 µm above the
liquid surface, held at a 15° tilt, and biased with a total power of 92
mW. Probes 1 and 4 were nonfunctional. Trajectories for 3
particles are marked with a square, triangle, and circle on
micrographs taken at 3 second intervals.
highly dependent on the geometry of the heat transmitted to
the liquid surface. Therefore, it is possible to obtain custom
flow patterns by arranging the heat sources in various
Subsurface particle flow, visualized by focusing the
microscope at the bottom of an 80 µm thick layer of water,
differs significantly from the doublet flow patterns observed
at the surface. Particles flow radially inward over time,
converging on a point directly below the tip of the
cantilever. Once at this point, the particles are accelerated
upwards towards the surface of the liquid film (Fig. 8). The
column of vertically-directed current may be due to
convection and/or localized evaporation driven by the high
liquid temperatures beneath the probe tip. Further modeling
and experimentation is needed to clarify the mechanism
driving both the surface and subsurface flow patterns
In summary, we have shown that high speed doublet
flow can be thermally generated by a micromachined heat
source operating without contact to the liquid, and a linear
flow profile can be achieved using by arraying the heat
sources. Characterization of the flow patterns indicate that it
is thermally driven by heat transmitted through the thin air
gap. The high-speed particle velocities and rotational
velocities have potential applications in pumping and
Partial support for this effort was provided by The
Whitaker Foundation (AB). The authors also acknowledge
Dr. Shamus McNamara for his assistance in probe
Fig 8: (a) Schematic of subsurface particle flow (80 µm below the
surface). Particles flow radially inward towards the area underneath
the microheater tip. Upon reaching this point, they are immediately
propelled upwards to the surface. (b) Sequential micrographs show
the particles (marked with a square, triangle, and circle) converge
towards the center and then disappear from the field of view as they
are propelled upwards.
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