Characterization of the Performance of Bin Blenders Part 2 of 3

Characterization of the Performance of Bin Blenders Part 2 of 3
Characterization of the
Performance of Bin Blenders
Part 2 of 3: Free-Flowing Mixtures
Albert Alexander, Osama Sudah, Paulo Arratia, Chris Goodridge, Laman Alani, and Fernando Muzzio*
In part two of a series of three articles,
mixing rates and mechanisms are examined
using rectangular bin blenders and two freeflowing mixtures.
Figure 1: The three blenders discussed in this article include a
14-L transparent, a 56-L stainless steel, and a 300-L stainless
steel tote-blender (Gallay, Birmingham, UK).
Albert Alexander and Chris
Goodridge are post-doctoral researchers,
and Fernando Muzzio, PhD, is a
professor, all in the Department of Chemical
and Biochemical Engineering at Rutgers
University, 98 Brett Road, Piscataway, NJ
08854, tel. 732.445.3357, fax 732.445.6758, Paulo Arratia is a
post-doctoral researcher at Haverford
College (Haverford, PA), Osama Sudah is
an engineering associate at Merck Research
Laboratories (Rahway, NJ), and Laman
Alani is the executive director at Merck
Research Laboratories (West Point, PA).
Fernando Muzzio, PhD, is also a member of
Pharmaceutical Technology’s editorial
advisory board.
*To whom all correspondence should be addressed.
Pharmaceutical Technology
JULY 2004
art one in this series of articles discussed the general approaches to determining the mixing performance of bin
blenders in terms of sampling methods and tools, variable analysis, and expected effects of common experimental settings (fill percentage, rotation rate, loading method),
followed by an example of a case study and a brief discussion
about the effects of discharge (1). In the second part of this series, mixing rates and mechanisms are examined using rectangular bin blenders and two free-flowing mixtures. Specifically,
the effects of loading conditions, fill level, baffle implementation, rotation rate, and scale-up are addressed for binary mixtures of colored sand and a mixture of granulated acetaminophen with common pharmaceutical excipients.
All of the experiments in this article have been performed in
rectangular bin blenders of various sizes. The three blenders,
of 14-, 56-, and 300-L total capacity, are shown in Figure 1. The
two larger blenders are manufactured by GEA Gallay (Birmingham, UK) and the smallest blender is a custom-made vessel that is run under stepper motor control. The geometry of
these blenders is formed by joining together a pyramidal hopper section and a rectangular bin section. The blenders are symmetrical in design (in a front-to-back and left-to-right sense)
but the rotation axis is offset 30% to the long axis of the blender,
which produces asymmetric flow patterns in the blender (see
Figure 2a). Each of the major dimensions for this blender geometry is identified in Figure 2b and the measured lengths and angles are shown in Table I.
In the two larger blenders, a circular opening is cut into the
top of the blender to enable access to the material within it. In
the 56-L blender, the opening is 11.75 in. in diameter, which enables direct access to 41% of the blender surface area, leaving 59%
of the mixture surface partially accessible (i.e., sampling must be
done on an angle or near the surface). In the 300-L blender, the
opening is 18 in. in diameter, which opens 35% of the surface
area to direct sampling. In the smallest vessel, the entire top is removable, enabling access to the entire mixture surface.
A diamond-shaped baffle is located in the center of each
blender perpendicular to the axis of rotation (identified in Figure 2). The purpose of the baffle is to aid axial mixing by inwww.phar
Figure 2: The rotational axis of Gallay tote-blenders are offset 30% to
the long axis of the blender (a). The various dimensions for this blender
geometry are sketched and labelled in section (b).
Table I: Bin blender dimensions (in.)
H denotes height, W denotes width, D denotes depth, V denotes
valve opening, denotes hopper angle.
Table II: Baffle dimensions (in.)
Baffle w denotes baffle width, Baffle h denotes baffle height,
Blender W denotes blender width, Relative baffle W denotes
relative baffle width.
creasing axial flow as the mixture tumbles in the blender. The
baffle is removable in the two smaller blenders but is permanently attached in the largest blender. The relative size of the
baffle, which can have a significant effect on mixing performance, is identified by comparing the width of the baffle to the
width of the blender, as shown in Table II.
The relative size of the baffle is greater in the 300-L blender,
than in the other two, and as a result the effect of the baffle on
axial mixing rates may also be greater in the 300-L blender. Furthermore, the lack of geometric similarity in baffle size with
increasing blender size may affect mixing performance when
Materials. The following two free-flowing mixtures will be
● Sand mixture: 50/50 w/w % mixture of black and white sand
particles of a similar size (400 m)
● Acetaminophen mixture: 25% by weight granulated acetaminophen (100 m), blended into a matrix of microcrystalline cellulose (Avicel PH102), mannitol, aspartame, and
magnesium stearate (MgSt).
The sand mixture is very free-flowing. The acetaminophen
mixture investigates mixing of a free-flowing active with a moderately free-flowing excipient.
Pharmaceutical Technology
JULY 2004
Sampling tools. For the sand experiments, core samplers were
used to gather samples from the mixture. Core samplers are hollow tubes with one end filed to create a sharp edge to minimize
bed disturbance when thrust into the mixture. Upon retrieval of
the sampler, the contents are extruded in a last-in–first-out manner (1, 2). During initial experimentation, the sand flowed out
of the core samplers when they were removed from the granular bed. Coating the insides of the tubes with a concentrated soap
solution to increase friction between the material and the wall
effectively retained the material within the tube upon the removal
of the sampler from the mixture. Each core was extruded into
5–15 samples of 8 g.
The acetaminophen mixture was sampled using the sidesampling groove thief because the material did not stay in the
core sampler when the sampler was removed from the powder
bed. Coating the samplers with soap solution was not workable
because the quantification method (near-infrared [NIR] spectroscopy) is sensitive to the addition of impurities in the samples, and adding fluid could dissolve some of the sample. The
groove sampler used in these experiments consisted of an outer
hollow sleeve (1 in. in diameter) with an opening running the
length of the pipe (66 in.), surrounding a rotating inner pipe
(1, 3). The sampler was inserted into the powder bed with an
open cavity. The inner tube is rotated to trap a core of material. The sample-bearing thief is placed on a frame and opened,
discharging the material into a series of adjacent trays. The sample size can be roughly varied by using trays of different widths.
In these experiments, the trays were 0.75 in. in width, which resulted in 4–8 samples of 1.6–2.1 g.
The sand mixtures were characterized using a gray-scale image
analysis technique developed by Wightman et al. to quantify
the component concentrations in binary mixtures of contrasting colors (4). For the mixture of black and white sand, each
collected sample was spread in a circular dish 2.25-in. in diameter. Under controlled lighting conditions, a picture of the
sample was taken using a digital camera. The resulting image
was then processed using Scion Image Software (Scion Corporation, Frederick, MD, and the National Institutes of Health,
Bethesda, MD) to give the mean gray-scale value of the sample. Using a calibration curve of known component concentration standards, the mean gray-scale value of each sample was
converted to concentration data.
Acetaminophen concentration in the powder experiments
was quantified using NIR spectroscopy. Two primary advantages of NIR spectroscopy are its nondestructive, nonintrusive
nature, which enables the acquisition of a spectra of solid samples with minimal or no pretreatment, and its relatively fast rate
of analysis, scanning each sample in 30 s. Both calibration
and experimental samples were placed in scintillation vials
(Fisher brand, 20-mL in volume, 1.5-cm in diameter, and 6-cm
in height) that were suitable for NIR analysis. The NIR spectrometer produces radiation that penetrates 4 mm into a powder sample before becoming too attenuated to produce a useful signal. Consequently, the size of a sample was selected to
produce a 4-mm height, resulting in a sample size of 2 g.
Figure 3: The two extreme initial condition possibilities are sketched.
Figure 3 (a) shows top-to-bottom and left-to-right loadings, which
emphasize radial and axial mixing, respectively (rotation is into the
page). The evolution of RSD is compared for these extreme loading
conditions in (b), showing that radial mixing is an order of magnitude
faster than axial mixing.
A rapid content analyzer manufactured by FOSS NIRSystems, Inc. (Silver Spring, MD) collected the NIR data, and the
company’s software (VISION 2.10) was used to evaluate the
data using a variety of mathematical treatment options. Descriptions of selected sampling of the use of NIR to identify
pharmaceutical ingredients are available (5, 6). Typically, the
spectrum of an unknown sample is analyzed with a model equation derived from a set of calibration samples of known concentrations. In this study, both the calibration and experimental NIR spectra were conditioned using the second derivative
and partial least square treatments over the entire spectrum
(1140–1830 nm). Good agreement was found between actual and
predicted values (3% error) and NIR was deemed suitable for
quantifying acetaminophen concentrations for this system.
Loading conditions. Probably the most important factor affecting mixing rates in tumbling blenders is the method by which
materials are loaded into the blender. Without a preblending
step, loading the blender results in an initial unmixed condition of the various components. For practical purposes, there
are only two extreme outcomes from blender loading: top-tobottom or left-to-right initial distributions. The two extreme
examples of completely segregated initial configurations within
a bin blender are sketched in Figure 3a. The difference in mixing rates that arose from these two initial conditions was quantified by comparing the evolution of mixture relative standard
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than axial mixing. The mixing constant, k, was defined
in Part 1 of this series of articles as the slope of the
lined formed by plotting ln
(RSD) versus revolutions
(1). For these experiments,
k was 0.253 for top-to-bottom loading and 0.011 for
left-to-right loading, which
quantifies the radial mixing
in a 56-L vessel as more than
20 times faster than axial
mixing for this free-flowing
mixture. Even though radial
mixing was very fast, there
will always be some degree
of axial variance (especially
because the initial conditions are not perfectly radially symmetrical) and axial
mixing will always control
asymptotic homogenization
(1). The order of magnitude
difference in the mixing rate
between the above cases underscores the importance of
loading conditions. Accidentally loading the blender
with left-to-right asymmetry can have significant consequences on mixture quality if the mixing protocol
assumed top-to-bottom
Figure 4: The effects of changing the fill percent in the
loading had occurred.
blender are shown for a 56-L blender loaded from top-toFill level. In previous studbottom with the acetaminophen mixture (a) and the sand
ies, the fill level of the
mixture (b). Results from left-to-right loading with the sand
blender has been shown to
mixture are shown in (c).
have a measurable effect on
the mixing rates of freedeviation, or RSD (RSD /M, in which flowing materials (7, 8). Increasing the fill
is standard deviation and M is the av- level decreases the relative amounts of maerage values of the samples used to gen- terial in the flowing region (the volume of
erate ). Changing the loading condition the flowing region does not significantly
has the effect of accentuating either radial change with variations in fill level). All
mixing (perpendicular to the axis of ro- mixing action must take place in the flowtation) for top-to-bottom loading, or axial ing region; therefore, decreasing the relamixing (parallel to the axis of rotation) tive size of the flowing region decreases
for left-to-right loading.
mixing rates. Also, at higher fill levels, each
The results from blending the sand mix- particle spends less time in the cascading
ture for top-to-bottom and left-to-right region during each blender revolution and
loading conditions in a 56-L bin blender dead zones can form. For the 56-L bin
at 60% fill without a baffle are shown in blender, with the baffle in place and using
Figure 3b. RSD decreases much faster in the
the top-to-bottom loaded experiment than acetaminophen mixture, the evolution of
in the left-to-right loaded experiment, in- top-to-bottom loaded experiments at
dicating that radial mixing is much faster 40%, 60%, and 80% fill is shown in Fig62
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JULY 2004
ure 4a. For top-to-bottom loading, there
was a notable difference in the early (20
revolutions) variance decay but all experiments reached an asymptotic variance
value near 32 revolutions, beyond which
there was little difference in mixture variance for the three fill levels. The mixing
rate was much slower at 80% fill but the
difference in mixture quality at different
fill levels was erased within 30 revolutions.
Furthermore, it is apparent that dead
zones did not form for the 80% case because RSD reached comparable levels at
128 revolutions. Also, the slower mixing
at 80% fill was still fast compared to typical blender mixing times (order 100–200
revolutions) such that the difference in
mixing rates does not have severe consequences on blender performance.
Similar results are noted for the sand
mixture when mixed in the 56-L blender
at 20%, 40%, 60%, and 80% fill with the
baffle (Figure 4b). For all fill levels below
80%, RSD dropped to a value near 5% in
16 revolutions and did not vary significantly
at 32 revolutions. In agreement with the
data from the acetaminophen mixture, the
mixing rate was considerably slower at 80%
fill but it appears that a similar RSD would
be achieved near 50 revolutions. Hence,
it appears that the change in mixing rates
at 80% fill will not be important when compared to typical mixing times for either of
these free-flowing mixtures (nor do dead
zones appear to form at 80% fill for either
mixture). For fill levels below 80%, the RSD
at 32 revolutions showed a gradation: the
60% fill case is less homogeneous than at
40% fill which is less homogeneous than a
system with 20% fill. These variations in
RSD likely arose because the two components in this sand mixture contained slightly
different size distributions and, hence,
showed a slight tendency to segregate rather
than mix perfectly.
The mixing rate was faster at 40% than
at 60%, which is in agreement with the acetaminophen data; however, the 20% results were slower than the 40% results,
which is a curious result. In principle, the
mixing rate at 20% should be faster than
at 40%, however, the sand mixture
slumped (i.e., there was slip at the vessel–
mixture interface) when loaded at 20%.
Slumping affects the amount of time it
takes for the mixture to “turn over” and
interferes with the basic striation-forming
Figure 5: (a) Probability density function (pdf) of axial velocities from DEM simulations when the blender is in
the upright position; a vertical red line is shown at 0. The orientation of the blender is shown from the side in (b).
mechanism that determines radial mixing rates (9). Mixture
turnover is defined as the time it takes for an individual particle to return to near its original position. Changes in fill level
have significant effects on turnover time; at low fill levels, the
mixture can undergo more turnovers/blender revolution than
at higher fill levels. These differences in turnovers/revolution indicate that variations in mixing performance with changes in
fill level do not necessarily reflect an increase in mixing efficiency
but may simply be an increase in mixing time. The true mixing
Figure 6: Sketch of the flow patterns
within the tote-blender. The mixture
travels down the cascade and then hits on
a slanted wall, which imparts axial flow to
the left in this configuration.
time scale for radial mixing is mixture turnover, not blender
For the left-to-right loaded case, there is no difference in the
observed mixing rates at 40% and 60% fill for the sand mixture
(see Figure 4c). This result is peculiar because if the major mechanism for axial mixing is dispersion, then the fill level should
have an effect on mixing rates. Higher fill levels cause the mixture to turn over fewer times than lower fill levels do for the
same number of revolutions and obviously involve larger
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JULY 2004
amounts of material, requiring more particle movement to reach
an equivalently mixed state. Because 40% and 60% mix at nearly
identical rates, the implication is that dispersion is not the only
mechanism at work.
Previous studies have demonstrated that axial mixing rates
were affected by changes in fill percentage for experiments done
in V-blenders and double cones (7, 8). Those blenders are symmetrical with respect to the plane bisecting the vessel perpendicular to the axis of rotation. This bin blender is rotated on an
axis 30 offset to the long axis of the blender, which induces an
asymmetrical flow topology during each complete blender revolution. The mixture within the blender flows into angled walls
(i.e., the walls are not perpendicular to the dominant flow direction) that impart axial velocity gradients to the mixture. Furthermore, the blender also is asymmetrical in a top-to-bottom
fashion and the flow patterns that evolve as the mixture flows
into and out of the hopper and the bin section are markedly
different, which has an effect on axial mixing. Axial mixing rates
are not likely to be affected by fill level in these bin blenders because the presence of geometrically induced axial flow effectively
causes convective axial mixing that exceeds dispersive mixing (10).
Computer simulations using the discrete elemental method
(DEM) allow for the study of axial flow gradients (1). The effects of blender geometry on particle velocities are investigated
by extracting the average axial velocity (i.e., parallel to the axis
of rotation) of all free-flowing particles at specific instances
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during a blender revolution. If dispersion is the dominant mode
of axial displacement, then the average axial velocity should be
0. A probability density function (pdf) of axial velocities when
the blender is in the upright position (as in Figure 1) is shown
in Figure 5a. At this orientation, the average axial velocity is
0.0083 cm/s in the positive direction (to the right), which is
2.7% of the average downstream velocity in the cascade (0.3
cm/s). This small but significant axial flow indicates that blender
geometry is inducing axial flow in a specific direction. The average axial velocity is shown in Table III for subsequent blender
positions, using 0 as the upright state.
The velocities in Table III indicate that axial flow in the bin
blender changes direction from right-to-left and back as the
blender undergoes one complete revolution. Axial flows develop
because the mixture in the blender does not flow in a geometrically symmetrical environment. In the upright position, the
mixture flows towards a wall that is sloped to the right, which
causes the entire mixture to flow to the right. Similarly, in the
inverted position, flow is toward a leftward slanting wall, causing a flow to the left (see Figure 6).
More-diverse flow patterns occur when the mixture is flowing into or out of the hopper section. As the mixture flows from
the hopper section into the bin section, particles on either side
of the mixture diverge as the bin section is filled. Simulations
capture this flow. At 1⁄4 turn, average axial velocities in the left
half of the blender are 0.0028 cm/s while in the right half av-
Table III: Average axial velocity at
specific blender orientations.
Average axial velocity
decrease in RSD that results from top-tobottom (Figure 7a) and left-to-right loaded
(Figure 7b) experiments with the sand mixture when the 56-L blender is run with and
without a baffle. For top-to-bottom loading, there is virtually no effect coming from
the presence of the baffle because axial mixing is not a mixing-limiting step for that
initial condition. However, when loaded
left-to-right, there is a modest increase in
the mixing rate resulting from the presence
of the baffle: the mixing constant increases
by a factor of 1.6 (0.0106 to 0.0165). The
modest increase in mixing rate with baffle
addition is far less than the order of magnitude improvements seen in work using
1-gal double-cone blenders and a different
type of baffle (8). However, the effects of
baffle use must be examined by comparing
baffle geometry, size, and location in the ex-
erage axial velocities are 0.019 cm/s. Particles in the left half are moving leftward
and in the right half are moving rightward,
and thus particles are diverging. The converse situation arises when the mixture
flows from the bin section into the hopper section. At 13⁄16 turn, average axial flow
in left half is 0.0053 cm/s and in the right
half is 0.014 cm/s indicating that particles are converging. Similar flow patterns
have been shown to lead to the formation
of segregation patterns in double-cone
blenders (11) and similar segregation patterns form in bin blenders (1). The aggregate effect of these leftward, rightward,
converging, and diverging flows is to induce axial flow in many directions as the
mixture tumbles in the blender. Because
the mixture does not turn over at the same
frequency as the blender rotates, different
portions of the mixture come into contact with all of these diverse flows. Thus,
mixing efficiency is maximized because
different portions of the mixture come
into contact with these different velocity
Baffle use
In many tumbling blenders, a baffle can
be installed in the vessel as a means of improving blending performance. The efficacy of these inserts has not been quantified but it is commonly believed that any
disruption of normal, regular flow patterns should have beneficial effects on
mixing rates. In this rectangular bin
blender, the baffle is diamond-shaped and
located in the center of the vessel, perpendicular to the axis of rotation (shown in Figure 2). The intended effect is to improve
axial mixing by increasing the amount of
axial displacement. Figure 7 compares the
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JULY 2004
Figure 7: The effects of a diamond-shaped baffle located in
the center of the blender are shown for top-to-bottom (a) and
left-to-right (b) loadings in the 56-L blender.
angle to the axis of rotation
in the middle of the blender.
In these double-cone experiments (with free-flowing
glass beads), the axial mixing
rate was improved by a factor of 20 when the baffle was
placed in the blender, compared to the nonbaffle condition. However, the blender
was only 24.5 cm in diameter, which means that the baffle was almost half the width
of the blender. Also, the baffle was not attached to the
blender shell and did not rotate, hence the baffle was
nearly perpendicular to the
flowing region at all times.
Clearly, this large nonrotating insert in the middle of the
blender will have an enormous impact on flow patterns and the resultant mixing rates. In comparison, the
baffles in the bin blenders
were much narrower relative
to blender width (11–20%,
see Table II) and would be
expected to have a lesser impact on flow patterns and
mixing rates.
Rotation rate
Another important factor
regarding the performance
of tumbling blenders is the
effect of rotation rate on
mixing rates. Clearly, very
slow (0.1 rpm) or very fast
Figure 8: The rotation rate of the blender has no effect on the
75 rpm) rotation rates
evolution of RSD for left-to-right loaded experiments at 60%
have large effects on mixing
fill in the 56-L blender.
because the mode of granular flow changes from being
periments because the effects of baffle use characterized by discrete avalanches to
are closely tied to these variables. Simply cataracting flow (i.e., as portions of the
adding a “baffle” of unspecified design and mixture become airborne) (12). However,
location is no guarantee of improved the operating range of commercial
blender performance.
blenders lies in an interval far from both
Comparing baffle effects in this bin of these two extreme flow conditions and
blender to those observed in a 1-gal capac- within a range of rotation rates for which
ity double-cone blender illustrates how re- flow characteristics are qualitatively very
sults from baffle use must be viewed in the similar (i.e., the rolling regime). This raises
context of baffle geometry and operating the question of whether mixing is affected
principle. The baffle in the double-cone by changes in rotation rate in the rolling
blender was a rectangular plexiglass sheet, regime.
12.5 cm 10 cm, that was placed at a 45
Previous work has indicated that RPM
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does not affect mixing rates for top-tobottom loading in double cones or rotating cylinders (7, 8) and has been shown
to hold true for bin blenders (13) because
the mechanism for radial mixing is the
same (iterative striation formation, 9). For
left-to-right loading, there was also no
RPM effect noted for double cones or
V-blenders (7, 8). However, because axial
mixing in bin blenders involves convection (axial mixing in the other blenders is
driven by dispersion), the effects of RPM
on left-to-right loading for free-flowing
mixtures may not be similar to other tumbling blenders. Therefore, only the effects
of rotation rate on axial mixing rates are
reported here for the bin blender. The results of experiments run at 6, 10, and 14
rpm are shown for experiments using the
sand mixture in the 56-L bin blender
loaded from left-to-right in Figure 8. Once
again, there is no difference in the mixing
rates. This result indicates that particle velocities do not affect axial mixing rates,
which signifies that convective and dispersive flow is not affected in a mixing
sense for free-flowing mixtures by rotation
rates or particle velocities.
The design of new batch manufacturing
processes often involves increasing the size
of the process equipment on progression
from lab- to pilot- to full-scale production equipment. The scale-up of mixing
rates in tumbling blenders remains dependent on heuristics and experience
rather than solid fundamental reasoning
backed by mechanistic explanations and
experimental testing. The results from experiments in 14-, 56-, and 300-L bin
blenders using the sand mixture loaded
from both top-to-bottom and left-to-right
at 60% fill are shown in Figure 9. For topto-bottom loading, there is virtually no
difference in the mixing rate among the
three blenders (covering a 20-fold increase in blender capacity). These results
indicate that blender performance for freeflowing mixtures and top-to-bottom loading conditions are nearly impervious to
changes in blender size, making the radial
mixing process scale-independent. While
the rate of mixing is nearly the same, the
asymptotic RSD increases with increasing
blender size (similar trends were seen with
increasing fill %, although not as stark).
spectively. Although a direct
relationship between blender
size and axial mixing rate
does not exist, there is probably a strong, although currently unknown, connection
between the two. Another
factor may be the relative
volume of the flowing mass
to the total volume of the
mixture. In this system the
surface area of the mixture
when the blender is upright
is 99 in.2 and 270 in.2 respectively for the 14-L and
56-L blenders. If we assume
that the flowing layer is constant in depth for both systems (which may or may not
be reasonable), then the ratio
of the flowing mass to the
total volume is 0.116 and
0.079 for the smaller and
Figure 9: The effect of changing the size of the blender is
larger blenders, respectively.
shown for top-to-bottom (a) and left-to-right (b) loading
Thus, there may be relatively
more mass in motion in the
smaller blender, which could
This gradation in asymptotic RSD could also be a factor affecting the axial mixing
be caused by segregation of the mixture rate. These results indicate that scaling rules
(the particle size range of the two batches are very dependent on the loading condiof colored sand were slightly different) or tions in the blender and that ensuring conby dispersive limitation. The differences sistency in the loading method and initial
in asymptotic RSD will subsist with fur- conditions may be much more important
ther revolutions if segregation is the cause to the overall scale-up of the process than
but will disappear if dispersive limitation changes in vessel particulars such as fill
level, blender size, or rotation rate.
is the cause.
Although radial mixing rates are independent of scale, the axial mixing rate, as Conclusion
seen by examining left-to-right loaded ex- Generally, free-flowing materials are wellperiments, does depend on blender size behaved and mixing results can be read(Figure 9b). For a change from 14 L to 56 ily explained and quantified. Radial mixL, there is a decrease in the axial mixing rate ing (which is stressed by top-to-bottom
by a factor of 2 (the mixing constant de- loading) is more than an order of magnicreased from 0.0203 to 0.0106). Although tude faster than axial mixing (emphasized
axial mixing is not completely dependent by left-to-right loading). Adding more maon dispersion, axial mixing rates are still terial into a blender (i.e., increasing the
very slow in comparison to radial mixing fill level) decreased radial mixing rates,
rates. Because a single particle does not de- but as long as dead zones did not form
viate axially by more than a few particle di- (which is typical for fill levels 60% and
ameters during a single pass down the cas- apparently true up through 80% fill for
cade, the width of the blender plays a large the mixtures tested here), the change in
role in the axial mixing rate in the blender. mixing rate would not have catastrophic
A direct relationship between blender width effects on mixture quality for typical mixand axial mixing rates does not exist. The ing times. The highest permissible fill level
blenders are 18 in. and 11 in. in width, re- that does not cause dead zones to form is
spectively, resulting in blender-width:mix- unclear and is likely dependent on both
ing-constant) ratios of 890 and 1040, re- blender geometry and mixture character-
istics. The fill level had no effect on axial
mixing rates (up through 60% fill) in the
asymmetrical bin blender because axial
mixing rates are controlled by convective
flow, not dispersive flow. The axial velocities imposed by rotating the blender on
a skewed axis increased the amount of
axial mixing by imposing axial flow gradients on the mixture. This result is noteworthy because fill level does affect axial
mixing rates in symmetrical blenders that
rely on dispersion for axial mixing.
The addition of relatively small baffle
(10–20% of the total blender width) had
no effect on radial mixing and a marginal
effect on axial mixing, with mixing rates
increased by a factor of 1.6. We remind
the reader that this baffle is not optimally
designed or located to aid in increasing
axial mixing rates. Similar to results seen
in previous work on other tumbling
blenders, the rotation rate had no effect
on mixing efficiency in this study. When
free-flowing materials are mixed in
blenders of increasing size, the loading
method plays a decisive role in determining the scale-up approach. For top-tobottom loading, there is little or no apparent difference in the mixing rates, but
for left-to-right loading, the width of the
blender plays an important role in determining the overall mixing rate. Using typical scaling criteria such as tangential velocity or the Froude number is irrelevant
as the rotation rate has no effect on mixing rate.
These results are compared and contrasted with similar experiments using cohesive materials in part three of this series
of articles. The effects of various experimental parameters on agglomerate comminution and lubrication processes are
also discussed.
1. A. Alexander et al., “Characterization of the
Performance of Bin Blenders, Part 1 of 3:
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