Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 8.7.1 - Direct measurement of shear-induced migration in microchannels
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 Material Information
Title: 8.7.1 - Direct measurement of shear-induced migration in microchannels Colloidal and Suspension Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Gilchrist, J.F.
Gao, C.
Xu, B.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: suspension
shear migration
mixing
microrheology
particle tracking
 Notes
Abstract: Many non-Newtonian properties of concentrated suspensions, including shear thinning, normal stress, and shear migration, are attributed to the evolution of structural anisotropy. Investigations of this anisotropy have largely been conducted using simulations such as Stokesian Dynamics and indirect measurement via scattering. Using high speed confocal laser scanning microscopy, we directly investigate the local structure via particle tracking after structural evolution in a pressure driven flow ranging from Péclet number (the ratio of convective to diffusive forces) of 0 < Pe < 2000 over bulk volume fractions 0.2 =  = 0.4. Due to the shear gradient, a single experiment allows both sampling over a range of Péclet numbers and concentrations that vary due to shear migration. Clear structural anisotropy similar to that demonstrated by simulations of Foss and Brady, 2000 and Morris and Katyal, 2002 show strong deviations from homogeneity in radial distribution profiles at high Péclet number and high volume fraction. Moreover, in regions of low Pe located in the center of the pressure driven flow, signatures of colloidal crystallization driven by the high concentration that results from the normal forces generated this anisotropy are apparent.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00212
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Resource Identifier: 871-Gilchrist-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Direct Measurement of Shear-Induced Migration in Microchannels


J. F. Gilchrist, C. Gao, and B. Xu

Lehigh University, Department of Chemical Engineering,
111 Research Dr., Bethlehem, PA 18015, USA,
gilchrist @lehigh.edu


Keywords: suspension, shear migration, mixing, microrheology, particle tracking




Abstract

Many non-Newtonian properties of concentrated suspensions, including shear thinning, normal stress, and shear migration, are
attributed to the evolution of structural anisotropy. Investigations of this anisotropy have largely been conducted using
simulations such as Stokesian Dynamics and indirect measurement via scattering. Using high speed confocal laser scanning
microscopy, we directly investigate the local structure via particle tracking after structural evolution in a pressure driven flow
ranging from P6clet number (the ratio of convective to diffusive forces) of 0 < Pe < 2000 over bulk volume fractions 0.2 = ( =
0.4. Due to the shear gradient, a single experiment allows both sampling over a range of P6clet numbers and concentrations
that vary due to shear migration. Clear structural anisotropy similar to that demonstrated by simulations of Foss and Brady,
2000 and Morris and Katyal, 2002 show strong deviations from homogeneity in radial distribution profiles at high P6clet
number and high volume fraction. Moreover, in regions of low Pe located in the center of the pressure driven flow, signatures
of colloidal crystallization driven by the high concentration that results from the normal forces generated this anisotropy are
apparent.


Introduction

Shearing suspensions of moderate to high particle volume
fractions has long been known to generate normal stresses.
This force primarily acts orthogonal to the direction of flow
and in the direction of shear gradient, and is generally
believed to be a result of multi-particle hydrodynamic
interactions. The isotropic normal stresses can be interpreted
as the tendency to dilate under deformation. In a fixed
volume, though the dilation does not occur, normal stresses
are measurable. Rheological measurements of these normal
stresses are challenging because the normal stresses are
small until jamming occurs at high solids volume fractions.
However recent macroscopic measurements in Couette flow
have successfully measured the effective osmotic pressure
due to the particle phase dilation in sheared suspensions
(Deboeuf et al., 2009). In the presence of nonlinear shear
fields, these normal stresses cause particles to migrate (Koh
et al., 1994) and the suspension de-mixes. The development
of constitutive equations to generally describe this behavior
has been slow due to the fact that these normal stresses are
the result of previously unmeasured structural anisotropies.
Detailed 3D particle-level information is necessary in order
to identify local structures. The development of a
fundamental understanding of these multi-particle
hydrodynamic interactions will influence suspension
process designs for mixing, separations, and transport, and
will facilitate a deeper understanding of natural processes
including sediment transport and blood flow.

Brownian and non-Brownian systems ranging in volume
fraction 0.3 < 4 < 0.5 have been studied extensively through


theory, simulations, and experiments looking at the effects
of shear-induced microstructural anisotropies on the
development of normal stresses. Both SD simulations (Foss
& Brady, 2000; Morris & Katyal, 2002) and dissipative
particle dynamics (DPD) (Pan et al., 2009) predict a higher
correlation of nearest neighbor interactions along the
compressive axes of the flow in the v-Vv projection of pair
distribution function, g(r). Pair-distribution functions
generated by SD simulation as a function of P6clet number
(Pe = 67a3Ty/kT) show anisotropy at high Pe. These
dynamics develop quickly with the onset of flow (Stickel et
al., 2007). While normal stresses disappear upon cessation
of flow, a phenomenon confirmed experimentally (Kolli et
al., 2002), in non-Brownian and low Re systems the
structural anisotropy is preserved. This anisotropy is
destroyed upon the reversal of flow direction then
suspensions reemerge with the opposite orientation (Stickel
et al., 2007). This connection between local structural
anisotropy and the discontinuities observed upon flow
reversal were confirmed by direct imaging experiments
(Parsi & Gadala-Maria, 1987) but without details available
with simulation. For 4 > 0.5 shear deformation results in a
higher degree of local order among particles including
chaining and crystallization (Butera et al., 1996).

We present experimental technique and resulting
measurements that demonstrate the anisotropy that develops
in suspensions at moderate volume fractions in a range of 0
< Pe < 1700. This technique determines particle locations
from three dimensional scanning of an arrested
pressure-driven flow after it reaches steady state in a
microchannel far from the entrance conditions. Our





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


measurements qualitatively confirm the structure that is
widely attributed to the generation of normal stresses and
shear thickening in concentrated suspensions.

Nomenclature


particle radius
gravitational constant (ms-1)
Boltzmann constant
velocity (m/s)
half height of channel (rnm)
temperature


Greek letters
y shear rate (1/s)
K Debye inverse screening length (1/nm)
r viscosity (Pas)
volume fraction

Subscripts
bulk average volume fraction


Experimental Facility

We present measurements taken via confocal laser scanning
microscopy (CLSM) of particle-level anisotropy generated
from shear in pressure-driven flow. Monosized suspensions
are composed of 2a = 1.01 rpm diameter SiO2 microspheres
in 3:1 glycerol:water at _bulk = 0.2, 0.24, 0.28, 0.32, 0.36
and 0.40. [NaNO3] and [NaOH] are used to adjust the pH
value to 8.0 and a screening of K1 = 1.5 nm and 0.1 mM
Rhodamine B is added to the suspension for imaging.
Compressed N2 with a pressure of 1 atm is applied to drive
suspensions through a 50 mm x 40 gm x 100 gm straight
microchannel. Figure 1 shows the experimental setup. The
coordinates (x, y, and z) that represent the flow, flow
gradient, and vorticity directions (v,v, V, V xv) are
reported as dimensionless quantities scaled by the 20 pm
half-height of the channel in the Vv direction.

The nonlinear shear gradient resulting from pressure-driven
flow induces significant suspension migration. The final
steady volume fraction profile far from the entrance, shown
in Fig. 2a, is increased at the center and decreased near the
walls. Local viscosity depends on local volume fraction, and
therefore the velocity profile deviates from that of a
Newtonian fluid. Fully developed flow far from the entrance
region thus generates a near-Poiseuille (parabolic) velocity
profile across the y-direction with a velocity of 1 mm/s in
the center as plotted in Fig. 2b. The local shear rate is nearly
linear and is used to define local Pe. The non-uniform
concentration results in shear rates in the z direction which
strongly deviates from that of a Newtonian fluid and are
small over a large region in the channel center.


Compressed N2

To air
To ar 3-way valve


~ 50 mm


100 gm
40 gm
Straight channel
X, V
Figure 1: Experimental setup. Three-way valve is added to
regulate the driving pressure from compressed N2 (blue
line position) and release the pressure on suspension (red
line position). The straight line (in blue) with arrows shows
the path of suspension flow.

a) 0 0.145 0.29 0.335 0.58
00 _


1.0
0.5
0
-0.5
-1.0
-2.5-2.0-1.5-1.0-0.5 0 0.5
z/H


1.0 1.5 2.0 2.5


y/H
Figure 2: a) Particle volume fraction profile transverse to
flow direction and ROI where data is sampled after flow
stopped. b) The measured velocity profile in the ROI
(triangles) and the parabolic profile (green line) for
comparison. The shear rate profile calculated from the
velocity in y axis (diamonds) fit with a linear trend line
(red).

Dynamic confocal laser scanning microscopy (VTeye,
Visitech Int.) allows single plane particle tracking and is
used to measure velocity profiles as well as particle
concentration patterns transverse to the flow direction (Gao
& Gilchrist, 2008; Gao et al., 2009). However, its scanning
speed is insufficient to track fast moving particles in 3D
space and allow microstructure investigations. After flowing
for 10 minutes to eliminate transients, we quickly stop the


Paper No






Paper No


flow, similar to experiments by Dendukuri et al. (2007) in
which they used stop flow lithography to synthesize
polymeric particles, and scan the entire depth of the channel
in the V v direction within a region of interest (ROI)
located at the center of the V xv direction (20 X 40 X
20 pm3). The ROI is far away from the channel entrance to
make sure that the suspension flow is fully developed (Nott
& Brady, 1994). Compressed N2 gives a stable driving
pressure and fast pressure release using a three-way valve
near the channel entrance allows rapid arrest of suspension


flow wit
matched s
are preser
not rever
suspension
with reso
allows tl
Brownian
local struck
to calcula
fraction
measure

0.6.

0.5-

0.4-
.2

0.3-
0)
E
2 0.2-
0

0.1

0
-1

Figure 3
(bulk = 0
0.354 (t


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

direction at various (bulk. Due to shear induced migration,
particles have the highest concentration at the channel
center and the lowest concentration near the channel wall.
Larger bulk correlates with higher particle concentration in
the channel center. While the highest particle concentration
at the channel center is not maximum packing fraction for
hard sphere, it is different than concentrations predicted by
previous modeling (Nott & Brady, 1994; Phillips et al.,
1992).


hout flow reversal. In non-Brownian density The pair distribution function showing the suspension
systems, the structures that produce normal stresses structure near the wall at high Pe for 0.224 < 4 < 0.334 is
-ved upon flow cessation provided the flow does shown in Fig. 4. In each of these experiments ) < (bulk due
se (Kolli et al., 2002; Stickel et al., 2007). After to cross channel shear migration (Fig. 3). With decreasing (,
n flow stops, the ROI is scanned at high speed the anisotropy in g(x, y) that shows structure in the v-Vv
lution 10 pixels/pm over 2.4 s. Fast scanning plane is less pronounced. At ( = 0.224 (Fig. 4a) the
he identification of particle locations before distribution of particles is more isotropic. Particle density
diffusion and sedimentation significantly alter the along the compressional flow axis of flow around a particle
cture. The average particle number density is used is roughly the same as that along the extensional axis. As 4
te the local volume; this provides accurate particle increases, there is first a higher correlation of pairwise
measurements (Fig. 3) that match well with interactions along the flow direction, then at higher volume
tents taken during flow. fractions an increased correlation in the y direction. Only at
) > 0.323 (Fig. 4e,f) does a clear depletion region form.
S(bulk= 0.411 ulk= 0.323 This lower than average probability region resides just
Outside of the nearest neighbor pairwise distribution, and the
5- bk= 0.386 tbulk 0.298 secondary anisotropic ring that forms is clear evidence that
ulk= 0.354 = .= 0.257 at these 4 more than pairwise interactions contribute to the
suspension structure. In Fig. 4f the intensity of first nearest
neighbor ring is higher in the x direction than in the y
direction, with the particle organization in the x direction
showing the effect of shear thinning at low Pe. In Fig. 4f the
intensity of first nearest neighbor ring is higher along the
compressional axis than the extensional axis, indicating
shear thickening at high Pe due to hydrocluster formation
along the compressional axis. The g(x, z) and g(z, y)
distributions also show a greater degree of homogeneity at
low ) and nearest neighbor pairwise interactions at r = 2a
.0 -6.8 -0".6 -0.4 -0.2 steadily increases with increasing )bulk. It should be noted
y/H that this unexpected anisotropy seen in g(x, z) and g(z, y) is
Also seen at lower volume fractions and for g(z, y) has the
.: Local particle concentration profiles in y axis for
same angular dependence even though these experiments
.257 (circles), 0.298 (asterisks), 0.323 (crosses), are conducted in different devices with different
riangles), 0.386 (squares), and 0.411 (diamonds), suspensions.


wIIerC y/f --1. lu y / = ait L channelllll wall and
center respectively. Pe > 1700 near the wall.

Results and Discussion

The experimental local volume fraction is a function of the
degree of migration. To sample various volume fractions at
different Pe, we perform a series of experiments with bulk
ranging from 0.257 to 0.411, with values determined
experimentally by averaging the density across the channel.
At these (bulk, sedimentation during flow is negligible (Gao
et al., 2009). While these experiments do not allow precise
control over local volume fraction, they do allow sampling
of the local structure at various volume fractions and y. An
additional concern is the variation in shear rate profile
across the channel. Note that the flow tends toward a
parabolic flow profile with decreasing (bulk.

Figure 4 shows particle concentration profiles in the y


There are two explanations for the observed trend. First, at
lower bulk there are fewer particles sampled in each
experiment; in this case the structural anisotropy may not be
evident because of lacking data. This likely has some effect
on the quality of the data presented. However, the decrease
in pairwise intensity is stronger for g(x, y) than in other
directions. Thus, a true change in the degree of structural
anisotropy is captured qualitatively. Second, multi-body
hydrodynamic interactions resulting in normal stress
increase in frequency with increasing 4 > bulk = 0.1 (Brady
& Vicic, 1995). In experiments migration occurs as low as
bulk = 0.04 (Brown et al., 2009), suggesting that normal
stresses exist. However, the structural anisotropy that drives
migration may be too weak to capture in these experiments.

In Fig. 5, measurements at the channel center also show an
increase in local pairwise interactions with increasing ).
Due to shear migration, 4 at Pe = 0 is greater than (bulk (Fig.






Paper No


3). The structure in g(z, y) shows similar angular
dependence to high Pe experiments. In g(x, y), g(x, z) and
g(z, y), the first three nearest-neighbor rings at 4 = 0.537
(Fig. 5f,l,r) decrease intensity at 4 = 0.302 (Fig. 5a,g,m).
When 0.479 < ( < 0.537 the first three nearest-neighbor
rings are quite similar, while static suspensions with 49.4%<
( < 54.5% fall into a liquid-solid phase (Pusey & van
Megen, 1986; Cheng et al., 2001), suggesting that fast
flowing suspensions at Pe = 0 may have similar phase
transitions found in static suspensions. When 4 > 0.43, the
first nearest-neighbor rings are independent to various
local, suggesting that _local has little effect on pairwise
interactions between near-contact particles. With Pe = 0, the
structure shown in g(x, z), is expected to be similar to that
of static samples. Because of the concentration gradient in
the y direction, g(x, y) and g(z, y) show essentially no
correlation in the V v direction.

Conclusions

In conclusion, CLSM-enabled 3D measurement of particle
locations in experiments enables direct microstructure
easurement and comparison with particle locations
generated through SD simulations for model validations.
The apparent anisotropies lead to shear migration in
nonlinear shear profiles and enable probing of various Pe
and ( in a single experiment. Experiment and simulation
pair distribution functions largely agree, though the details
deviate possibly due to the lateral confinement of the
suspension in the z-direction. Evolution of pair distribution
functions at low )bulk and Pe shows that higher )bulk
strengthens particle pairwise interactions, and higher Pe
intensifies anisotropic structure in sheared suspension.

Acknowledgements

We thank Prof Jeffrey Morris (CCNY) and Prof John
Brady (Caltech) for discussions. We also thank Prof Eric
Weeks for his development of the 3D particle tracking
algorithms and code. This research was in part supported
by the North American Mixing Forum Startup Grant and
Lehigh University.

References

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Brown, J.R., Fridjonsson, E.O., Seymour, J.D. & Codd, S.L.
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Cheng, Z., Chaikin, P.M., Russel, W.B., Meyer, W.V., J.
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Deboeuf, A., Gauthier, G., Martin, J., Yurkovetsky, Y. &


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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