Direct numerical

simulations are considered on the motion of

large ensembles (more than 1000 in number) of deformable particles

in a channel bounded by two parallel walls.

Particles are modeled as capsules, that is, liquid drops surrounded by

infinitesimally thin

hyperelastic membranes. Here we assume that the

membrane follows the

neo-Hookean constitutive law. The undisturbed flow, in absence

of the particles, is a parabolic flow driven by a constant

pressure gradient (Poiseuille flow). The particle Reynolds number,

based on the centerline velocity of the Poiseuille flow,

the undeformed particle diameter, and suspending fluid viscosity,

can vary from 0.01 to 10. The capillary number, based on the

suspending fluid viscosity, centerline velocity and

surface tension or membrane elastic modulus, ranges

from 0.05 to 0.5. Particle volume fraction ranges from 5 to 30%.

The ratio of the channel height to particle diameter varies from

1.25 to 15. The liquids interior and exterior

of the particles are Newtonian.

The numerical methodology is based on

a mixed finite-difference/Fourier transform method for

the flow solver and a

front-tracking method for the deformable particles.

In the simulations, the flow field is resolved using up to 280X280X280

grid points, and each particle surface is resolved by 1280 marker points.

Instantaneous snapshots of particle distribution from the simulations

are analyzed to study the interaction between the deformable

particles in a multi-particle environment.

Results are presented on

the time-dependent particle velocity and

trajectory, mean and time-dependent apparent viscosity of the suspension,

mean fluid and particle velocity across the channel, and

pair-wise distribution function.

Particles near the walls are seen to deform more and align with the

mean flow direction, whereas those near the channel center have less deformation.

Two competing mechanisms, namely, deformation-induced migration, and

dispersion due to multi-particle interaction, are studied for

varying Reynolds number, volume fraction, and size ratio. Fluctuations

in particle velocity and trajectory are analyzed. DNS results show that

fluctuations are higher for intermediate volume fractions (10-15%).

Time-averaged velocity in presence of the

particles deviates from the parabolic profile, and shows a 'plug' profile with decreasing velocity

as the volume fraction and size ratio are increased.

The effective viscosity of the suspensions shows nearly an

order of magnitude variation over the range of the parameters considered.

The effective viscosity increases with increasing particle volume fraction,

and the size ratio, in agreement with previous experimental results.

The DNS results are then used to validate the two-phase model of suspension

in a pressure-driven flow in which the flow is divided in to

a particle-depleted layer near the wall and a particle-rich layer

near the center of the channel. The thichness of the particle-depleted layer,

and the variation of viscosity over the channel cross-section are

estimated from the DNS results as functions of volume fraction, capillary number,

and size ratio. It is shown that the two-phase model underpredicts

the mean velocity obtained from the DNS results. The underprediction is

due to overestimation of the local viscosity in the vicinity of the

interface between the particle-depleted and particle-rich regions.

We then propose a three-layer model in which the flow is divided in to

a particle-depleted layer near the wall, a particle-rich layer

near the center, and a transition regime between the two layers

where viscosity varies linearly rather than a step-like manner assumed

in the two-phase model. A closed-form expression for mean velocity is obtained

for the three-layer model. The values of the parameters of the model

are directly obtained from the DNS data. The predicted velocity using the

three-layer model gives excellent agreement with the DNS results.

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