Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow

Abstract

A structure-tensor-based model is used to compute the microstructure and velocity field of concentrated suspensions of hard spheres in a fully developed, pressure-driven channel flow. The model is comprised of equations governing conservation of mass and momentum in the bulk suspension, conservation of particles, and conservation of momentum in the particle phase. The equations governing the relation between structure and stress in hard-sphere suspensions were developed previously and were shown to reproduce quantitatively results obtained by Stokesian dynamics simulations of linear shear flows. In nonhomogeneous, pressure-driven flows, the divergence of the particle contribution to the stress is nonzero and acts as a body force that causes particles to migrate across streamlines. Under steady conditions, the model predicts that the resulting migration causes particles to move to the center of the channel, where the concentration approaches the maximum packing for hard-sphere suspensions. In oscillatory flow, the behavior depends strongly on the amplitude of the strain. For oscillations with large strains, the particles migrate to the channel center. However, when the strain is small, the maximum concentration is located either at a position between the channel center and walls or, in the limit of very small strains, at the wall. The migration to the wall induced by small-strain oscillation occurs in conjunction with the suspension microstructure becoming ordered. This behavior agrees qualitatively with experimental observations reported in the literature. However, the predicted rate of migration toward the wall in the simulations is significantly slower than what is observed experimentally.

The suspension balance model revisited

“…Despite the aforementioned flaws, many studies [19][20][21]24 have used the suspension balance model with success to capture the observed features of particle migration in many simple flows. This suggests that the phenomenological form of ⌺ h͑p͒ assumed in these studies may be qualitatively similar to that of the particle phase stress.…”

“…However, the normal stress differences of the particle phase are not the same as that of the suspension. The numerous studies [19][20][21][22][23][24][25][26][27] that have used and extended the SBM have retained the error of equating ͗ h ͘ p with ⌺ h͑p͒ . The outline of this paper is as follows.…”

Dynamics of concentrated suspensions of non-colloidal particles in Couette flow

“…To predict the behaviour of the suspensions in such a flow condition, there have been several attempts to develop a continuum model (Leighton & Acrivos 1987;Nott & Brady 1994;Morris & Boulay 1999;Miller & Morris 2006;Yapici et al 2009). One of the successful approaches is proposed by Morris & Boulay (1999), in which the constitutive law for the particle stress for shear flows is given by (4.16) In this formulation, μ n is the normal stress viscosity defined as 17) where K n is a rheological fitting parameter.…”

A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in Newtonian fluids

“…By a systematic fitting procedure of the parameters, he obtained numerical results in quantitative agreement with shear reversal experiments [7,31]. Also in 2006, Stickel et al [34] (see also [35,36]) defined the conformation tensor on the base of particle mean free path, and simplified the expression of the stress to be linear in the deformation rate and the conformation tensor. Their model nevertheless also involves 13 free parameters.…”