(400c) A Pairwise Hydrodynamic Theory and Boundary Layer Analysis for Particle De-Mixing in Wall-Bounded Suspension Flows

A pairwise hydrodynamic theory is developed for de-mixing in polydisperse particle suspension flows, where transport coefficients are calculated analytically by quadrature of pair mobility functions. Particle distributions evolve according to a Boltzmann-like master equation where particle transport is governed by a balance between particle fluxes due to hydrodynamic diffusion down-gradients in species concentration and a wall-migration velocity. Stationary particle distributions are determined by the solution of a coupled set of nonlinear, differential equations. A phenomenological boundary layer analysis is presented for bidisperse suspensions of particles with size ratio near the critical value where the collision cross-section between pairs of particles vanishes. This boundary layer analysis reveals that margination of small or large species near the wall is controlled by a single coefficient depending on species bulk concentrations, particle physical parameters (e.g., particle size and deformability), particle hydrodynamic interactions, and near contact phenomena. Results are presented in the context of emulsions of drops in the spherical limit. We present a small-size-ratio approximation for near-wall drop distributions valid for low- to moderate-viscosity ratios where the critical size ratio is small compared to unity. In this regime, the small-size-ratio approximation can be derived from the near-critical boundary layer analysis yielding a two-parameter set of equations where the particle transport for small species has a one-way coupling (i.e., the distribution of small drops is affected by the presence of larger drops, but the distribution of larger drops is unaffected by the presence of smaller ones). We further analyze the effect of heterogeneous interactions of bidisperse emulsions of drops with equal size and varying viscosity ratio or surface tension.