(354e) Theory for Flow-Induced Particle Segregation in Suspension Flows

Hydrodynamic particle migration in flows of non-Brownian suspensions can be described by a transport equation balancing the diffusive flux of particles down-gradients in concentration and in shear rate. According to this model, a singular behavior for the particle concentration profile is predicted at points where the shear rate vanishes if the transport coefficients are based solely on the local velocity. Mechanistic theories based on an ad hoc non-local stress contribution to the shear rate have been proposed to alleviate this unphysical divergence. We revisit this problem and propose an alternative theory based on irreversible displacements resulting from pairwise particle interactions (similar to Rivera, Zhang and Graham, 2016). The irreversibility of pair interactions results from short-range interactions, e.g., particle roughness or deformation. We show that the singularity in particle concentration is eliminated by correctly resolving the local behavior of the transport coefficients. We obtain transport coefficients from quadrature of particle mobility functions and present results for particle distributions in planar Poiseuille flow. Specifically, we consider suspensions of rough particles, porous particles, and emulsion drops. The resulting distributions agree qualitatively with experimental results in the literature for moderately concentrated colloidal suspensions (Frank, Anderson, Weeks and Morris, 2003).