Shear-induced self-diffusivity in dilute suspensions with repulsive interactions

TL;DR

This paper derives universal scaling laws for shear-induced self-diffusivity in dilute suspensions with repulsive interactions, validated by numerical simulations, revealing structural anisotropy and the influence of interaction profiles.

Contribution

It provides closed-form asymptotic scaling laws for shear-induced diffusivity considering various repulsive forces, highlighting universality and structural anisotropy.

Findings

Gradient component shows logarithmic enhancement over vorticity component.

Scaling laws are universal across different repulsive mechanisms.

Numerical validation confirms the asymptotic predictions.

Abstract

In a dilute non-Brownian suspension undergoing simple shear, pairwise hydrodynamic interactions are fore-aft symmetric at zero Reynolds number and produce no net cross-streamline displacement. A weak central repulsive force between particles breaks this symmetry, deflecting trajectories and generating irreversible transverse displacements that cumulatively yield a shear-induced self-diffusivity. We derive, via matched asymptotic expansions in the limit of weak repulsion, closed-form scaling laws for the gradient and vorticity components of this diffusivity. The gradient component exhibits a logarithmic enhancement relative to the vorticity component, a structural anisotropy that persists for all monotonically decaying repulsive potentials. The specific interaction enters only through integral functionals of the force profile weighted by hydrodynamic mobility functions, establishing that the scaling is universal across physically distinct mechanisms, such as electrical double-layer repulsion, steric interactions, or any other short-range central force. We validate the asymptotic predictions against full numerical trajectory integration for the representative case of electrostatic repulsion, modelled using the Gouy-Chapman description of the electrical double layer, and find excellent agreement in the expected regime.