Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres

TL;DR

This paper reveals a wall-induced particle migration mechanism in shear flow that causes particles to swap positions across streamlines, explaining previously observed high self-diffusivity in dilute sphere suspensions.

Contribution

It introduces a new class of binary particle trajectories caused by wall proximity, leading to cross-streamline migration and quantifies its impact on self-diffusivity.

Findings

Wall proximity induces cross-streamline particle swapping.

The new migration mechanism explains high self-diffusivity in experiments.

Quantitative agreement with experimental self-diffusivity data.

Abstract

Binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. The spheres on these new trajectories do not pass each other (as they would in free space) but instead they swap their cross-streamline positions. To determine the significance of the wall-induced particle migration, we have evaluated the hydrodynamic self-diffusion coefficient associated with a sequence of uncorrelated particle displacements due to binary particle encounters. The results of our calculations quantitatively agree with the experimental value obtained by \cite{Zarraga-Leighton:2002} for the self-diffusivity in a dilute suspension of spheres undergoing shear flow in a Couette device. We thus show that the wall-induced cross-streamline particle migration is the source of the anomalously large self-diffusivity revealed by their experiments.