Surfactant-induced migration of a spherical drop in Stokes flow

TL;DR

This paper demonstrates that surfactant redistribution on a spherical drop in Stokes flow causes it to migrate laterally, breaking symmetry and moving towards the flow centerline, with analytical expressions derived for weak surfactant non-uniformities.

Contribution

It introduces a theoretical analysis of surfactant-induced migration of spherical drops in Stokes flow, revealing the migration mechanism and deriving analytical expressions for velocity.

Findings

Drop migrates towards flow centerline due to surfactant redistribution.

Analytical expressions for migration velocity are derived for weak surfactant non-uniformities.

Migration direction is always towards the flow centerline.

Abstract

In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts that the direction of migration is always towards the flow centerline.