Kinematic irreversibility in surfactant-laden interfaces

TL;DR

This paper demonstrates that particle motion in surfactant-laden interfaces causes kinematic irreversibility due to surface-pressure-dependent viscosity, revealing novel force and trajectory behaviors in low-Reynolds-number flows.

Contribution

It introduces a perturbative method to compute irreversibilities caused by pressure-dependent surface viscosity without solving complex nonlinear equations.

Findings

A translating or rotating disk experiences a force perpendicular to boundaries.

Unbounded monolayers exhibit non-intuitive trajectories similar to the Magnus effect.

The approach can be extended to complex geometries and suspensions.

Abstract

The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface-pressure-dependent surface viscosity. In particular, we show that a disk translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analog of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to 2D suspensions more generally.