Non-Brownian diffusion and chaotic rheology of autophoretic disks

TL;DR

This paper investigates the chaotic motion and rheology of autophoretic disks, revealing non-Brownian diffusion and flow-dependent transitions from chaos to steady states through numerical simulations.

Contribution

It introduces a minimal model for autophoretic disk dynamics, demonstrating non-Brownian diffusion and flow-induced rheological transitions in active particle suspensions.

Findings

Mean-square displacement is linear at long times but non-Brownian.

Chaotic stresslet behavior persists under weak shear flows.

Chaotic rheology transitions to steady state with increasing flow.

Abstract

The dynamics of a two dimensional autophoretic disk is quantified as a minimal model for the chaotic trajectories undertaken by active droplets. Via direct numerical simulations, we show that the mean-square displacement of the disk in a quiescent fluid is linear at long times. Surprisingly, however, this apparently diffusive behavior is non-Brownian, owing to strong cross-correlations in the displacement tensor. The effect of a shear flow field on the chaotic motion of a 2D autophoretic disk is examined. Here, the stresslet on the disk is chaotic for weak shear flows; a dilute suspension of such disks would exhibit a chaotic shear rheology. This chaotic rheology is quenched first into a periodic state and ultimately a steady state as the flow strength is increased.