Dynamics of a trapped Brownian particle in shear flows

TL;DR

This paper investigates how shear flows affect the motion and distribution of a Brownian particle in a harmonic trap, revealing anisotropic distributions, shear-induced correlations, and flow-dependent shifts in particle position.

Contribution

It introduces new insights into particle dynamics under shear flows, including anisotropic distributions and methods to measure shear-induced correlations.

Findings

Particle distributions become elliptical or parachute-shaped under shear.

Shear induces asymmetric cross-correlations between orthogonal fluctuations.

Flow causes shifts in particle mean positions perpendicular to the flow.

Abstract

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distribution takes either an elliptical or a parachute shape or a superposition of both depending on the mean particle position in the shear plane. Simultaneously, shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are asymmetric in time. In Poiseuille flow thermal particle fluctuations perpendicular to the flow direction in the shear plane induce a shift of the particle's mean position away from the potential minimum. Two complementary methods are suggested to measure shear-induced cross-correlations between particle fluctuations along orthogonal directions.