Anisotropic Diffusion in Driven Convection Arrays.

Yunyun Li,Pulak K Ghosh,Fabio Marchesoni,Vyacheslav R Misko

doi:10.3390/e23030343

Abstract

We numerically investigate the transport of a Brownian colloidal particle in a square array of planar counter-rotating convection rolls at high Péclet numbers. We show that an external force produces huge excess peaks of the particle’s diffusion constant with a height that depends on the force orientation and intensity. In sharp contrast, the particle’s mobility is isotropic and force independent. We relate such a nonlinear response of the system to the advection properties of the laminar flow in the suspension fluid.

Highlights

Under quite general conditions, the fluctuation-dissipation theorem relates the response of a system to an external perturbation with its equilibrium dynamics [1]
An archetypal example of nonlinear response is represented by the dynamics of a tracer particle moving in a complex medium under the action of an external force F
The response of an overdamped Brownian particle driven-advected in a 2D square convection array shows large deviations from the predictions of the linear response theory

Summary

Introduction

The fluctuation-dissipation theorem relates the response of a system to an external perturbation with its equilibrium dynamics [1]. AED takes place at high Péclet numbers, Pe = DL/D0 1, whereby D turns out to be larger than the free diffusion constant, D0 This effect has been explained [19,20,21,25,26,27] by noticing that, at low noise, an unbiased particle jumps between convection rolls thanks to advection, which drags it along the outer layers of the convection rolls, or flow boundary layers (FBLs), centered around the ψ(x, y) separatrices. Square free-boundary convection array of Equation (1), κ 1.07 [19], consistent with previous numerical results [24] The crossover between these diffusion regimes is well localized around D0 DL [27]; AED occurs for D0 < DL. More numerical evidence of the critical nature of the dynamical transition taking place at F ∼ Fc will be provided in an upcoming full-length paper [33]

Diffusion Anisotropy

Diagonal Diffusion

Longitudinal and Transverse Diffusion

Findings

Conclusions