Interactions enhance dispersion in fluctuating channels via emergent flows

Abstract

Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or increase the dispersion of tracer particles. Entropic trapping in the wall bulges slows dispersion, and hydrodynamic flows induced by wall fluctuations enhance dispersion. Previous studies primarily concentrated on the case of a single Brownian tracer either embedded in an incompressible fluid or in the ideal case where the presence of fluid is ignored. Here we address the question of what happens when there is a large ensemble of interacting Brownian tracers -- a common situation in applications. Introducing repulsive interactions between the tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon strongly reminiscent of that seen in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of a single tracer, numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Then, interactions between the fluctuating wall and the now-nearby particles drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, the perturbation theory we derive quantifies dispersion in generic advection-diffusion systems with arbitrary spatiotemporal drift.