Long-time diffusion and energy transfer in polydisperse mixtures of particles with different temperatures

TL;DR

This paper investigates how long-time diffusion and energy transfer in dilute mixtures of particles with different temperatures depend on size, composition, and interactions, providing a theoretical framework supported by simulations.

Contribution

It introduces a model for long-time transport and energy transfer in nonequilibrium polydisperse particle systems, extending to soft potentials and comparing with Brownian-dynamics simulations.

Findings

Viscosity and energy flux depend nonlinearly on particle size.

Transport rates are enhanced by interactions in size- and composition-dependent ways.

The formalism reveals scenarios relevant for biological systems and active colloids.

Abstract

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.