Demixing of two species via reciprocally concentration-dependent diffusivity

TL;DR

This paper introduces a model where two species demix due to their density-dependent diffusivity, with both analytical and numerical evidence showing how reciprocal sensing influences phase separation.

Contribution

It presents a novel density-dependent diffusion model for two species that captures demixing driven by reciprocal sensing effects, supported by analytical and numerical analysis.

Findings

Demixing occurs due to reciprocal concentration-dependent diffusivity.

Nonlocal sensing radius resolves numerical ambiguities in the local model.

Steady states confirm phase separation driven by diffusivity feedback.

Abstract

We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is determined by the surrounding density of the respective other species within a sensing radius $r_s$. A higher concentration of the first (second) sort will enlarge the diffusion and, in consequence, the intensity of the noise experienced by the second (first) sort. Numerical and analytical investigations of steady states of the macroscopic equations prove the demixing of particles due to this reciprocally concentration-dependent diffusivity. An ambiguity of the numerical integration scheme for the purely local model ($r_s\to 0$) is resolved by considering nonvanishing sensing radii in a nonlocal model with $r_s > 0$.