Domain Growth Kinetics in Active Binary Mixtures

TL;DR

This paper investigates the phase separation dynamics in active binary mixtures using a coarse-grained bacterial model, revealing how morphology and domain growth depend on mixture composition and activity differences.

Contribution

It introduces a detailed study of MIPS in active mixtures through evolution equations and scaling analysis, highlighting the effects of composition and activity on domain morphology.

Findings

Domain size grows as t^{1/3}, indicating diffusive coarsening.

Structure factor follows Porod's law at high wave numbers.

Morphology depends on mixture composition and activity difference.

Abstract

We study motility-induced phase separation (MIPS) in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields $\rho_i(\vec r, t)$. Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function $C(r, t)$ and the structure factor $S(k, t)$, both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, $\Delta$. For $k\rightarrow\infty$, $S(k, t)$ follows Porod's law: $S(k, t)\sim k^{-(d+1)}$ and the average domain size $L(t)$ shows a diffusive growth as $L(t)\sim t^{1/3}$ for all mixtures.