Domain Growth in the Active Model B: Critical and Off-critical Composition

Abstract

We study the ordering kinetics of an assembly of active Brownian particles (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter (Formula presented.),where (Formula presented.) and (Formula presented.) denote space and time, respectively. The model is similar to the Cahn-Hilliard equation orModel B (MB) for a conserved order parameter with an additional activity term of strength (Formula presented.). This model has been introduced by Wittkowski et al., Nature Comm. 5, 4351 (2014), and is termed Active Model B (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity (Formula presented.) governs the asymptotic growth kinetics for the off-critical AMB, where (Formula presented.) denotes the average order parameter. For negative (Formula presented.),the domain growth law is the usual Lifshitz-Slyozov growth law with (Formula presented.). For positive (Formula presented.),the growth law shows a crossover to a novel growth law (Formula presented.). Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on (Formula presented.) and (Formula presented.). We also study the effects of both additive and multiplicative noise on the AMB. © 2021 Taylor & Francis Group, LLC.