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

Abstract

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 ,where and 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 . 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 governs the asymptotic growth kinetics for the off-critical AMB, where denotes the average order parameter. For negative ,the domain growth law is the usual Lifshitz-Slyozov growth law with . For positive ,the growth law shows a crossover to a novel growth law . Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on and . We also study the effects of both additive and multiplicative noise on the AMB.