Phase behaviour of active Brownian particles: the role of dimensionality

TLDR

Activity‑induced phase separation in suspensions of active Brownian particles has attracted much attention, but most studies have been limited to two dimensions. This study investigates activity‑induced phase separation in three dimensions and compares the results with both previous and new two‑dimensional simulations. We carried out large‑scale Brownian dynamics simulations of up to 40 million ABPs to eliminate finite‑size effects in 3D. The simulations confirm that 3D active Brownian particles undergo phase separation analogous to equilibrium gas–liquid spinodal decomposition, yet the phase boundaries differ markedly from 2D and the 3D coarsening follows the classical diffusive \(t^{1/3}\) law rather than the subdiffusive exponent seen in 2D.

Abstract

Recently, there has been much interest in activity-induced phase separations in concentrated suspensions of "active Brownian particles" (ABPs), self-propelled spherical particles whose direction of motion relaxes through thermal rotational diffusion. To date, almost all these studies have been restricted to 2 dimensions. In this work we study activity-induced phase separation in 3D and compare the results with previous and new 2D simulations. To this end, we performed state-of-the-art Brownian dynamics simulations of up to 40 million ABPs -- such very large system sizes are unavoidable to evade finite size effects in 3D. Our results confirm the picture established for 2D systems in which an activity-induced phase separation occurs, with strong analogies to equilibrium gas-liquid spinodal decomposition, in spite of the purely non-equilibrium nature of the driving force behind the phase separation. However, we also find important differences between the 2D and 3D cases. Firstly, the shape and position of the phase boundaries is markedly different for the two cases. Secondly, for the 3D coarsening kinetics we find that the domain size grows in time according to the classical diffusive $t^{1/3}$ law, in contrast to the nonstandard subdiffusive exponent observed in 2D.