Dynamics and phase separation of active Brownian particles on curved surfaces and in porous media

Abstract

The effect of curvature on an ensemble of repulsive active Brownian particles (ABPs) moving on a spherical surface is studied. Surface curvature strongly affects the dynamics of ABPs, as it introduces a new time scale τ=R/v_{0}, with curvature radius R and propulsion velocity v_{0}, in addition to the rotational diffusion time τ_{r}. The time scale τ is related to a stop-and-go motion caused by the recurrent alignment of the propulsion direction with the surface normal. This implies that motility-induced phase separation (MIPS) disappears for small R. Furthermore, it causes a narrowing of the MIPS regime in the phase diagram of Péclet number Pe and particle area fraction ϕ. Also, the phase-separation boundary at low ϕ attains a turning point at small R, allowing for the possibility of a reentrant behavior. For a system of two pores with unequal radii connected by a small passage, the density in each pore is found to be inversely proportional to local particle mobility. Notably, this relation breaks down when MIPS occurs in either sphere or when the noise is high. ABPs move against the density gradient owing to their spatially varying velocity. The magnitude of the directional flux from one pore to the other is proportional to the particles effective diffusion constant in the pore. Moreover, fluctuations in the number of ABPs within the pores near the MIPS transition are found to induce transient MIPS states.