Anomalous behavior of the diffusion coefficient in thin active films

Abstract

Inspired by recent experiments in cell biology, we elucidate the visco-elastic properties of an active gel by studying the dynamics of a small tracer particle inside it. In a stochastic hydrodynamic approach for an active gel of finite thickness L, we calculate the mean square displacement of a particle. These particle displacements are governed by fluctuations in the velocity field. We characterize the short-time behavior when the gel is a solid as well as the limit of long times when the gel becomes a fluid and the particle shows simple diffusion. Active stresses together with local polar order give rise to velocity fluctuations that lead to characteristic behaviors of the diffusion coefficient that differ fundamentally from those found in a passive system: the diffusion coefficient can depend on system size and diverges as L approaches an instability threshold. Furthermore, the diffusion coefficient becomes independent of the particle size in this case. © IOP Publishing and Deutsche Physikalische Gesellschaft.