A deterministic two-phase model for an active suspension with non-spherical active particles using the Eulerian spatial averaging theory

Abstract

We derive a closed system of equations modeling an active suspension using the Eulerian spatial averaging theory under the assumption of a low-Reynolds flow Re≪1. The suspension consists of a Newtonian fluid and multiple identical active, non-spherical Janus particles. The volume-averaged mass, linear momentum, angular momentum, and orientation balance equations are derived for the fluid and solid phases separately. The focus of the present work is to derive closure relations for the resulting equations, based on fluid–particle and particle–particle interactions. Also included is a numerical study of a channel flow, driven by the active forces of the particles and a pressure gradient or/and a moving wall. The numerical results indicate the importance of the Saffman effect for an active suspension.