From active stresses and forces to self-propulsion of droplets

Abstract

We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming micro-organisms or artificial micro-swimmers. In contrast to approaches that start from active velocity fields produced by the system, we consider active interface tractions, body force densities and active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity, we compute the external and internal flow fields as well as the centre of mass velocity and angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed rigid but sparse (cyto)-skeleton that is immersed in the droplet interior. We calculate examples of trajectories of a droplet and its skeleton from force densities or stresses, which may be explicitly time-dependent in a frame fixed within the skeleton.