Theory of soft active equilibrium wetting

We must address active matter in the context of soft boundaries to bridge the gap between our understanding of active matter and the dynamics of biological systems (represented as active matter) under natural conditions. However, the physics of such active drops (matter) in contact with a soft and deformable surface has remained elusive. In this paper, we attempt to fill this gap and develop a theory for soft, active wetting. Our theory, which accounts for the various free energies for passive substrate and active drops as well as the active stresses, provides an equilibrium description of (active) particle orientation inside the drop and an equilibrium shape of the drop–soft-solid system. We obtain an analytical equation relating the activity to the internal pressure of an active drop. The equilibrium calculation further yields an ordered state of the polarisation field inside the drop. As compared to the non-active drops, the active drops with extensile activity press more into the soft surface, while the active drops with contractile activity either rise out of the soft surface (for smaller magnitude of negative activity) or make the soft surface bulge (for larger magnitude of negative activity). Finally, the three-phase contact line undergoes a rotation that depends on the strength of activity. These findings shed light on the manner in which the active stresses interact with surface tension and elasticity at the fundamental level.