Surface tension of soft active Brownian particles

Active-matter systems consist of components that locally consume energy to move, exert forces or perform chemical reactions, thus being inherently out of equilibrium. Simple models have been developed to capture their emergent behavior, including the active Brownian particle (ABP) where each colloid is self-propelled by an active force. Even in the absence of any attractive potential, at sufficient activity, the system undergoes a non-equilibrium phase separation (liquid/gas). One question that we aimed to resolve was how should we define stress in active systems and its balance at steady state? Unique to active systems, active forces align at the interface. Extending equilibrium statistical mechanics to our non-equilibrium systems by using a volume-averaged swim pressure results in unrealistic surface tensions. We derived a continuum theory to investigate the relationship between the interparticle pressure, swim pressure, and macroscopic pressure in the momentum equation. We found that formulating the point-wise macroscopic pressure as the interparticle pressure and modeling the particle activity through a spatially variant body force-as opposed to a volume-averaged swim pressure-results in a surface tension that is negligible and intrinsic to all ABP steady states.