Surface tension between coexisting phases of active Brownian particles

The confliction between the stable interface in phase-separated active Brownian particles and its negative surface tension, obtained mechanically via the active pressure, has sparked considerable debate about the formula of active surface tension. Based on the intrinsic pressure of active system, we here derive a mechanical expression of active surface tension by calculating the work required to create a differential interface area, while remaining the interfacial profiles of intensive quantities invariant (not considered previously). Our expression yields a significantly positive surface tension that increases with the particle activity, which is further supported by mechanical stability analysis of both steady-state droplet and fluctuating interface. Our work is thus promising to resolve the contradiction related to active surface tension.