  Purely repulsive active particles spontaneously undergo motility-induced
phase separation (MIPS) into condensed and dilute phases. Remarkably, the
mechanical tension measured along the interface between these phases is
negative. In equilibrium this would imply an unstable interface that wants to
expand, but these out-of-equilibrium systems display long-time stability and
have intrinsically stiff boundaries. Here, we study this phenomenon in detail
using active Brownian particle simulations and a novel frame of reference. By
shifting from the global (or laboratory) frame to a local frame that follows
the dynamics of the phase boundary, we observe correlations between the local
curvature of the interface and the measured value of the tension. Importantly,
our analysis reveals the presence of sustained local tangential motion of
particles within a surface layer in both the gas and the dense regions. The
combined tangential current in the gas and self-shearing of the surface of the
dense phase suggest a stiffening interface that redirects particles along
itself to heal local fluctuations. These currents restore the otherwise wildly
fluctuating interface through an out-of-equilibrium Marangoni effect. We
discuss the implications of our observations on phenomenological models of
interfacial dynamics.
