  Phase separation of multicomponent lipid membranes is characterized by the
nucleation and coarsening of circular membrane domains that grow slowly in time
as $\sim t^{1/3}$, following classical theories of coalescence and Ostwald
ripening. In this work, we study the coarsening kinetics of phase-separating
lipid membranes subjected to nonequilibrium forces and flows transmitted by
motor-driven gliding actin filaments. We experimentally observe that the
activity-induced surface flows trigger rapid coarsening of non-circular
membrane domains that grow as $\sim t^{2/3}$, a 2$\times$ acceleration in the
growth exponent compared to passive coalescence and Ostwald ripening. We
analyze these results by developing analytical theories based on the
Smoluchowski coagulation model and the phase field model to predict the domain
growth in the presence of active flows. Our work demonstrates that active
matter forces may be used to control the growth and morphology of membrane
domains driven out of equilibrium.
