We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of a class of Glauber+Zero-range particle systems. The Zero-range part moves particles while preserving particle numbers, and the Glauber part governs the creation and annihilation of particles and is set to favor two levels of particle density. When the two parts are simultaneously seen in certain different time-scales, the Zero-range part being diffusively scaled while the Glauber part is speeded up at a lesser rate, a mean-curvature interface flow emerges, with a homogenized `surface tension-mobility parameter reflecting microscopic rates, between the two levels of particle density. We use relative entropy methods, along with a suitable `Boltzmann-Gibbs principle, to show that the random microscopic system may be approximated by a `discretized Allen-Cahn PDE with nonlinear diffusion. In turn, we show the behavior of this `discretized PDE is close to that of a continuum Allen-Cahn equation, whose generation and propagation interface properties we also derive.
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