Speaker
Description
Viscoelastic phase separation is thought to play an important role in cell biology. Differences in mechanical properties and relaxation times of the constituents can induce dynamic asymmetry during demixing, generating complex morphological transitions such as phase inversion, a characteristic feature of viscoelastic phase separation. In this talk, we determine the interface dynamics arising from formal sharp-interface asymptotics in a degenerate Cahn–Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable. We obtain non-local, lower-order counterparts of the classical surface diffusion flow: for a constant coupling function, we recover the intermediate surface diffusion flow, whereas phase-dependent coupling leads to a class of fractional interface laws whose propagation operator, at principal order, is the square root of the minus Laplace–Beltrami operator.