Kinetics of phase separation on curved manifolds: Soft matter

We study kinetics of phase separation in soft condensed matter systems (e.g. vesicles, tubules, membranes, etc.) for both non-conserved (Model A) and conserved (Model B) dynamics. We first consider phase separation on one-dimensional planar curves for illustrative purposes. We then classify curved manifolds in terms of the presence of either an axis of translation or rotation and derive expressions for the Laplace-Beltrami operator. Numerical results are presented for a circular cylinder, an elliptic cylinder and a torus. We find that, in general, local curvature affects the kinetics and shape of the domains.