Curvature-dependent diffusion flow on a surface with thickness.

Particle diffusion in a two-dimensional curved surface embedded in R3 is considered. In addition to the usual diffusion flow, we find a flow with an explicit curvature dependence. Diffusion equation is obtained in ϵ (thickness of surface) expansion. As an example, the surface of elliptic cylinder is considered, and curvature-dependent diffusion coefficient is calculated.