Curvature Dependent Diffusion Flow on Surface with Thickness

TL;DR

This paper introduces a new curvature-dependent diffusion flow on curved surfaces with finite thickness, deriving a modified diffusion equation and calculating the curvature-dependent diffusion coefficient for an elliptic cylinder.

Contribution

It presents a novel diffusion flow explicitly dependent on surface curvature and derives a corresponding diffusion equation considering surface thickness effects.

Findings

Derived a new curvature-dependent diffusion equation.

Calculated the curvature-dependent diffusion coefficient for an elliptic cylinder.

Demonstrated the impact of surface curvature on diffusion processes.

Abstract

Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$ (thickness of surface) expansion. As an example, the surface of elliptic cylinder is considered, and curvature dependent diffusion coefficient is calculated.