Rate of Curved Step Advance in Isolation or under Curved Chernov Diffusion

The rate of step propagation for an isolated, continuous and curved step with bulk diffusion is solved within the steady-state approximation and it is noted that the Chernov model of parallel sequence of step advance is without effort adapted to the curved step. The solution of the Laplace equation in toroidal coordinates for a diffusion layer of arbitrary extension yields the diffusion flux density to the step perimeter expressed as a Legendre series. For the special case of diffusion without advection (infinitely thick diffusion layer), the step velocity is found to vanish as an inverse square-root of the radius of curvature for large values of the same. For a sequence of steps, this effect should be even more pronounced.