Anomalous diffusion in a circular comb with external velocity field

Abstract

Transport of particles confined in a branched circular medium under influence external force is a common phenomenon in nature and science. In this paper, the diffusion of particles, under an external homogeneous and inhomogeneous velocity field, in a circular comb has been studied and the impact of the geometry on the process has been discussed. The process is a circular motion under external velocity for fixed radius r=R and is interspersed with a radial motion inward and outward of the circle. The diffusion-advection equation that describes this process has been derived and solved numerically. The results show an enhance in the diffusion process in the circular direction according to the external force and the radius of the circle, where a transition between sub and normal diffusion in the case of homogeneous velocity, and a transition between sub and fast diffusion in the case of in-homogeneous velocity. However, due to the finite region of the structure, the process tends to saturate the structure with time. On the other hand, the speed of enhancement in the diffusion process and its saturation decreases as the radius of the circle increases. This model can be served in the analysis of the restricted diffusion of spin-bearing particles in circular layers in in-homogeneous magnetic fields.