Fractional anomalous convection diffusion in comb structure with a non-Fick constitutive model

Abstract

A novel constitutive model that contains the fractional, convection velocity, and macroscopic and microcosmic relaxation parameters is proposed to describe anomalous diffusion in the comb model. The formulated governing equation contains mixed derivatives of time and space, and the solutions are obtained by a numerical method in which the L1 scheme is used. The temporal evolution mechanism of the monotonically decreasing distribution of particles and the monotonically increasing distribution of the mean square displacement with the involvement of different parameter effects is presented and analyzed in detail. Power functions are applied to fit the distributions of the mean square displacement with five kinds of modified models and the power law indexes are estimated. It is noteworthy that subdiffusion occurs for the Fick model and superdiffusion occurs for short-time behavior, while subdiffusion occurs for long-time behavior with the Cattaneo and dual-phase-lag models, and superdiffusion occurs for the Cattaneo–Christov model and the newly proposed model.