Abstract
We consider the problem of diffusion in regions containing a finite number of continuously distributed families of high-diffusivity paths. We assume linear diffusion processes and we provide differential expressions for the partial and total concentrations. The basic equations are specialized to study in detail diffusion in media with a single family of high-diffusivity paths. In this case we derive a system of two simultaneous second-order linear differential equations for the concentrations at the regular and high-diffusivity paths. Uncoupling of the equations yields a fourth-order linear differential equation for the total concentration. The various differential equations show the coupling of the partial diffusion processes and the non-Fickean character of the total diffusion process. Certain steady and non-steady boundary-value problems are formulated and solved to illustrate the departure of our findings from the classical interpretations.
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