We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B , leading to a spatially and temporarily dependent diffusion ‘‘coefficient’’ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbule...

A continuum nonlinear diffusion model is developed to describe molecular transport in ordered porous media. An existing generic van der Waals equation of state based free volume theory of binary diffusion coefficients is modified and introduced into the two-dimensional diffusion equation. The resulting diffusion equation is solved numerically with the alternating-direction fully implicit method...

Mass Transfer ................................................................................................................................................ 1 What it is and what it isn't ......................................................................................................................... 1 What it is for. Applications .........................................................

Mass Transfer ................................................................................................................................................ 1 What it is and what it isn't ......................................................................................................................... 1 What it is for. Applications .........................................................

A generalization of the Hopf–Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimen...

Mass Transfer ................................................................................................................................................ 1 What it is and what it isn't ......................................................................................................................... 1 What it is for. Applications .........................................................

It may often be tempting to take a fractional diffusion equation and simply create a fractional reactiondiffusion equation by including an additional reaction term of the same form as one would include for a standard Fickian system. However, in real systems, fractional diffusion equations typically arise due to complexity and heterogeneity at some unresolved scales. Thus, while transport of a c...

We introduce the nonlocal Cattaneo-Vernotte equation by including a relaxation effect in the nonlocal diffusion equation, both of which are models for anomalous diffusion. This equation has two different interpretations: as a generalization of Fick’s first law in terms of a nonlocal flux and memory kernel and as an equation arising from the generalized master equation for a continuous time rand...