More on the concentration dependence of Fick's laws

We show that concentration-dependent diffusivities that enter Fick's laws can be derived from random-walk models of diffusion. In particular, Darken's phenomenological expression for that dependence results if the transition frequencies depend on the occupation of final states. We develop the one-dimensional discrete-to-continuum passage with some care, and, in particular, we show that fluxes must be defined at the midpoint between lattice sites, even for nonlinear problems.© 1986, American Association of Physics Teachers. All rights reserved.