Isothermal nonstandard diffusion in a two-component fluid mixture: A Hamiltonian approach (Q1289091)

(From the authors' abstract.) We present nonlinear formalism describing non-Fickian diffusion in a two-component mixture at uniform temperature. The formalism is based on a Hamiltonian description and is constructed by introducing two potentials: the thermodynamic free energy potential, and the so-called dissipative potential. The evolution equations are expressed in terms of Poisson's brackets whose generating potentials are the two above-mentioned potentials. In view of a better understanding, the paper is presented in a rather pedagogical way, starting with a simple Hamiltonian description of classical hydrodynamics before examining classical Fickian diffusion and non-Fickian diffusion in ordinary fluids, including non-local effects.