Nonequilibrium thermodynamics of nonlinear diffusion flux in a nonideal electrolyte solution.

Abstract

The nonlinear diffusion-dispersion flux of the total mole concentrations in nonideal electrolyte solution is represented by a Korteweg--de Vries (KdV) type of equation in equilibrium. With small perturbations of the KdV equation's coefficients, we can obtain its nonequilibrium steady-state flux. One finding is that the nonequilibrium flux is separated into the nonlinear wave propagation and the diffusion process for entropy production. By means of the perturbation procedure, we further studied the individual chemical component fluxes. The major finding is that in the stationary state, the macroscaled space fluxes between individual components still remain in the no-total-flux system. From this finding, it follows that there is a hierarchy in the thermodynamical flux. Then we obtain Onsager's relations in the nonlinear form and the entropy production for each hierarchy of the flux.