Higher-Order Hydrodynamics: Extended Fick'S Law, Evolution Equation, And Bobylev'S Instability

A higher-order hydrodynamics for material motion in fluids, under arbitrary nonequilibrium conditions, is constructed. We obtain what is a generalized-to that conditions-Fick-type Law. It includes a representation of Burnett-type contributions of all order, in the form of a continuous-fraction expansion. Also, the equation includes generalized thermodynamic forces. which are characterized and discussed. All kinetic coefficients are given as correlations of microscopic mechanical quantities averaged over the nonequilibrium ensemble, and then are time- and space-dependent as a consequence of accounting for the dissipative processes that are unfolding in the medium. An extended evolution equation for the density of particles is derived, and the conditions when it goes over restricted forms of the type of the telegraphist equation and Fick's diffusion equation are presented. (C) 2002 American Institute of Physics.