Energy dissipation in porous media for equilibrium and nonequilibrium translational motions

In the modelling of translational motion, the concepts of frequency-dependent (of the angular fluctuations of the velocity field) self-diffusion and the dispersion tensor are commonly used in its characterisation. Both of these parameters are related to velocity autocorrelation. An alternative means of modelling translational motion is via the equilibrium and nonequilibrium fluctuation-dissipation theorem in classical statistical mechanics. This alternative approach provides further insight into the molecular level processes occurring in the system. Here both of these theoretical fluctuation-dissipation approaches are employed to determine expressions for energy dissipation in simple equilibrium systems exhibiting asymptotic and preasymptotic diffusion and dispersion phenomena and also in a nonequilibrium preasymptotic system involving dispersion within and beyond the upper limit of heterogeneity of an isotropic porous medium. As an example the permeability of porous media due to diffusion and dispersion are studied and it is shown how a frequency-dependent permeability can be treated as a phasor.