NONLOCAL DISPERSION IN MEDIA WITH CONTINUOUSLY EVOLVING SCALES OF HETEROGENEITY

General nonlocal diffusive and dispersive transport theories are derived from molecular hydrodynamics and associated theories of statistical mechanical correlation functions, using the memory function formalism and the projection operator method. Expansion approximations of a spatially and temporally nonlocal convective-dispersive equation are introduced to derive linearized inverse solutions for transport coefficients. The development is focused on deriving relations between the frequency- and wave-vector-dependent dispersion tensor and measurable quantities. The resulting theory is applicable to porous media of fractal character.