NONEQUILIBRIUM STATISTICAL-MECHANICS OF PREASYMPTOTIC DISPERSION

Turbulent transport in bulk-phase fluids and transport in porous media with fractal character involve fluctuations on all space and time sca les. Consequently one anticipates constitutive theories should be nonl ocal in character and involve constitutive parameters with arbitrary w avevector and frequency dependence. We provide here a nonequilibrium s tatistical mechanical theory of transport which involves both diffusiv e and convective mixing (dispersion) at all scales. The theory is base d on a generalization of classical approaches used in molecular hydrod ynamics and on time-correlation functions defined in terms of nonequil ibrium expectations. The resulting constitutive laws are nonlocal and constitutive parameters are wavevector and frequency dependent. All re sults reduce to their convolution-Fickian, quasi-Fickian, or Fickian c ounterparts in the appropriate limits.