NONEQUILIBRIUM STATISTICAL-MECHANICAL DERIVATION OF A NONLOCAL DARCY LAW FOR UNSATURATED SATURATED FLOW

As illustrated variously by wetting and drying scanning curves, flow i n unsaturated porous media is inherently nonlocal. This nonlocality is also manifest in hysteresis in the classical Darcy conductivity. It i s the authors' belief that most current theories of unsaturated/satura ted flow are often inadequate, as they do not account for spatial nonl ocality and memory. Here we provide a fundamental theory in which nonl ocality of the flow constitutive theory is a natural consequence of fo rce balances. The results are derived from general principles in stati stical physics and under appropriate limiting conditions, the classica l Darcy's Law is recovered for saturated flow. A notable departure in this theory from other nonlocal flow theories is that a classical Darc y type equation on a small scale need not exist.