Скачать или смотреть Physics colloquium by Professor Alex Hansen, NTNU - Norwegian University of Science and Technology

Statistical Mechanics of Flow in Porous Media

Abstract:
Immiscible two-phase flow in porous media is the competition between two fluids that do not like each other for the same pore space. One may for example try to squeeze one of the two fluids into a porous medium already saturated with the other fluid. Depending on the properties of the two fluids, their viscosity, the surface tension between them and the wetting properties of the fluids with respect to the porous matrix, the interfaces between the defending and the invading fluid will take on different, but complex structures. For example, if the flow is so slow that the capillary forces dominate compared to the viscous forces, the fluids will generate percolation clusters.

However, this is not the only way to study this problem. If one instead inject both fluids simultaneously and at a steady rate, the fluids will mix by forming clusters that break up and merge, but in such a way that there is an equilibrium. This is steady-state flow. Can one then ask questions about this state that are similar to those that an be answered for gases in steady-state using statistical mechanics? In other words, can one construct a statistical mechanics for immiscible two-phase flow in porous media under steady-state flow conditions? I claim yes, and I will explain how in the talk.