Fluctuation-dissipation theorems and the measurement of the Onsager coefficients for two-phase flow in porous media

Abstract

We propose a new methodology for the experimental measurement of the Onsager coefficients of porous media flows by application of the fluctuation-dissipation theorem. The experimental setup consists of a steady-state flow condition in which two incompressible fluids are simultaneously injected into a modified Hele-Shaw cell. The cell is transparent and allows direct visualization of the dynamics via regular optical imaging methods. The fluctuations in the phase saturations are obtained and, by computing the temporal correlations of their time derivatives, we gain access to the Onsager coefficients. This work gives experimental grounding to recent theoretical development on the applications of the fluctuation-dissipation theorems to porous media flows.