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

TL;DR

This paper introduces a novel experimental method using fluctuation-dissipation theorems to measure Onsager coefficients in two-phase porous media flows, validated through a visualizable Hele-Shaw cell setup.

Contribution

It presents the first experimental approach to determine Onsager coefficients in porous media flows via fluctuation-dissipation relations, bridging theory and practical measurement.

Findings

Successful measurement of Onsager coefficients using optical imaging.

Validation of fluctuation-dissipation theorem in porous media flow.

Provides experimental support for recent theoretical models.

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.