Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Fluctuation-Dissipation Theorems for Flow in Porous Media

Version 1 : Received: 9 November 2021 / Approved: 10 November 2021 / Online: 10 November 2021 (12:11:49 CET)

How to cite: Bedeaux, D.; Kjelstrup, S. Fluctuation-Dissipation Theorems for Flow in Porous Media. Preprints 2021, 2021110204 (doi: 10.20944/preprints202111.0204.v1). Bedeaux, D.; Kjelstrup, S. Fluctuation-Dissipation Theorems for Flow in Porous Media. Preprints 2021, 2021110204 (doi: 10.20944/preprints202111.0204.v1).

Abstract

A thermodynamic description of nano-porous media must handle the size- and shape-dependence of the media properties. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course grained scale, applying Hill's thermodynamics for small systems to the subsystems. we argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to di¤erences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation- dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of porous media permeabilities. Practical possibilities are further discussed.

Keywords

porous media; Gibbs relation; entropy production; constitutive equations; Fluctuation-dissipation theorems

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