Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media.

Area of Science:

• Thermodynamics
• Materials Science
• Fluid Dynamics

Background:

• Porous media properties depend on size and shape, especially at the nanoscale.
• Immiscible phases, contact areas, and lines influence these dependencies.
• Existing thermodynamic models often overlook these small-system effects.

Purpose of the Study:

• To develop a thermodynamic description for porous media that incorporates size and shape dependence.
• To derive average densities suitable for coarse-grained analysis.
• To formulate fluctuation-dissipation theorems for porous media transport.

Main Methods:

• Application of Hill's thermodynamics of small systems to subsystems.
• Definition of average densities obeying the Gibbs equation.
• Derivation of entropy production from Gibbs and balance equations.
• Formulation of fluctuation-dissipation theorems.

Main Results:

• A consistent thermodynamic framework for porous media, including nanoscale effects.
• Average densities that obey the Gibbs equation.
• Linear relations between thermodynamic fluxes and forces.
• Novel formulation of fluctuation-dissipation theorems for porous media.

Conclusions:

• The proposed thermodynamic approach accurately describes multi-phase fluid transport in porous media.
• The derived fluctuation-dissipation theorems offer new methods for determining transport properties.
• This framework has practical implications for understanding and modeling porous materials.