The Relation Between Dissipation and Memory in Two‐Fluid Displacements in Disordered Media

Abstract

Abstract We show that the return‐point memory of cyclic macroscopic trajectories enables the derivation of a thermodynamic framework for quasistatically driven dissipative systems with multiple metastable states. We use this framework to sort out and quantify the energy dissipated in quasistatic fluid‐fluid displacements in disordered media. Numerical computations of imbibition–drainage cycles in a quasi‐2D medium with gap thickness modulations (imperfect Hele‐Shaw cell) show that energy dissipation in quasistatic displacements is due to abrupt changes in the fluid‐fluid configuration between consecutive metastable states (Haines jumps), and its dependence on microstructure and gravity. The relative importance of viscous dissipation is deduced from comparison with quasistatic experiments.

Keywords

• flows in porous media
• Hele‐Shaw flows
• nonequilibrium and irreversible thermodynamics
• random and disordered media
• driven interfaces
• quasistatic displacements