The last publication from Alex Hansen and Santanu Sinha entitled “Thermodynamics-like formalism for immiscible and incompressible tow-phase flow in porous media” was selected as cover for the journal Entropy in February 2025 (Volume 27, issue 2).
Congratulations!
The picture on the cover shows a porous medium stylized as a network of pores. Two immiscible fluids move through the pores—one is red, and the other is blue. Imagine now, billions of such pores forming, e.g., a porous geological formation. At such scales, the porous medium would act as a continuum. And here is the central question we pose: How should we describe the simultaneous flow of two immiscible fluids at this continuum scale? We solve the problem by considering a representative elementary area orthogonal to the flow direction, shown as a black disk. We may describe the dynamics of the flow through the disk in the context of equilibrium statistical mechanics. This would lead to a thermodynamics-like formalism at the continuum scale, which we describe in detail in the paper.
Abstract:
It is possible to formulate an immiscible and incompressible two-phase flow in porous media in a mathematical framework resembling thermodynamics based on the Jaynes generalization of statistical mechanics. We review this approach and discuss the meaning of the emergent variables that appear, agiture, flow derivative, and flow pressure, which are conjugate to the configurational entropy, the saturation, and the porosity, respectively. We conjecture that the agiture, the temperature-like variable, is directly related to the pressure gradient. This has as a consequence that the configurational entropy, a measure of how the fluids are distributed within the porous media and the accompanying velocity field, and the differential mobility of the fluids are related. We also develop elements of another version of the thermodynamics-like formalism where fractional flow rather than saturation is the control variable, since this is typically the natural control variable in experiments.
Read the publication here: Thermodynamics-like Formalism for Immiscible and Incompressible Two-Phase Flow in Porous Media