Hierarchical Reference Theory of critical fluids in disordered porous media

TL;DR

This paper explores the critical behavior of fluids in disordered porous media using an adapted Hierarchical Reference Theory, linking it to the universality class of the random-field Ising model and proposing a new theoretical framework.

Contribution

It develops a foundational approach for applying Hierarchical Reference Theory to fluids in disordered porous media, addressing previous limitations and connecting to the random-field Ising universality class.

Findings

Initial HRT implementation was unsatisfactory

Critical behavior aligns with the random-field Ising model

Lays groundwork for a proper HRT formulation in disordered media

Abstract

We consider the equilibrium behavior of fluids imbibed in disordered mesoporous media, including their gas-liquid critical point when present. Our starting points are on the one hand a description of the fluid/solid-matrix system as a quenched-annealed mixture and on the other hand the Hierarchical Reference Theory (HRT) developed by A. Parola and L. Reatto to cope with density fluctuations on all length scales. The formalism combines liquid-state statistical mechanics and the theory of systems in the presence of quenched disorder. A straightforward implementation of the HRT to the quenched-annealed mixture is shown to lead to unsatisfactory results, while indicating that the critical behavior of the system is in the same universality class as that of the random-field Ising model. After a detour via the field-theoretical renormalization group approach of the latter model, we finally lay out the foundations for a proper HRT of fluids in a disordered porous material.