Hierarchical Reference Theory of critical fluids in disordered porous 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.

23 pages. Article for Luciano Reatto's festschrift

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Cited by in corpus (4)

• The nonperturbative functional renormalization group and its applications
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
• Same universality class for the critical behavior in and out of equilibrium in a quenched random field