Kinetics of the dispersion transition and nonergodicity of a system consisting of a disordered porous medium and a nonwetting liquid

Abstract

An approach has been proposed for the description of the dispersion transition of a nonwetting liquid in confinement. This approach describes intrusion and extrusion processes for the ground state of a disordered porous medium, which is characterized by the formation of a fractal percolation cluster. The observed transition of the system of liquid nanoclusters in confinement to a metastable state in a narrow range of degrees of filling and temperatures has been explained by the appearance of a potential barrier owing to fluctuations of the collective "multiparticle interaction" of liquid nanoclusters in neighboring pores of different sizes on the shell of the fractal percolation cluster of filled pores. The energy of the metastable state forms a potential relief in the space of the porous medium with many maxima and minima. The volume of the dispersed liquid in the metastable state has been calculated within the analytical percolation theory for the ground state with the infinite percolation cluster. The extrusion-time distribution function of pores has been calculated. It has been found that the volume of the nonwetting liquid remaining in the porous medium decreases with time according to a power law. Relaxation in the system under study is a multistep process involving discontinuous equilibrium and overcoming of many local maxima of the potential relief. The formation of the metastable state of the trapped nonwetting liquid has been attributed to the nonergodicity of the disordered porous medium. The model reproduces the observed dependence of the volume of the dispersed liquid both on the degree of filling and on the temperature.

On the scaling of the interface energy of the liquid clusters in the disordered nanoporous medium

“…In references [6,7], it was shown that at the intrusion and extrusion of liquids, the consideration of such non-uniform geometric configurations can be done by the functions W and W 1 , respectively. In the case of extrusion, the quantity W ðz; θ 1 Þ takes into account the interaction liquid clusters in neighbouring pores and is determined as the difference between the average number of menisci before and after the depletion of the pore per nearest neighbour.…”

“…According to the authors in References [6,7] and considering a narrow pore size distribution of the porous medium, it can be assumed that the function W 1 depends only on the degree of filling, and the number of nearest neighbours can be taken constant, then with this in mind, the sum in Equation (1) can be calculated analytically:…”

“…At θ 1 > θ c (the percolation cluster of filled pores appearing at the degree of filling θ > θ c ), the function W ðθ 1 > θ c Þ should be defined as the average difference between the numbers of menisci after and before the depletion of the pore [6,7]:…”

“…Growing interest in the practical use of systems, which consist of a disordered porous medium immersed in the non-wetting liquids in various fields, such as dampers, [1] actuators [2] and smart materials, [3] raises many new fundamental questions. It is known [4][5][6] that the spontaneous transition of the liquid into a dispersed state which is characterised by the formation of liquid clusters in the interconnected pores occurs at the critical value of the excess pressure in the system consisting of a non-wetting liquid and nanoporous medium. Recently, it has been found [5][6][7] that at the critical values of the temperature and the initial degree of filling in such systems a dispersion transition may be experienced when, at reduced excess pressure, liquid clusters in the pores turn into a metastable state.…”

“…It is known [4][5][6] that the spontaneous transition of the liquid into a dispersed state which is characterised by the formation of liquid clusters in the interconnected pores occurs at the critical value of the excess pressure in the system consisting of a non-wetting liquid and nanoporous medium. Recently, it has been found [5][6][7] that at the critical values of the temperature and the initial degree of filling in such systems a dispersion transition may be experienced when, at reduced excess pressure, liquid clusters in the pores turn into a metastable state. At temperatures higher than the critical temperature, a dispersion transition is not observed.…”