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Observation of the Anomalously Slow (Power-Law) Relaxation of the System of Interacting Liquid Nanoclusters in the Disordered Confinement of a Random Porous Medium

The time evolution of the system of water in the Libersorb 23 (L23) disordered nanoporous medium after the complete filling at excess pressure and the subsequent removal of excess pressure has been studied. It has been found that three stages can be identified in the relaxation of the L23-water system under study. At the first stage, a portion of water at the removal of excess pressure rapidly flows out in the pressure reduction time, i.e., following a decrease in the pressure. It has been shown that, at temperatures below the dispersion transition temperature $T < T_d = 284 K$, e.g., $T = 277 K$, the degree of filling $θ$ decreases from 1 to 0.8 in 10 s, following the variation of excess pressure. At the second stage of relaxation, the degree of filling $θ$ varies slowly according to a power law $θ \sim t^{-α}$ with the exponent $α < 0.1$ in the time $t \sim 10^5$ s. This corresponds to a slow relaxation of the formed metastable state of the nonwetting liquid in the porous medium. At the third stage when $t > 10^5$ s, the formed metastable state decays, which is manifested in the transition to a power-law dependence $θ(t)$ with a larger exponent. The extrusion-time distribution function of pores has been calculated along with the time dependence of the degree of filling, which qualitatively describes the observed anomalously slow relaxation and crossover of the transition to the stage of decay with a power-law dependence $θ(t)$ with a larger exponent. It has been shown that the relaxation and decay of the metastable state of the confined nonwetting liquid at $θ>{θ_c}$ are attributed to the appearance of local configurations of liquid clusters in confinement and their interaction inside the infinite percolation cluster of filled pores.