Anomalously slow relaxation of the system of liquid clusters in a disordered nanoporous medium according to the self-organized criticality scenario

We propose a physical model of a relaxation of states of clusters of nonwetting liquid confined in a random nanoporous medium. The relaxation is occurred by the self-organized criticality (SOC) scenario. Process is characterized by waiting for fluctuation necessary for overcoming of a local energy barrier with the subsequent avalanche hydrodynamic extrusion of the liquid by surface forces of the nonwetting frame. The dependence of the interaction between local configurations on the number of filled pores belonging to the infinite percolation cluster of filled pores serves as an internal feedback initiating the SOC process. The calculations give a power-law time dependence of the relative volume θ of the confined liquid θ∼t−ν (ν∼0.2) as in the picture of relaxation in the mean field approximation. The model of the relaxation of the porous medium with the nonwetting liquid demonstrates possible mechanisms and scenarios of SOC for relaxation of other disordered systems.