Cooperative transport of a nonwetting liquid in a random system of pores

A new mechanism has been proposed for the cooperative transport of a nonwetting liquid in a nanoporous medium. The description of transport is based on the theory of critical dynamics of multiscale phenomena in atomic systems. Transport is described as a time-multiscale process of interaction of a fluctuating filling–escape mode, macroscopic spontaneous filling mode, and filling mode caused by the critical pressure of compression of a dynamic percolation transition. The model is based on the solution of the system of kinetic equations for the distribution function of accessible and filled pores, which allows calculating macroscopic quantities describing processes at various time scales. A case where macroscopic transport modes are developed simultaneously in two different time scales is considered. A “nanoscopic” model of filling of nanopores under the development of the spontaneous mode taking into account the conservation of the volume of the suspension at the equality of rates of development of the modes at different time scales has been proposed. The predicted time dependences of the flux and volume of filled pores correspond to dissipationless transport in the system of nanopores. Theoretical dependences describe known and new experimental data. Unusual dynamic properties correspond to the properties of systems with positive feedback.