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

Thermodynamics of fluctuations based on time-and-space averages

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

The Formation and Decay of an Unstable State of a Suspension of Hydrophobic Nanoporous Particles under Rapid Compression

The study of non-wetting liquid transport in a nanoporous medium is stimulated by the possible use of this process to absorb or accumulate mechanical energy. The filling of nanopores of suspended particles with a non-wetting liquid under decay of the unstable state, when the pressure increase rate is much higher than the rate of volume change, is studied. Based on the new experimental data and a theoretical model of the interacting modes of the spontaneous filling and filling under rapid compression, a picture of the percolation transition and a mechanism of liquid transport under such conditions are proposed. It is shown that a new dynamic filling threshold P0 is reached. It is shown that the filling of the porous medium is the result of the slow mode of impact compression when the fast mode of spontaneous filling is continuously adjusted to the slow mode on a small time scale. The theoretical model of the interacting modes is based on the solving of a system of kinetic equations for the distribution functions f(n,t) and F(n,t) clusters of filled pores under rapid compression, respectively. It is shown that filling at P=const corresponds to the non-dissipative transport of liquid on a time scale smaller than the characteristic filling time. The proposed model quantitatively describes the experimental data. So, the response of suspension to impact is characterized by the positive feedback.

Anomalously slow relaxation of interacting liquid nanoclusters confined in a porous medium

Anomalously slow relaxation of clusters of a liquid confined in a disordered system of pores has been studied for the (water-L23 nanoporous medium) system. The evolution of the system of confined liquid clusters consists of a fast formation stage followed by slow relaxation of the system and its decay. The characteristic time for the formation of the initial state is τ(p)∼10 s after the reduction of excess pressure after complete filling. Anomalously slow relaxation has been observed for times of 10(1)-10(5) s, and decay has been observed at times of >10(5) s. The time dependence of the volume fraction θ of pores filled with the confined liquid is described by a power law θ∼t(-α) with the exponent α<0.15. The exponent α and temperature dependence α(T) are qualitatively described theoretically for the case of a slightly polydisperse medium in a mean-field approximation with the inclusion of the interaction of liquid clusters and averaging over various degenerate local configurations of clusters. In this approximation, slow relaxation is represented as a continuous transition through a sequence of metastable states of the system of clusters with a decreasing barrier.