Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

Abstract

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates ͑adsorption͒ and liquid bridges ͑adsorption and desorption͒ which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.

Modeling Relaxation Processes for Fluids in Porous Materials Using Dynamic Mean Field Theory: An Application to Partial Wetting

“…Our presentation of DMFT follows closely that of Monson [37], which is in turn based on that of Gouyet et al [21]. The theory gives an approximation to the time evolution of the density distribution averaged over an ensemble of many kinetic Monte Carlo simulations of the lattice gas model.…”

“…For a nearest neighbor lattice gas in an external field the Hamiltonian can be written [14,16,22,37,48] …”

“…The approach we take here is to develop a theory of the time dependent molecular density distribution in the system [37]. We then consider the dynamic evolution of this distribution in terms of the probabilities of transitions between states of the system governed by a master equation.…”

“…In previous work we have applied the DMFT to model pores where the solidfluid interaction was sufficiently strong to give rise to complete wetting [37,38] (in referring to wetting states here we have in mind the behavior of the free solid-fluid interface for the same solid-fluid interaction as we have for the fluid in the pore). This is the typical situation encountered in nitrogen adsorption experiments.…”

On a New Mechanism for Separating two Components in a Stationary Flow through Mesopores

“…It further is known that the density of the liquid formed in the pores is somewhat smaller than of the liquid under normal conditions at equilibrium. Thus, the situation of capillary condensation leads to so called 'expanded' liquids [1]. The related pressure in the liquid is not only small, but usually takes on even negative values.…”