Dynamic mean field theory of condensation and evaporation processes for fluids in porous materials: Application to partial drying and drying

Abstract

We study the dynamics of evaporation for lattice gas models of fluids in porous materials using a recently developed dynamic mean field theory. The theory yields a description of the dynamics that is consistent with the mean field theory of the thermodynamics at equilibrium. The nucleation processes associated with phase changes in the pore are emergent features of the dynamics. Our focus is on situations where there is partial drying or drying in the system, associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We consider two systems in this work: (i) a two-dimensional slit pore geometry relevant to the study of adsorption/desorption or intrusion/extrusion dynamics for fluids in porous materials and (ii) a three dimensional slit pore modeling a pair of square plates in a bath of liquid as used in recent theoretical studies of dewetting processes between hydrophobic surfaces. We assess the theory by comparison with a higher order approximation to the dynamics that yields the Bethe-Peierls or quasi-chemical approximation at equilibrium.

Modeling the Influence of Side Stream and Ink Bottle Structures on Adsorption/Desorption Dynamics of Fluids in Long Pores

“…[24][25][26][30][31][32][33][34] The theory provides a mean field approximation to the master equation for the dynamics of a lattice gas 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 …”

“…Several applications of the theory have been published in recent years. [25][26][27][28][29] In a recent paper we applied DMFT to the case of the filling of closed end pores and were able to identify two dynamic regimes depending on the pore length. 30 In this paper we build on that work by applying DMFT to the study of some of the pore geometries found in the TEM studies of Psi, specifically ink bottle structures and side stream pores, as well as to long chains of such pore geometries.…”

Fluids Confined in Porous Materials: Towards a Unified Understanding of Thermodynamics and Dynamics

“…We can consider higher order approximations beyond the mean field approximation using the path probability method [58]. Our work on this so far indicates that the qualitative picture is unchanged by going to the higher order theory [35].…”

“…Implementation of DMFT involves a numerical solution of Eq. (6) and Euler's method [27,35] is typically used. More implementation details are described in [27, 34 -36].…”

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

“…Since then, there have been numerous refinements and applications of the DDFT methods for both continuous and discrete systems, ranging from spinodal decomposition to molecular diffusion, wetting, condensation-evaporation, imbibition-drainage, etc. 5,[7][8][9][10][11][12] Based on its formal derivation, the DDFT method describes the relaxation of Brownian particles in a medium, with two important approximations: (a) the adiabatic approximation and (b) that the local velocity distribution is close to the Maxwellian. 13 The former assumption implies that one can approximate the spatial correlations in the non-equilibrium fluid with those of an equilibrium fluid with the same one-body density profile.…”