Description of far-from-equilibrium processes by mean-field lattice gas models

Gouyet, J. F.; Plapp, Mathis; Dieterich, W.; Maass, Philipp

doi:10.1080/00018730310001615932

Cited by 98 publications

(139 citation statements)

References 197 publications

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“…Our presentation of MFKT follows closely that of Gouyet et al 21 We begin by writing the ensemble average density for site i at time t i ͑t͒ as…”

Section: B Mean Field Kinetic Equationsmentioning

confidence: 99%

“…A significant difference is that this lattice based theory yields an explicit expression for the mobility in terms of the local densities 21 based on the dynamics used to describe the flux between sites-Metropolis transition probabilities in this case. The question of whether to incorporate stochastic noise into DDFT's as a means of modeling fluctuations has been discussed in the literature.…”

Section: Relationship With Cahn-hilliard and Dynamic Density Functmentioning

confidence: 99%

“…[27][28][29][30][31] As emphasized by Gouyet et al, however, MFKT incorporates the dependence of the mobility on the local density. 21 For long times, the theory yields thermodynamic behavior identical to that of the lattice model in mean field theory ͑e.g., the Bragg-Williams approximation for the case of a binary alloy͒. The theory provides an approximation to the dynamics obtained by averaging over an ensemble of trajectories generated by Kawasaki dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, we adapt the analysis presented by Gouyet et al 21 to the case of a fluid confined in a pore, but it is important to note that the equations we derive are equivalent to those presented recently by Aranovich and co-workers [32][33][34] in their work on diffusion in porous materials. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a dynamic Monte Carlo simulation of the system, as a theory of diffusion, or as a DDFT.…”

Section: Introductionmentioning

confidence: 99%

“…A recent and comprehensive review by Gouyet et al 21 describes a mean field approach to Kawasaki dynamics, referred to as mean field kinetic theory ͑MFKT͒, with an emphasis on the phase separation in solid state metal alloys. The approach originates from the works of Martin 22 and Penrose.…”

Section: Introductionmentioning

confidence: 99%

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

Monson

2008

The Journal of Chemical Physics

100

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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.

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“…Our presentation of MFKT follows closely that of Gouyet et al 21 We begin by writing the ensemble average density for site i at time t i ͑t͒ as…”

Section: B Mean Field Kinetic Equationsmentioning

confidence: 99%

Section: Relationship With Cahn-hilliard and Dynamic Density Functmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Monson

2008

The Journal of Chemical Physics

100

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Lattice Model of Fluid Transport in Mixed Matrix Membranes

Yuan

Sarkisov

2022

Advcd Theory and Sims

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This work offers a computationally efficient theoretical framework to investigate transport phenomena in complex systems such as mixed matrix membranes (MMMs). It is demonstrated here that a wide variety of heterogeneous, disordered geometries can be constructed using lattice models. These geometries combined with the dynamic mean field theory (DMFT) provide useful insights on the distribution of density and flux in the structures. From this work, the DMFT emerges as a theoretical playground to explore transport phenomena in MMMs under a variety of conditions and probe some of the assumptions involved in the commonly used macroscopic models. As a case study, a comparison of the predictions of the DMFT is considered with several classical macroscopic theories. In the preliminary observations, the study points to a much greater impact of the pore blocking effects on the overall transport of the composite system in comparison with the macroscopic models.

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Modeling permporometry of mesoporous membranes using dynamic mean field theory

et al. 2015

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Mesoporous inorganic membranes have significant potential for important small‐molecule separations like carbon dioxide recovery from stack emissions. However, tailoring materials for a given separation remains an outstanding problem. Preferential adsorption, layering and capillary effects, and surface flow are key mechanisms that determine permeation rates and are ultimately linked to the mesopore characteristics. To further the understanding of these systems, a modeling approach based on dynamic mean field theory, which has previously been used to study the dynamics of adsorption in mesoporous materials, is proposed. This theory describes both relaxation dynamics and nonequilibrium steady states in membranes and is fully consistent with a mean field density functional theory of the thermodynamics. The capabilities and promise of the approach by modeling a permporometry experiment, in which a light gas permeates through a mesopore in the presence of a condensable vapor at a controlled relative pressure, are demonstrated. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2958–2967, 2015

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Description of far-from-equilibrium processes by mean-field lattice gas models

Cited by 98 publications

References 197 publications

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

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

Lattice Model of Fluid Transport in Mixed Matrix Membranes

Modeling permporometry of mesoporous membranes using dynamic mean field theory

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