Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field

Abstract

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.

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

“…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.…”

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

“…It is also possible to configure a different type of steady state where we remove the periodic boundaries in the x-direction and place a control layer at each end of the system. If the control layers have different chemical potentials then the system can describe steady state mass transfer of fluid through the pore, as has been done by Matuszak et al [32].…”

“…It has its origin in the dynamic mean field theories of the Ising [43] and binary alloy [30] models first developed almost 20 years ago and reviewed by Gouyet et al [21]. It has also been used to model diffusion in membranes and bulk fluids by Matuszak et al [31][32][33].…”

Diffusion in fluids with large mean free paths: Non-classical behavior between Knudsen and Fickian limits

“…A similar limitation was obtained using a phenomenological derivation of the differential mass balance and finite-difference diffusion equations [11,17]. (Some numerical aspects of solving finite-difference thermodynamic equations with multiple solutions were considered in [18,19] which can be useful for analysis of finite differences in fluid equilibrium [20][21][22] and diffusion [23][24][25]. )…”