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

Edison, John R.; Monson, P. A.

doi:10.1007/s10909-009-9916-9

Cited by 36 publications

(32 citation statements)

References 51 publications

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“…Ref. 65 explains that one way of obtaining a physically reasonable value for the particle-vacancy jump attempt rate w 0 is by comparing between estimated (D) and experimental (D s ) self-diffusion coefficients. IfD is obtained from KMC simulations in dimensionless units, the desired correspondence would be D s =Da 2 w 0 , where a is the lattice spacing.…”

Section: Discussionmentioning

confidence: 99%

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Castro

Sollich

2017

Phys. Chem. Chem. Phys.

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New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation after a quench into the coexistence region. The critical point and the relevant spinodal curves are determined analytically, with the latter depending only on three moments of the overall composition. The results for the early-time spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal that excludes fractionation and so allows only density fluctuations at fixed composition. This effect occurs for dense systems, in agreement with a conjecture by Warren that, at high density, fractionation should be generically slow because it requires inter-diffusion of particles. We verify this conclusion by showing that the observed qualitative changes disappear when direct particle-particle swaps are allowed in the dynamics. Finally, the rich behaviour beyond the spinodal regime is examined, where we find that the evaporation of gas bubbles with strongly fractionated interfaces causes long-lived composition heterogeneities in the liquid phase; we introduce a two-dimensional density histogram method that allows such effects to be easily visualized for an arbitrary number of particle species.

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Section: Discussionmentioning

confidence: 99%

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Castro

Sollich

2017

Phys. Chem. Chem. Phys.

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“…[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 …”

Section: Model and Theorymentioning

confidence: 99%

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

2014

Self Cite

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We apply dynamic mean field theory to study relaxation dynamics for lattice models of fluids confined in linear pores with side streams and with ink bottle structures. Our results show several mechanisms for how the pore structure affects the dynamics, and these are amplified in longer pores. An important conclusion of this work is that features such as side streams and ink bottle segments can substantially slow the equilibration of fluids confined in long pore systems where the pore lengths can be more than 100 micrometers, such as in porous silicon. This may make it difficult to properly equilibrate these systems for states close to those where the pores should be completely filled with liquids. The presence of trapped bubbles in the system may change the desorption characteristics of the system and the shape of the hysteresis loops.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Kikkinides

Monson

2015

The Journal of Chemical Physics

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Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

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

Cited by 36 publications

References 51 publications

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

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

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

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