Gibbs Ensemble Monte Carlo Simulation of Fluids in Confinement: Relation between the Differential and Integral Pressures

Erdős, Máté; Galteland, Olav; Bedeaux, Dick; Kjelstrup, Signe; Moultos, Othonas A.; Vlugt, Thijs J. H.

doi:10.3390/nano10020293

Cited by 22 publications

(25 citation statements)

References 33 publications

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“…In particular, one would like to be able to predict how thermodynamic properties of the system change with size. We have earlier documented how the thermodynamic factors and the pressures of some systems scale with a characteristic inverse system size (surface area over volume) [8][9][10]. The aim of the present work is to continue this line of work and present a geometric scaling law for the pressure of a nanopore.…”

Section: Introductionmentioning

confidence: 80%

“…This assumption was tested using Gibbs ensemble Monte Carlo simulations for two values of p f (0.2 and 6.0 reduced units). The method is the same as reported recently by Erdős et al [10]. In the simulations, two simulation boxes were defined.…”

Section: Gibbs Ensemble Monte Carlomentioning

confidence: 99%

“…Also the integral pressure, p, as defined by Hill was required to describe the degree of confinement in the REV. In Hill's [11] terminology, one distinguishes between the integral pressure p, and the differential pressure, p. Erdos et al [10] provided an expression for the ratio of the driving forces for adsorption into a pore, by means of the integral and differential pressures. They expressed the ratio by the cross-correlation of the volume and the integral pressure.…”

Section: Introductionmentioning

confidence: 99%

“…Hill defined the difference of the two pressures times the volume by the subdivision potential = (p − p)V [11]. The integral pressure can differ significantly from the differential pressure in confined systems [10,18]. In the limit of a bulk fluid, they are the same, however.…”

Section: Introductionmentioning

confidence: 99%

“…Molecular dynamics and Monte Carlo simulations [10,21] are excellent tools for equilibrium studies of confined systems. Two fluid phases will be simulated in a slit pore of varying width.…”

Section: Introductionmentioning

confidence: 99%

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Two-Phase Equilibrium Conditions in Nanopores

et al. 2020

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It is known that thermodynamic properties of a system change upon confinement. To know how, is important for modelling of porous media. We propose to use Hill’s systematic thermodynamic analysis of confined systems to describe two-phase equilibrium in a nanopore. The integral pressure, as defined by the compression energy of a small volume, is then central. We show that the integral pressure is constant along a slit pore with a liquid and vapor in equilibrium, when Young and Young–Laplace’s laws apply. The integral pressure of a bulk fluid in a slit pore at mechanical equilibrium can be understood as the average tangential pressure inside the pore. The pressure at mechanical equilibrium, now named differential pressure, is the average of the trace of the mechanical pressure tensor divided by three as before. Using molecular dynamics simulations, we computed the integral and differential pressures, p ^ and p, respectively, analysing the data with a growing-core methodology. The value of the bulk pressure was confirmed by Gibbs ensemble Monte Carlo simulations. The pressure difference times the volume, V, is the subdivision potential of Hill, ( p − p ^ ) V = ϵ . The combined simulation results confirm that the integral pressure is constant along the pore, and that ϵ / V scales with the inverse pore width. This scaling law will be useful for prediction of thermodynamic properties of confined systems in more complicated geometries.

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Section: Introductionmentioning

confidence: 80%

Section: Gibbs Ensemble Monte Carlomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Molecular dynamics and Monte Carlo simulations [10,21] are excellent tools for equilibrium studies of confined systems. Two fluid phases will be simulated in a slit pore of varying width.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two-Phase Equilibrium Conditions in Nanopores

et al. 2020

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Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

et al. 2022

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Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between $$5.7 \times {10^{-20}} \hbox {m}^2$$ 5.7 × 10 - 20 m 2 and $$5.5 \times {10^{-17}} \hbox {m}^2$$ 5.5 × 10 - 17 m 2 , showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.

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