Simulation of fluid flows in the nanometer: kinetic approach and molecular dynamic simulation

Guo, Zhaoli; Zhao, Tianshou; Xu, C.; Shi, Yong

doi:10.1080/10618560601001049

Cited by 14 publications

(18 citation statements)

References 32 publications

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“…However, the BGK approximation is known to be crude, in which the relaxation time is taken as the reciprocal of the collision frequency, and is therefore inaccurate for a nanoscale system where strong density gradients exist and mean free paths are density-dependent and not small in comparison to the pore size. No quantitative comparison of the transport properties with those from MD simulations in nanopores is reported in these papers, and the results of Guo et al 153 show only rough qualitative consistency in trends of the change of slip-length with interaction energy parameter. In an attempt to overcome the problem of a centre of mass-based frame of reference Kerkhof and Geboers 125 modified the Enskog solution of the Boltzmann equation for dilute gases by expanding around the species average velocity based frame of reference.…”

Section: Transport In the Presence Of Adsorption Fieldsmentioning

confidence: 83%

Molecular transport in nanopores: a theoretical perspective

Bhatia

Bonilla

Nicholson

2011

Phys. Chem. Chem. Phys.

150

154

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Molecular transport in nanopores plays a central role in many emerging nanotechnologies for gas separation and storage, as well as in nanofluidics. Theories of the transport provide an understanding of the mechanisms that influence the transport and their interplay, and can lead to tractable models that can be used to advance these nanotechnologies through process analysis and optimisation. We review some of the most influential theories of fluid transport in small pores and confined spaces. Starting from the century old Knudsen formulation, the dusty gas model and several other related approaches that share a common point of departure in the Maxwell-Stefan diffusion equations are discussed. In particular, the conceptual basis of the models and the validity of the assumptions and simplifications necessary to obtain their final results are analysed. It is shown that the effect of adsorption is frequently either neglected, or treated on an ad hoc basis, such as through the division of the pore flux into gas-phase and surface diffusion contributions. Furthermore, while it is commonplace to assume that cross-sectional pressure is uniform, it is demonstrated that this violates the Gibbs-Duhem relation and that it is the chemical potential that essentially remains constant in the cross-section, as near-equilibrium density profiles are preserved even during transport. The Dusty Gas model and Maxwell-Stefan model for surface diffusion are analysed, and their strengths and weaknesses discussed, illustrating the use of conflicting choices of frames of reference in the former case, and the importance of assigning appropriate values for the binary diffusivity in the latter case. The oscillator model, developed in this laboratory, which is exact in the low density limit under diffuse reflection conditions, is shown to represent an advance on the classical Knudsen formula, although the latter frequently appears as a fundamental part of many transport models. The distributed friction model, also developed in this laboratory for the study of multi-component transport at any Knudsen number is discussed and compared with previous approaches. Finally, the outlook for theory and future research needs are discussed.

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Section: Transport In the Presence Of Adsorption Fieldsmentioning

confidence: 83%

Molecular transport in nanopores: a theoretical perspective

Bhatia

Bonilla

Nicholson

2011

Phys. Chem. Chem. Phys.

150

154

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“…Knudsen (1909), von Smoluchowski (1910, Pollard and Present (1948), and Mason et al (1967) described confined fluid particles as hard spheres and took into consideration the momentum exchange between the fluid particles and the solid wall when the fluid-fluid interactions could be neglected, and later considered the effect of density on the mobility of the confined gases. More recently, theoretical developments have attempted to consider dispersive and longer-ranged fluid-fluid interactions (Guo et al 2005(Guo et al , 2006. Building on the Chapman-Enskog kinetic theory approach (Davis 1992), Jepps et al (2003) provided a significant improvement in our theoretical understanding of the diffusion of confined Lennard-Jones fluids by developing the "oscillator model" theory, which is exact at low confined fluid densities (i.e., low-pressure gases).…”

Section: Properties Of Confined Fluids: Do They Differ Compared To Thmentioning

confidence: 99%

Hydrocarbon Behavior at Nanoscale Interfaces

Cole¹,

Ok²,

Striolo³

et al. 2013

Reviews in Mineralogy and Geochemistry

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“…Rigorous attempts to include long range interactions via the Chapman-Enskog kinetic theory approach 8 or other mechanical models 9 have had only limited success, and have proved intractable when the additional complexities of intermolecular interactions are incorporated. More recent approximate models 10,11 based on the Chapman-Enskog kinetic theory have yielded some qualitative success, but require further investigation and development.…”

Section: Introductionmentioning

confidence: 99%

“…With the explosive growth in new carbon and silica based nanomaterials of controlled porosity and pore size such as carbon nanotubes, MCM-41, as well as a host of other materials, [12][13][14] interest in the subject has again increased, 10,11,[15][16][17][18][19] with much effort being devoted to developing improved models of transport in nanopores. A major step forward, arising from this laboratory, has been the development 19 of a new theory for Lennard-Jones fluids, incorporating more realistic fluid-wall as well as fluid-fluid interactions, that is exact in the low density limit.…”

Section: Introductionmentioning

confidence: 99%

Anomalous transport in molecularly confined spaces

Bhatia

Nicholson

2007

The Journal of Chemical Physics

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We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.

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Simulation of fluid flows in the nanometer: kinetic approach and molecular dynamic simulation

Cited by 14 publications

References 32 publications

Molecular transport in nanopores: a theoretical perspective

Molecular transport in nanopores: a theoretical perspective

Hydrocarbon Behavior at Nanoscale Interfaces

Anomalous transport in molecularly confined spaces

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