Diffusion of Alkane Mixtures in Zeolites:  Validating the Maxwell−Stefan Formulation Using MD Simulations

Krishna, Rajamani; Baten, J.M. van

doi:10.1021/jp044257l

Cited by 130 publications

(147 citation statements)

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“…The commonly used uniform fluid approximation [3,5,9,10,15] is clearly in serious error, particularly for micropores. Other developments, specific to micropore transport [17,18] and therefore neglecting viscous contributions, also involve this questionable uniform fluid assumption but have shown much success due to the use of phenomenological coefficients, some of which are empirical.…”

Section: Prl 100 236103 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Modeling Mixture Transport at the Nanoscale: Departure from Existing Paradigms

Bhatia

Nicholson

2008

Phys. Rev. Lett.

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We present a novel theory of mixture transport in nanopores, which represents wall effects via a species-specific friction coefficient determined by its low density diffusion coefficient. Onsager coefficients from the theory are in good agreement with those from molecular dynamics simulation, when the nonuniformity of the density distribution is included. It is found that the commonly used assumption of a uniform density in the momentum balance is in serious error, as is also the traditional use of a mixture center of mass based frame of reference. DOI: 10.1103/PhysRevLett.100.236103 PACS numbers: 68.43.Jk A fundamental understanding of the processes affecting the transport of fluid mixtures in nanoscale confinements is crucial to numerous emerging applications in nanotechnology, materials science, membrane science, and biology, as well as a host of other areas. For a long time, the modeling of mixture transport has relied on highly respected statistical mechanical theories, which relate the hydrodynamic stress tensor for any component to the rate of strain for the mixture motion as a whole [1,2]. Such theories involve expansion of the species velocities around the mixture center of mass velocity, but despite their rigor they have failed to provide satisfactory solutions to problems involving mixture transport over a wide range of densities. Indeed, there exists no definitive treatment even for a simple classical experiment known as the Stefan tube. The approaches have recently been criticized by Kerkhof and Geboers [3], who suggest expansions around the individual species center of mass velocities, as they can be very different from the mixture center of mass velocity. While also considered earlier by Snell, Aranow, and Spangler [4], such an expansion has not evoked much interest due to its complexity and the use of partial viscosities for which there is no simple prescription.For porous materials, perhaps the most commonly used approach is the dusty gas model [5], which also uses of the mixture center of mass as a frame of reference. Additionally, the approach neglects density gradients arising from the fluid-solid interaction and relies on the classical Poiseuille flow model for uniform fluids. Further, it neglects dispersive interactions, demonstrated by us [6,7] to be as much as an order of magnitude in error in estimating the low pressure diffusivity. It is the neglect of dispersive interactions which leads to the flux expression comprising additive viscous and diffusive terms, the latter including Knudsen (i.e., wall-mediated) diffusion. Thus, there exists no unambiguous way to introduce wall effects in the modeling. Finally, there is much confusion as to whether Onsager coefficients relate to the total flux or the diffusive component alone [8][9][10].Here we present a tractable theory that overcomes all of the above limitations and for the first time is able to handle mixture transport in nonuniform fluids from the nanopore to the mesopore range of confinement. We consider the one-dimensional axial ...

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Section: Prl 100 236103 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Modeling Mixture Transport at the Nanoscale: Departure from Existing Paradigms

Bhatia

Nicholson

2008

Phys. Rev. Lett.

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“…9͑d͒, showing the large deviation between simulation and theory when the density field is taken to be uniform at the mean pore density. The approximation of a uniform pore density is common to existing formulations, 9,10,23,24,[28][29][30][31][32][33][34]55 but is clearly in serious error, particularly for micropores where the inhomogeneity in the potential energy profile is stronger. Nevertheless, as indicated earlier, success in interpreting transport data from simulation or experiment is often found because of the presence of a few empirical phenomenological parameters.…”

Section: Transport In Binary H 2 /Ch 4 Mixturesmentioning

confidence: 99%

“…Here j i is the total flux of species i, ٌ j the chemical potential gradient of species j and ⍀ ij the Onsager coefficients. For narrow nanopores, or micropores ͑typically having diameter Ͻ2 nm͒, there has been much work reported on the development of phenomenological models for multicomponent transport by Krishna and co-workers, [30][31][32][33][34] based on the Maxwell-Stefan approach. These models also overlook the presence of inhomogeneity due to adsorption forces which, as will be shown, has a strong influence on the equilibrium and transport properties in narrow micropores.…”

Section: Introductionmentioning

confidence: 99%

“…These models also overlook the presence of inhomogeneity due to adsorption forces which, as will be shown, has a strong influence on the equilibrium and transport properties in narrow micropores. Nevertheless, much success in modeling mixture transport in microporous zeolites 31,32 and carbon nanotubes 34 has been reported, using phenomenological parameters from pure component transport. The prediction of these parameters based on molecular principles, as well as the consideration of inhomogeneity in micropores, remain fundamental challenges.…”

Section: Introductionmentioning

confidence: 99%

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Friction based modeling of multicomponent transport at the nanoscale

Bhatia

Nicholson

2008

The Journal of Chemical Physics

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We present here a novel theory of mixture transport in nanopores, which considers the fluid-wall momentum exchange in the repulsive region of the fluid-solid potential in terms of a species-specific friction coefficient related to the low density transport coefficient of that species. The theory also considers nonuniformity of the density profiles of the different species, while departing from a mixture center of mass frame of reference to one based on the individual species center of mass. The theory is validated against molecular dynamics simulations for single component as well as binary mixture flow of hydrogen and methane in cylindrical nanopores in silica, and it is shown that pure component corrected diffusivities, as well as binary Onsager coefficients are accurately predicted for pore sizes sufficiently large to accommodate more than a monolayer of any of the components. It is also found that the assumption of a uniform density profile can lead to serious errors, particularly at small pore diameter, as also the use of a mixture center of mass frame of reference. The theory demonstrates the existence of an optimum temperature for any fluid, at which the fractional momentum dissipation due to wall friction is a minimum.

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“…2 is often referred to as the Green-Kubo relation. Similar equations exist for computing transport (collective) diffusion [15,18,19].…”

Section: Introductionmentioning

confidence: 99%