Predicting diffusivities in dense fluid mixtures

Bonilla

Phys. Chem. Chem. Phys.

2011

149

154

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.

Section: Remains)mentioning

confidence: 99%

Molecular transport in nanopores: a theoretical perspective

Bonilla

Phys. Chem. Chem. Phys.

2011

149

154

“…The bulk viscosity, η(F), and self-diffusivity, D 11 (F), may be obtained by MD simulations for the pure bulk fluid, whereas the total density profile, F t (r), may be obtained from GCMC simulation or density functional theory. MD simulation-based correlations for the bulk viscosity and self-diffusivity exist for LJ fluids 44,45 and have been employed by us earlier. 37,38 However, the accuracy of such correlations is within about 20%, and in the present work, we have determined the bulk viscosity and selfdiffusivity by MD simulation.…”

Section: Theorymentioning

confidence: 99%

Modeling Self-Diffusion of Simple Fluids in Nanopores

2011

J. Phys. Chem. B

The recent frictional model of the transport of fluid mixtures in nanopores developed in this laboratory is extended here to formulate a new theory of the self-diffusion of Lennard-Jones fluids in cylindrical pores by considering the problem of diffusion of identical molecules that differ only in color. The new theory is found to predict the self-diffusivity accurately over a wide range of densities and pore sizes, extending from molecularly narrow pores to large mesopores. However, deviations from the theory appear near to the critical temperature where the correlation length of the fluid diverges and when intermolecular interactions are important in molecularly narrow pores. Under such circumstances, local averaging of the fluid-fluid density to obtain a local viscosity does not adequately capture the effects of viscous friction. A new criterion is developed for determining the significance of fluid-fluid intermolecular interactions in a nanopore by considering the ratio of oscillation times of a fluid molecule in the force field of the surrounding fluid molecules and that in the force field of the pore wall. The ratio is shown to give good predictions of the region where intermolecular interactions are important and explains the region of deviation between theory and simulation in molecularly narrow pores.

“…A number of such correlations, specifically developed for LJ as well as molecular fluids are available in the literature. [40][41][42][43][44][45] Here we have used the method of Galliéro et al 41 for the mixture viscosity, and for the mutual diffusivities we used the method of Reis et al 43 Further, equilibrium density distributions, which are required in the theory, may be obtained from either density functional theory or grand canonical Monte Carlo ͑GCMC͒ simulation. Here we have used the latter.…”

Section: Theorymentioning

confidence: 99%

Friction based modeling of multicomponent transport at the nanoscale

The Journal of Chemical Physics

2008

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.