Friction based modeling of multicomponent transport at the nanoscale

Abstract

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.

Prediction of carbon dioxide permeability in carbon slit pores

“…The self-and collective diffusivities increase with increasing pore width (H) and temperature (T), which is in accord with the observation of Jepps et al [26] for methane in carbon slit pores. As the pore width increases, the friction between the molecules and pore wall is effectively reduced at sizes below that at which levitation occurs and a maximum in diffusivities is found [45,46]. For comparison, the self-diffusivity of CO 2 ranged from 0.7 × 10 −9 to 1.0 × 10 −9 m 2 /s over 0.1-30 bar at 273 K in a ZIF (zeolitic imidazolate framework) with the pore spacing of d = 1.03 nm [47], using a three-charged LJ potential of rigid linear CO 2 molecule.…”

Molecular transport in nanopores: a theoretical perspective

“…The superposition of the viscous and diffusive contributions used in the derivation of eqn (56) and (57) is, however, arbitrary. Furthermore, assuming the partial viscosities to be equivalent to the mixture viscosity is incorrect, as it violates the condition that the sum of the shear stresses on all the components must match the total shear stress on the mixture.…”

“…All of the above problems have been overcome in a recent modification of eqn (43) to not only incorporate the LADM with a Newtonian shear stress model, but also a distributed friction coefficient, leading to the equation of change for species i, 56 …”

“…Fig. 24 56 depicts the variation of the Onsager coefficients with methane density for a CH 4 /H 2 mixture, in cylindrical silica pores of diameter 1.57 nm and 3.84 nm at 300 K for an adsorbed H 2 density of 1 nm À3 , calculated by means of the distributed friction model and by EMD simulations. Despite the widely different mobilities of H 2 and CH 4 , the agreement of the model with simulation is excellent when the density distribution is accounted for (Fig.…”

Hybrid Reverse Monte Carlo simulation of amorphous carbon: Distinguishing between competing structures obtained using different modeling protocols

“…The inapplicability of conventional transport models for materials with nanoscale confinement is now well established [2][3][4]. Further, for amorphous materials, the geometry of the pore wall, as well as morphology of the solid-fluid interface is highly irregular at microscopic scales, so that the complexity of the boundary conditions makes the established theoretical analysis of the particle motion and fluid transport essentially intractable [5].…”