Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

Abstract

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed.

Spreading in narrow channels

“…[25,26,27,28,29,30,31,32,33,34]). Such systems show the interesting feature of non-diffusive behavior of tracer particles, which stimulated experimental (see, e.g., Refs.…”

“…Such systems show the interesting feature of non-diffusive behavior of tracer particles, which stimulated experimental (see, e.g., Refs. [33,34]) and numerical [27,29,30,31] interest. Here we present a lattice model for ultrathin films in which multiple occupancy of a site is allowed (generalizing the single-occupancy model of Refs.…”

Membrane Separation Technology in Carbon Capture

“…The gas travels with speed between collisions and loses all the momentum when colliding on the wall. This model is a more recent development in mass transfer theory by Bhatia et al [78,79]. From Newton's law,…”

Momentum Transfer Effects in the Transport of Adsorbate at a Nano-Patterned Surface

“…Recently, we have demonstrated Nicholson 2002, 2003;Bhatia et al 2004Bhatia et al , 2005) that the transport flux can be expressed as a combination of two momentumtransfer processes: that between fluid molecules --associated with viscous phenomena --and that between the fluid and the surface --associated with friction. The latter involves the population of molecules vibrating around the minimum of the adsorption potential well, with wall collisions occurring as molecular trajectories are reversed in the steeply repulsive side of this minimum.…”

“…The model has been tested against simulation in model pores with ideal diffuse reflection at the surface, as first proposed by Knudsen in discussing his classical experiments on gas flow in glass capillaries. With more realistic, atomically detailed, surfaces, it has been found that the ideal diffuse reflection hypothesis is not valid (Arya et al 2003a,b;Bhatia et al 2004;Bhatia et al 2005;Skoulidas et al 2002;Sokhan et al 2001;Sokhan and Quirke 2004). Indeed, it is very far removed from the behaviour observed for smooth graphitic surfaces, where the molecular reflection condition is close to being specular in nature.…”