Adsorbate Transport in Nanopores
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Adsorbate Transport in Nanopores SURESH K. BHATIA∗, OWEN G. JEPPS AND DAVID NICHOLSON Division of Chemical Engineering, The University of Queensland, Brisbane QLD 4072, Australia [email protected]
Abstract. We present a tractable theory of transport of simple fluids in cylindrical nanopores, considering trajectories of molecules between diffuse wall collisions at low-density, and including viscous flow contributions at higher densities. The model is validated through molecular dynamics simulations of supercritical methane transport, over a wide range of conditions. We find excellent agreement between model and simulation at low to medium densities. However, at high densities the model tends to over-predict the transport behaviour, due to a large decrease in surface slip that is not well represented by the model. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores. Keywords: transport phenomena, diffusion, nanopores, statistical mechanics, slip flow Introduction The problem of transport in confined spaces is one of long-standing interest, now receiving renewed attention due to its importance to the numerous applications of new materials. The history of the subject dates back to the seminal work of Knudsen (1909) and Smoluchowski (1910), subsequently extended to include the effect of intermolecular collisions (Pollard et al., 1948). Nevertheless, despite this long history, our understanding of the subject is still relatively rudimentary. Efforts to incorporate more realistic interactions have had limited success, with mechanical models fast becoming intractable. It is therefore still common to empirically treat the transport as activated, and the validity of such procedures is unclear. In larger pores the ‘dusty gas’ model (Mason, 1967) superposes diffusive and viscous flow contributions to give an overall diffusion coefficient Dt =
Do +
r 2p ρk ˆ BT 8η
∂ln( f ) ∂ln(ρ) ˆ
(1) T
The Poiseuille viscous term in Eq. (1) assumes that the density profile is homogeneous, which is inaccu∗ To
whom correspondence should be addressed.
rate in microporous transport. Work in our laboratory (Bhatia et al., 2003a,b) has refined a recent viscous model for strongly inhomogeneous transport (Bitsanis et al., 1988), introducing a slip condition to reflect the non-vanishing transport coefficient observed at low densities, and assuming that the chemical potential (rather than the pressure) is constant across the pore cross-section. These refinements yield a densitydependent transport coefficient 2 ro 1 2k B T Dto (ρ) ˆ = rρ(r ) dr ρr ˆ 2p kro ρ(ro ) 0 2 ro r dr (2) + r ρ(r ) dr ¯ )) 0 0 r η(ρ(r for temperature T , Boltzmann’s constant kB , local density ρ, locally-averaged density ρ, ¯ viscosity η, mean pore density ρ, ˆ radius at the potential minimum ro , and pore radius r p , and wall collision rate k. The viscosity is determined based on the locally averaged density. We identify diffusive and viscou
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