Modeling Self-Diffusion of Simple Fluids in Nanopores

Abstract

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.

Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid

“…This potential leads to a significant reduction in the diffusion coefficient compared to that obtained with the Knudsen formulation [5]. Fig.…”

“…Parameters in Eqs. (5) and (6) can be determined with the empirical relations [10], ε/k = 0.77T c , σ = 0.841 × 10 − 8 V c 1/3 , where T c and V c are the critical temperature and critical volume, and all the quantities are in SI units. The strongly repulsive molecular forces at short range have an important effect to create the short-range order, which is the main characteristic of liquid structure [21].…”

“…To understand at the microscopic level the direct influence of confinement on molecular motion and hence on dynamical properties is still a difficult task [4]. Nevertheless, modeling the transport of fluids in narrow pores and confined spaces has attracted considerable attentions among scientists and engineers for over a century, due to its importance to a variety of applications of industrial interest [5]. Mass transfer can be principally attributed to two different mechanisms: macroscopic transport via convection and microscopic transport from diffusion.…”

“…Mass transfer can be principally attributed to two different mechanisms: macroscopic transport via convection and microscopic transport from diffusion. In pores of a few nanometers in diameter, diffusion is the primary mechanism [5]. Self-diffusion is one of the most important mass transport properties, which is the diffusion of tagged particles in a fluid where all particles are chemically identical, and it is characterized by self-diffusion coefficient.…”

“…Currently the research methods for the liquid confined in nanopores are mainly based on computer simulations [4][5][6][7]. For example, Sofas et al [8] investigated the transport properties of liquid argon flowing through a nanochannel with non-equilibrium molecular dynamics simulations; Sun et al [9] investigated the transport properties of Ar-Kr binary mixture confined in a nanochannel by equilibrium molecular dynamics simulation.…”