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We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements ( approximately 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics.

Using Compressibility Factor as a Predictor of Confined Hard-Sphere Fluid Dynamics