Self-diffusivity of dense confined fluids
Corral-Casas C, Gibelli L, Borg MK, Li J, Al-Afnan SFK, Zhang Y, Journal of Chemical Physics 33 :082009 (2021).
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Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffu- sive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick’s law, provided boundary effects are considered when using Fick’s setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.