Knudsen minimum disappearance in molecular-confined flows

Abstract

It is well known that the Poiseuille mass flow rate along microchannels shows a stationary point as the fluid density decreases, referred to as the Knudsen minimum. Surprisingly, if the flow characteristic length is comparable to the molecular size, the Knudsen minimum disappears, as reported for the first time by Wu et al. (J. Fluid Mech., vol. 794, 2016, pp. 252–266). However, there is still no fundamental understanding why the mass flow rate monotonically increases throughout the entire range of flow regimes. Although diffusion is believed to dominate the fluid transport at the nanoscale, here we show that the Fick's first law fails in capturing this behaviour, and so diffusion alone is insufficient to explain this confined flow phenomenon. Rather, we show that the Knudsen minimum disappears in tight confinements because the decay of the mass flow rate due to the decreasing density effects is overcome by the enhancing contribution to the flow provided by the fluid velocity slip at the wall.

Non-equilibrium flow of dense inhomogeneous fluids in nano-channels

“…The non-dimensional slip velocity is different for hard-sphere and real fluids at different confinements, indicating that both confinement and real fluid effects play their roles. This is similar to the disappearance of the Knudsen minimum for dense gases under confinements observed in previous studies [6,8]. Therefore, fluid flows under confinements are controlled by both confinement and real fluid effects.…”

“…As the gas pressure dramatically increases, e.g. natural gas development from unconventional shale gas reservoirs [13,14,15] and geological storage of carbon dioxide [16,17], the size of a gas molecule becomes comparable with both the gas mean free path and the characteristic length of flowfield, as shown in Figure 1(b), consequently the real fluid and confinement effects come into play [18,8]. The finite size of fluid molecules (i.e.…”

“…The Boltzmann equation has been widely adopted to capture the non-equilibrium effect of dilute gas flows based on the assumption that the gas molecule size (σ) is negligibly smaller than the gas mean free path (λ), i.e. gas molecules are point-like with no finite spatial expansion [6,7,8], as shown in Figure 1(a). This assumption is appropriate for gas flows at relatively low pressures such as aeronautics and astronautics [9], micro-electromechanical systems [10,11], and vacuum technology [12].…”

Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids

“…dense gas flows) (Cercignani & Lampis 1988;Sadr & Gorji 2017;Wang et al 2020) or (ii) the characteristic length of the flow domain (e.g. nanoscale confined flows) (Shan et al 2020;Sheng et al 2020;Corral-Casas et al 2022). Enskog (1921) extended the localised Boltzmann collision operator to a non-localised one by considering the finite size of gas molecules, so that the instantaneous collisional transfer of momentum and energy over a molecule size comes into play (Frezzotti 1999).…”