“Law of the nano-wall” in nano-channel gas flows

Abstract

Molecular dynamics simulations of force-driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas–wall interactions. This duality enables definition of an inner-layer scaling, $$y^{*}$$ , based on the molecular dimensions. For gas–wall interactions determined by Lennard–Jones potential, the velocity distribution for $$y^{*} \le 3$$ exhibits a universal behavior as a function of the local Knudsen number and gas–wall interaction parameters, which can be interpreted as the “law of the nano-wall.” Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok–Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1):43–77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows.