Density and confinement effects on fluid velocity slip

Understanding the velocity slip of fluids in channels of molecular length scales is essential for accurately manipulating their flow in engineering applications, such as in water desalination or, by reversing the process, osmotic power generation. This study addresses two major open questions, namely (a) the range of validity of the Navier-Stokes equations with slip boundary conditions in describing fluid flows within channels of molecular confinement, and (b) the effect of fluid density and confinement as well as surface properties, such as microscopic roughness and curvature, on fluid slippage along walls. Using a hard-sphere fluid model and describing the fluid-wall interactions by the Maxwell scattering kernel, an event-driven molecular dynamics simulation study was performed in planar and cylindrical channels of different sizes and accommodation coefficients with varying fluid densities. The results show that the well-known criterion for the slip solution, which is valid in rarefied conditions, also holds for a dense gas, i.e., the predictive accuracy improves with decreasing Knudsen numbers, as long as the channel size is larger than about ten molecular diameters. We also find that the key quantity influencing the friction coefficient of a fluid is the peak density at the walls, rather than the nominal density, the fluid confinement, or the channel curvature, as found in previous studies. In particular, higher nominal densities lead to higher density peaks, and therefore a decrease in slip, while tighter confinements lead to lower density peaks, and therefore an increase in slip, regardless of channel geometry. Furthermore, the velocity slip depends on the microscopic roughness via the Smoluchowski factor. These findings are a stepping stone towards a deeper understanding of the molecular mechanisms underlying fluid velocity slip in molecular-scale channels.