Rarefaction slip phenomena within a viscous disk pump with molecular mean free path sized surface roughness elements

Abstract

The present investigation considers roughness elements which are generally very small relative to the principal flow length scale, and about the same order of magnitude as the molecular mean free path of helium. Significantly different rarefaction flow behavior is produced using three roughness arrangements, which have different character and structure in regard to distributions of larger ridges, as well as sizes, shapes, and distributions of smaller roughness elements. Measured distributions of slip velocity and associated tangential momentum accommodation coefficients are provided as they vary with Knudsen number Kn, disk rotation speed ω, and mean roughness height Ra. Results are given for helium and air as working fluids, three different surface roughness types, different disk rotational speeds ω, different volumetric flow rates, and different flow passage heights h. Knudsen number values range from 5.21 × 10^–3 to 2.15 × 10^–2 for helium, and from 1.82 × 10^–3 to 7.53 × 10^–3 for air. The device employed to produce these data is a viscous disk pump (VDP). With smallest mean roughness height, all of the elements on the surface are about the same size, which is about the same as the molecular mean free path of helium, and a larger percentage of molecules are subject to specular reflection resulting in substantial slip velocity magnitudes. With largest mean roughness height, a diversity of roughness element sizes, shapes, and heights is present, and a larger percentage of molecules are subject to diffuse reflection resulting in relatively small slip velocity magnitudes.