Mass Flow Rate Measurements Through Metallic Microtubes in the Slip and Transition Regimes

The exchange of momentum and energy in gas flows through microchannels is significantly influenced by the gas-surface interaction. At this scale often the gas is rarefied and therefore non-equilibrium effects in the fluid flow can arise in a layer which extends for a distance equivalent to the mean free path from the walls. Typical examples of non-equilibrium phenomena for rarefied gas flows are slip at the wall, thermal transpiration and temperature jump at the wall. The aim of the present study is to experimentally investigate the non-equilibrium effects present in an isothermal pressure induced flow for a large range of rarefaction conditions. The isothermal slip at the wall is usually characterized by the tangential momentum accommodation coefficient (TMAC). This coefficient depends on the molecular nature of the gas and on the physical characteristics of the surface, such as material and roughness. In particular this paper explores the influence of the surface material on the TMAC through measurements of the mass flow rate in capillaries for the special case of nitrogen. Commercially available microtubes of three different metallic materials — stainless steel, copper, and brass — were considered in the analysis. Measurements were performed with a dynamic measurement technique based on the constant volume method and comprehend the transitional flow regime and most part of the slip regime. Theoretical results obtained from the solution of the Boltzmann equation via the BGK kinetic model, which is a simplified approximation for the collisional term, were compared to the experimental results.