Mass flow rate measurements in microtubes: From hydrodynamic to near free molecular regime

An experimental investigation of the reflection/accommodation process at the wall in a single silica microtube and isothermal stationary flow conditions was carried out. Several gases and different diameters were studied through various regimes. Especially for helium, the Knudsen number range was investigated as far as the free molecular regime. This kind of investigation requires a powerful experimental platform to measure mass flow rates, which we have carried out. An analytic expression of the mass flow rate, based on the Navier–Stokes equations with second order boundary condition, was used to yield the tangential momentum accommodation coefficient (TMAC) in the 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate were compared with theoretical values calculated from kinetic approaches using variable TMAC as parameter over the 0.3–30 Knudsen number range, and an overall agreement appears through the comparison. Finally, whatever the theoretical approach the TMAC obtained from gas (nitrogen, xenon, argon, and helium)-surface (fused silica) pairs is similar and lower than unity. A tendency of the TMAC values seems to appear according to the molecular mass of the gases. In addition for each gas, the second order slip coefficient magnitude seems to decrease when the tube diameter increases.