Mass flow and momentum flux in nanoporous membranes in the transitional flow region

An experimental study of momentum transfer in nanoporous polymeric track-etched membranes with pore diameters ranging from 100 to 1300 nm and nanochannel lengths of 12-20 μm was performed using He, N₂, CO₂, and SF₆ propellants in a wide range of plenum and background pressures. Mass flux through the membranes was elaborated as a combination of Knudsen diffusion and viscous flow at Knudsen numbers above 0.1 and become choked at lower Knudsen numbers. The discharge coefficient for the membranes attained was 0.6, making the permeation rate similar to that of thin orifices. The effect is attributed to the mirror reflection of the molecules from the pore walls at low angles of incidence. The exhaust gas velocity is found to be dependent on the plenum to background pressure ratio and channel length-to-diameter ratio, reaching 0.9 of the velocity of the gas expanded to vacuum (up to 2 M). Close to an isothermal expansion occurs in nanochannels of all sizes. A general quantitative description for gas expansion in nanochannels is provided. The highest thrust is generated in the choked flow regime with the SF₆ propellant and a value of 4.5 N cm^-2 is attained at a propellant consumption of 0.165 kg (cm² s)^-1 for the membranes with 1300 nm nanochannels. The specific impulse of 138 s is reached for helium. The results show the prospects of the utilization of nanoporous membranes in cold gas propulsion systems.