Gaseous flow in microtubes at arbitrary Knudsen numbers

Abstract

New models that describe gas flow behaviour in microtubes are presented. To avoid time-consuming calculations in solving the integral equation which is obtained from the microscopic point of view, the high-order slip-flow boundary condition is utilized to correct the gas flow in such a micron or submicron spacing. The proposed model can be applied to arbitrary Knudsen number conditions under the assumption that the bulk flow velocity is negligible compared with the sonic velocity of the gas. The analytical solution of the pressure distribution for the first-order slip-flow model is obtained. The results show that the first-order slip-flow model is in good agreement with this model. The nonlinear pressure distribution is due to gas compressibility. The dominant mechanism influencing the nonlinear pressure distribution comes from the rarefaction of gas and the inlet pressure. The rarefaction effect increases the pressure drop at the inlet region of the channel and decreases the pressure drop at the exit region of the channel. The decrease of inverse Knudsen number changes the pressure distribution from concave to almost linear and increases the mass flow.