A Strict Kinetic Solution of the Finite Length Microchannel Flow Problem

In finite length tube or channel gas flow the pressure gradient is determined by the global mass conservation law. In the continuum and slip flow the pressure distribution determined by the global mass conservation is given analytically. In the transitional flow regime an equation containing the flow rate of the Poiseuille flow solved by the strict kinetic theory is obtained and is shown to be the degenerated Reynolds equation for the lubrication theory. The integration of the equation is illustrated in the case of full diffuse reflection of the channel wall. The pressure distribution thus obtained is shown to be in excellent agreement with experimental data of long microchannels and the simulation results of the information preservation method. The results as having the strict kinetic theoretical merit are used to confirm the unfeasibility of the Lattice Boltzmann method in the transitional flow regime.