Gas Flow in Micro Channels-Experimental, Computational and Kinetic-Theoretical Investigations

Ching      Shen

Abstract

The investigation of fluid flow in a tube or channel commenced from studying experimentally the liquid flow along a circular tube under the pressure difference imposed at both the ends, the results were verified by the exact solution of the Navier-Stokes Eq. under constant pressure gradient assumption (Poiseuille flow). The experimental work has been playing a pioneering role in the investigation of channel flows. In the case of gas for the tube (or channel) flow, according to the global mass conservation law, the pressure gradient is never a constant. The theoretical studies on rarefied gas Poiseuille flow based on constant pressure gradient assumption still compared well with the early experimental work because when pressure difference between the inlet and the outlet is small in comparison with the average pressure, the pressure distribution is approximately a linear one. Recently non-linear pressure distribution was experimentally found in the integrated micro- channel/pressure sensor systems with gas flow in the transitional regime. The mass flow rate of micro channel was exactly measured, challenging the rarefied gas dynamics community to put forward computation or simulation means for the calculation of micro-channel flow, and the flow characteristics in other micro devices. This paper reviews some of these computational efforts. It also presents a strict kinetic solution of the finite length micro-channel flow problem based on the global mass conservation and the exact kinetic theoretical solution of the Poiseuille flow at each section. Calculations and simulations are compared with reviewed experiments to check the agreement between the computational or theoretical results with experimental data.

Keywords: Microchannel flow, Poiseuille flow, finite length channel flow, gas flow in channels, lattice Boltzmann method (LBM), information preservation (IP) method, kinetic theoretical solution of microchannel flow, global mass conservation for channel flow