Gaseous Flows in Microchannels

Abstract

The objective of this study is to broaden the fundamental understanding of the emerging field of microfluidics especially in a long channel. The quasi gasdynamic (QGD) equations, originally developed on the basis of a kinetical model are used for numerical and analytical simulation. A two-dimensional analysis of the QGD equations with a first order slip velocity boundary conditions demonstrates that both compressibility and rarefied effects are present in long microchannels. Analytical solutions for the pressure and the velocity profiles are derived from the quasi gasdynamic equations by undertaking perturbation expansions according to a small parameter e (the height-to-length ratio of the channel) and using the isothermal flow assumption. The deduced expression for the mass flow rate is similar to the analytical expression obtained from the Navier-Stokes equations with a second order slip boundary condition and gives results in agreement with the measurements. The effects of the rarefaction and of the compressibility on pressure distributions are analyzed. The analytical expression of the pressure predicts accurately the measured pressure distribution. The Knudsen numbers calculated at the exit of the channel and based on the channel height vary from 10 i3 to 0:4. The comparisons of analytical and numerical solutions confirm the validity of the analytical approach.