Microfluid Mechanics: Principles and Modeling

Gas-surface interactions involve many, such as physical and chemical, mechanisms that occur near the interface. The result of these interactions, however, can influence the operation characteristics of the microdevices. In the near surface region, behavior of the individual molecules cannot be ignored and the gas cannot be regarded as in equilibrium. For instance, the momentum and the energy transfer between the gas molecules and the surface need to be considered. Such regime or sublayer, which is estimated to be about a few mean free paths thick, is called the Knudsen layer. In the Knudsen layer, the gas behavior should be considered from gas kinetic theory. This will bring in the Boltzmann equation and the Liouville equations, which have been discussed earlier. In the cases where the local Knudsen number is small and the effect of the Knudsen layer is not significant, the continuum solution for bulk flow can be extrapolated satisfactorily to the surface, implying that the interactions of gas molecules and surface are the same as those between the gas molecules and a gas/surface in equilibrium. This then results in the average velocity and temperature of gas on the wall being continuous and equal to the velocity and the temperature of the wall. At high Knudsen number, the collision frequency can be low and the distribution function of the gas near the surface will not be an equilibrium distribution. The gas-surface interactions then need to be considered microscopically. The boundary conditions for the distribution function of a...