The Free-Molecular Regime.

The theoretical treatment of gas flow problems for extremely high Knudsen numbers (the free-molecular regime) is very different from that typically encountered in conjunction with the hydrodynamics of media having the higher number densities most people are used to working with. The theoretical frameworks encountered at these extremes are connected via various fundamental relationships between the Kinetic Theory of Gases and the mechanics of media that exhibit continuum type behaviors (the continuum regime). The continuum equations may be obtained from the Boltzmann equation if one uses the summational invariants of encounters as molecular properties with which to construct a system of moment equations. This moment system, however, is indeterminate unless one knows the relationships between the basic hydrodynamic values and the stress tensor or the thermal flux vector. These relationships may be derived by using the Chapman-Enskog method of solution of the Boltzmann equation. It is very important in the continuum regime that such gas characteristics as the viscosity and thermal conductivity coefficients be determined independently of the boundary conditions. [ABSTRACT FROM AUTHOR]