Introduction

Even though a fluid is composed of a large number of particles, ordinarily the fluid is so dense that we may consider it as continuous media in the treatment of fluid mechanics. However, if the fluid is very rarefied, one would expect that the coarse structure of molecules would affect the flow phenomena, and in the extremely rarefied gas, the gas should behave like individual particles. There are two different approaches in the theoretical investigations of the flow of a fluid: the microscopic point of view and the macroscopic point of view. The microscopic treatment is the more accurate way of analysis in which the motion of individual particles and their interactions are analyzed. Such an analysis is known as the kinetic theory of fluids. Because of many physical and mathematical difficulties, it is not possible at present to treat the flow problem of fluids exactly by molecular theory. Many simplified assumptions about molecular forces and collision phenomena have to be made in the formation of the theory ^{1 , 2 , 3} and the resultant equations can only be solved approximately. The most successful molecular theory for fluids is the kinetic theory of gases. Recently considerable efforts have been made to develop the kinetic theory of plasma ² . The basic equation of the kinetic theory of gases is known as the Boltzmann equation which is a nonlinear partial differentiointegral equation. At the present time it is not possible to solve the Boltzmann equation even for rather simple practical flow problems. We would not expect to use the molecular theory of fluids to analyze flow problems in the near future. But, the Boltzmann equation serves two important aspects in the study of gasdynamics. In the first place, the fundamental equations of gasdynamics may be derived from the Boltzmann equation as the first approximation. Thus we may have some guides about the validity of the fundamental equations for a macroscopic description of the fluid flow from the analysis of Boltzmann equation. In the second place, the Boltzmann equation may give valuable information on the transport coefficients such as the coefficient of viscosity and heat conductivity. In the macroscopic analysis, these transport coefficients are simply introduced as known functions of physical quantities of 2gasdynamics such as temperature and pressure. We shall discuss these points in detail in Chapter XVII.