Applications of Molecular Beams to Problems in Rarefied Gas Dynamics

Abstract

In classical aerodynamics the air is considered as a continuum and its flow characteristics are described by the equations of fluid mechanics. From the standpoint of kinetic theory, the validity of these equations is based on the physical assumption that the behavior of the fluid is determined almost exclusively by the interactions between the individual molecules and only to a very minor, generally negligible, ex tent by the interaction between molecules and solid boundaries. Another expression of this physical situation is contained in the statement that under the conditions encountered in classical fluid mechanics, the mean free paths between individual molecules is very small compared with the dimensions of the bodies in contact with the fluid. If, however, the density of the gas is gradually being decreased to reach such values as, for instance, exist in tne upper atmosphere, the mean free path which is inversely proportional to the density will gradually increase until the condition mentioned above is no longer valid. We are then reaching the regime known as rarefied gas dynamics, which is characterized by a mean free path λ between the molecules of the gas of the same order or even larger than the critical dimension d of the system. The ratio between this mean free path λ and the characteristic dimension K=λ/d, commonly called the Knudsen number, divides gas dynamics into the various flow regimes, values of K<0.01 represent continuum flow, those of K>10 free molecular flow, and intermediate values the re gions commonly called slip and transition flow. In this series of lectures we will be concerned only with the regions of very large K's, that is with free molecular flow, also called Knudsen flow. In this flow regime individual molecules will make many collisions with the solid walls bordering on the system before they will have a chance to collide with one another. As a result, the flow characteristics are determined by the interactions between solid surfaces and gas molecules while the continuum quantities such as viscosity and heat conductivity lose their importance.