Collisionless expansion of gases into vacuum

Abstract

The free-molecule limit of several free-flow problems is studied on the basis of the collisionless Boltzmann equation. It is shown that the density in the free expansion of a gas cloud obeys, under certain conditions, a diffusion equation with a coefficient directly proportional to the time, and the resulting flow field is described in terms of a thick ‘diffusion front’ travelling asympotically at a definite velocity and growing linearly with time. It is also show that in any free-molecule free expansion the stresses and heat flux can be expressed in terms of viscosity and conductivity coefficients, which however increase linearly with time but are such that the Stokesian relation is always valid and the Prandtl number has the value 5/6.The flow field due to sources and jets is also discussed, and it is found that the jet has a width inversely proportional to the Mach number if the Mach number is sufficiently high. Finally, a procedure is indicated for taking approximate account of collisions among the molecules.