Some Aspects of Shock Structure According to the Bimodal Model

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Abstract
Calculations are made of the shock thickness for several realistic intermolecular force laws, viz., those derived from the Lennard‐Jones 6–12, the modified Buckingham exp−6, and the exponential repulsive potentials. Argon and helium are explicitly considered for these calculations; agreement with recent experimental results is good. The central feature of the results for such force laws, as well as for point centers of force, is the interminable broadening of the shock zone with increasing Mach number. It is demonstrated that the shock zone is bounded by an appropriately defined mean free path localized anywhere in the gas, although the definition of a mean free path is not necessary for the calculation of shock thickness. The relationship and properties of the density, velocity, and temperature profiles are investigated. It is found that the center of the temperature profile is upstream of the center of the velocity profile which, in turn, is upstream of the center of the density profile. These results are obtained without explicit evaluation of the extent of the shock zones. Calculations have been made of the number of collisions suffered by a typical molecule in traversing the density and velocity shock zones. These collision numbers approach a finite, nonzero limit as the Mach number increases without limit.