Kinetic-Theory Approach to the Problem of Shock-Wave Structure in a Binary Mixture

The method of Mott-Smith is extended to the study of the shock-wave structure in a mixture of two monatomic inert gases. Given the steady state ahead of the shock and assuming a bimodal velocity distribution function for each component gas, the steady state behind the shock is obtained with the help of the conservation equations. One additional transfer equation is needed to obtain differential equations giving number-density distribution within the shock; the collision integral for this equation is calculated on the assumption that the molecules obey Maxwellian law of force. The case where the initial mixture contains only a small fraction (α) of the second gas is studied in detail: expanding various characteristics in power series of α, analytical expression for the first approximation is obtained. The solution is, for all values of the shock strength and for all values of the mass ratio of the two gases, free from the anomaly found by Sherman who solved this problem in the frame-work of Navier-Stokes equations. For two specific cases, the velocity profiles calculated from this approximation are explicitly given.