CALCULATION OF MATRIX ELEMENTS OF THE BOLTZMANN COLLISION OPERATOR FOR GAS MIXTURES

Abstract

We have calculated matrix elements of the Boltzmann collision operator for nonequilibrium gas mixtures in the framework of the generalized torque method. The value of the partial change in the momentum due to collisions is obtained, which is expressed through the matrix elements for an arbitrary law of interaction between particles of a nonequilibrium mixture with a large temperature difference between the component and the relative velocity comparable to the thermal speed, when the function of the zero approximation is the Maxwell function. Decomposition for a partial change in the momentum due to collisions includes terms regarding hydrodynamic variables up to third degree and, therefore, the scope of its applicability applies to small, but finite values. Moreover, the contribution of higher moments strongly depends on the law of interaction between colliding particles and is evaluated for the power-law interaction. We have derived an equation for the evolution of the partial chaotic energy. We have estimated the contribution of nonlinear terms of the hydrodynamic variables to the desired expression.