On the collision kernels for gas mixtures

Integral representations of the linearized Boltzmann equation facilitate the direct analysis of and numerical studies of gas flows, and have been available for both simple gases and dilute gases since the work of Hilbert (1912) and Enskog (1917). Williams (1976) reported general representations associated with mixtures of arbitrary composition using integrations on delta functions. An alternate derivation of these representations is given here and the results agree fully with those of Williams. The derivation of these representations involves a considerable increase in difficulty over the related results for simple gases and dilute gases regardless of the method used. The agreement between these two independent derivations is important because the representations that are obtained are critical to the continuing development of the theory for gas mixtures and for obtaining numerical solutions to specific problems