The physical significance of formulae for the thermal conductivity and viscosity of gaseous mixtures

Abstract

A physical interpretation is made of various complicated formulae which have been given for the thermal conductivity A and viscosity n of mixtures of gases. The interpretation is based on the recognition of two principal effects operating in the transport of heat or momentum through gaseous mixtures. The first (and larger) effect is that molecules of one species impede transport of heat or momentum by other species. The second effect is a transfer of the transport of heat (or momentum) from one species to another. When the transfer of transport is neglected, equations of the form proposed by Sutherland (1895) and Wassiljewa (1904) follow immediately. For the thermal conductivity (symbols used are defined in the main text): A = E{ n i /( n i A i -1 +Ea ij n j )] There is an identical expression for the viscosity, though the values of a ij are different from those for the thermal conductivity. The significance to be given to each term of the sum over i is that of a quotient of (i) a force driving conduction, proportional to n i , and (ii) a resistance due to species i(n i A i -1 ) and to all other species (En j a ij ). Here A i -1 is the resistance offered by species i to its own transport, a ij and the resistance offered by the species j to transport by i . When the transfer of transport is taken into account, two simultaneous linear equations have to be solved for a binary mixture, and the solution has the form of the quotient of quadratics familiar in the theoretical analysis of mixtures of monatomic gases. For a mixture of N constituents, the resulting expression for A appears as a quotient of determinants. Application of the same principles also throws light on the transport of internal energy in mixtures of polyatomic gases. The total thermal conductivity may be divided into contributions from each species, and each such contribution may be further subdivided into internal and translational parts: thus for a binary mixture it is necessary to replace the pair of simultaneous equations by four. Such linear equations represent a direct generalization of the equations of Mason & Monchick (1962) for a simple gas. In an appendix, the physically significant parameters of the generalized approach employed here are compared explicitly with the predictions of rigorous analysis for mixtures of monatomic gases.