Chapman–Enskog solutions to arbitrary order in Sonine polynomials III: Diffusion, thermal diffusion, and thermal conductivity in a binary, rigid-sphere, gas mixture

摘要: Abstract The Chapman–Enskog solutions of the Boltzmann equation provide a basis for computation important transport coefficients both simple gases and gas mixtures. These include viscosity, thermal conductivity, diffusion coefficient. In preceding paper (I), simple, rigid-sphere (i.e. single-component, monatomic gases) we have shown that use higher-order Sonine polynomial expansions enables one to obtain results arbitrary precision are free numerical error and, in second (II), extended our initial work modeling viscosity binary, rigid-sphere, mixture. this latter reported an extensive set order 60 which believed constitute best currently available benchmark values It is purpose similarly report investigation relatively high-order (order 70), standard, diffusion- conductivity-related binary mixtures molecules. We note work, as previous retained full dependence solution on molecular masses, sizes, mole fractions, intermolecular potential model via omega integrals. For gases, all relevant integrals needed these analytically evaluated thus, any desired can be obtained. obtained using converge therefore, exact conductivity given degree convergence determined with certainty by expanding sufficiently high order. used Mathematica® its versatility permitting symbolic high-precision computations. Our also establish confidence recently other authors who direct techniques solve equations. While methods more-or-less calculations need carried out each variation parameters, has utilized explicit, general expressions necessary matrix elements retain complete parametric problem only inversion at final step parameter varied. This indicates how similar may more realistic models gas-mixture problems addressed some additional effort.