Nonlinear transport processes in gases

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Abstract
By applying the modified moment method to nonlinear transport phenomena in dilute gases and from the stationary solutions of the evolution equations derived from the Boltzmann equation, we have obtained in this paper nonlinear transport coefficients which are given, for example, by the formula ζ(Ω)=ζ0 sinh−1γΩ/γΩ, ζ=2η or λ, where Ω=∥[∇u](2)∥ or ∥∇ logT∥, γ=[ζ0(μ r k B T/2)1/2]1/2/p d, and ζ0=2η0 or λ0 with u, T, μ r , p, d, η0, and λ0, respectively, being the fluid velocity, temperature, reduced mass of particles, pressure of the gas, the size parameter (diameter) of the particle, the Chapman–Enskog shear viscosity, and heat conductivity. The formula reduces, if Ω is small, to the Chapman–Enskog theory transport coefficient and, if the density is vanishingly small, to the rarefied gas dynamics result for the transport coefficient. The γ as given provides for the first time a completely molecular expression for the ’’relaxation time’’ in Eyring’s theory of non‐Newtonian flow.

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