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Analysis of slip and temperature jump coefficients in a binary gas mixture. (English. Russian original) Zbl 0729.76091

Fluid Dyn. 25, No. 6, 937-944 (1990); translation from Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1990, No. 6, 152-159 (1990).
Summary: The possibility of simplifying the formulas obtained by the Maxwell- Loyalka method for the “velocity” \(\xi_ u\), temperature \(\xi_ T\) and diffusion \(\xi_ d\) slip coefficients and the temperature jump coefficient \(\tau\) in a binary gas mixture with frozen internal degrees of freedom of the molecules is considered. Special attention is paid to gases not having sharply different physicochemical properties. The formulas are written in a form convenient for use without linearization in the thermal diffusion coefficient. They are systematically analyzed for mixtures of inert gases, \(N_ 2\), \(0_ 2\), \(CO_ 2\), and \(H_ 2\) at temperatures extending from room temperature to 2500\(\circ K\). It is shown that for the molecular weight ratios \(m^*=m_ 2/m_ 1\) considered the expressions for \(\xi_ u\) and \(\tau\) can be radically simplified. With an error acceptable for practical purposes (up to 10 %) it is possible to employ expressions of the same structural form as for a single-component gas: for \(\xi_ u\) if \(1\leq m^*\leq 6\), and for \(\tau\) if \(1\leq m^*\leq 3\). When \(1\leq m^*\leq 2\) the expression for \(\xi_ T\) can be simplified with a maximum error of 5 %. Within the limits of accuracy of the method the expression for \(\xi_ T\) can be linearized in the thermal diffusion coefficient. An approximate expression convenient for practical calculations is proposed for \(\xi_ d\). Finally, the \(\tau\), \(\xi_ u\), and \(\xi_ T\) for a single-component polyatomic gas with easy excitation of the internal degrees of freedom of the molecules are similarly analyzed; it is shown that these expressions can be considerably simplified.

MSC:

76T99 Multiphase and multicomponent flows
82B40 Kinetic theory of gases in equilibrium statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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References:

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