Abstract
An analytic solution of the problem of second-order thermal creep is obtained. A method for solving the half-space boundary value problem for an inhomogeneous linearized kinetic BGK equation forms the basis of the solution. The general solution of the input equation is constructed in the form of an expansion of the corresponding characteristic equation in terms of the eigenfunctions. Substitution of the solution in the boundary conditions leads to a Riemann boundary value problem. The unknown thermal creep velocity is found from the condition of solvability of the boundary value problem. The numerical analysis performed confirms the existence of negative thermophoresis (in the direction of the temperature gradient) for high-conductivity aerosol particles at low Knudsen numbers.
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REFERENCES
L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. 6. Hydrodynamics [in Russian], Nauka, Moscow (1986).
C. Cercignani, Mathematical Methods in Kinetic Theory, Macmillan, New York (1969).
E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics [in Russian], Nauka, Moscow (1979).
H.A. Dwyer, "Thirteen-moment theory of the thermal force on a spherical particle," Phys. Fluid, 10, 976 (1967).
S. L. Gorelov, "Thermophoresis and photophoresis in a rarefied gas," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 178 (1976).
Takeo Soga, "A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in monatomic gas," Phys. Fluid, 29, 976 (1986).
E. G. Mayasov, A. A. Yushkanov, and Yu. I. Yalamov, "Thermophoresis of a nonvolatile spherical particle in a rarefied gas at low Knudsen numbers," Pis'ma v Zh. Tekh. Fiz., 14, 498 (1988).
J. Ferziger and H. Kaper, Mathematical Theory of Transport Processes in Gases, North-Holland, Amsterdam (1972).
A.V. Latyshev, "Use of the Case method for solving a linearized kinetic BGK equation in the temperature jump problem," Prikl. Mat. Mekh., 54, 581 (1990).
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Latyshev, A.V., Popov, V.N. & Yushkanov, A.A. Analytic Solution of an Inhomogeneous Kinetic Equation in the Problem of Second-Order Thermal Creep. Fluid Dynamics 38, 491–500 (2003). https://doi.org/10.1023/A:1025110509457
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DOI: https://doi.org/10.1023/A:1025110509457