×
Bakanov, S. P.; Roldugin, V. I.

The effect of a phase transition on the boundary conditions for rarefied gases. (English. Russian original) Zbl 0913.76080

J. Appl. Math. Mech. 60, No. 5, 753-758 (1996); translation from Prikl. Mat. Mekh. 60, No. 5, 761-767 (1996).
Summary: We calculate the entropy production at the interface between a liquid and a binary vapour-gas mixture by using a phenomenological approach. The consideration is confined to the case of the mixture flow over a slightly curved surface, the radius of curvature of which is much larger than the mean free path of the gas molecules. The presence, close to the interface, of kinetic boundary layers in which mass, momentum and energy transfer occurs, is borne in mind. Using the entropy production obtained, we construct a system of phenomological equations for scalar, vector and tensor surface fluxes and forces. Finally, we discuss new effects which arise from the non-equilibrium thermodynamic relations obtained.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics

Keywords:

entropy production; binary vapour-gas mixture; phenomenological approach; slightly curved surface; kinetic boundary layers
Cite Review PDF
Full Text: DOI

References:

[1] Lifshits, Ye. M.; Pitayevskii, L. P., Physical Kinetics (1978), Nauka: Nauka Moscow
[2] Landau, L. D.; Lifshits, Ye. M., Hydrodynamics (1986), Nauka: Nauka Moscow
[3] Sone, Y., Kinetic theory of evaporation and condensation. Linear and nonlinear problems, J. Phys. Soc. Japan, 45, 1, 315-320 (1978)
[4] Onishi, Y.; Sone, Y., Kinetic theory of slightly strong evaporation-hydrodynamic equation and slip boundary conditions for finite Reynolds number, J. Phys. Soc. Japan, 45, 5, 1676-1685 (1979) · Zbl 1334.82005
[5] Vestner, H.; Waldmann, L., On the theory of boundary conditions, Physica, 80A, 3, 523-549 (1975) · Zbl 1434.82072
[6] Vestner, H.; Kübel, L.; Waldmann, L., Higher-order hydrodynamics and boundary conditions, Nuovo Cimento. Ser. B, 25B, 405-412 (1975)
[7] Bakanov, S. P.; Roldughin, V. I., Two methods of constructing a theory of the thermophoresis of large aerosol particles, Kolloid. Zh., 39, 6, 1027-1038 (1977)
[8] Bakanov, S. P.; Roldughin, V. I., Diffusophoresis in gases, Kolloid. Zh., 42, 6, 1043-1050 (1980)
[9] Bakanov, S. P.; Roldughin, V. I., The problem of the boundary conditions in rarefied gas dynamics, (Rarefied Gas Dynamics. Proceedings of the Sixth All-Union Conference, Vol. 1 (1980), Inst. Thermal Physics, Sib. Otd. Akad. Nauk SSSR: Inst. Thermal Physics, Sib. Otd. Akad. Nauk SSSR Novosibirsk), 37-41
[10] Bakanov, S. P.; Roldugin, V. I., Diffusiophoresis in gases, J. Aerosol Sci. and Technol., 7, 3, 249-255 (1987)
[11] Kuscer, I., Irreversible thermodynamics of rarefied gases, Physica, 133A, 3, 397-412 (1985)
[12] Roldughin, V. I., Non-equilibrium thermodynamics of boundary conditions for slightly rarefied gases, J. Non-equilibr Thermodyn., 16, 1, 13-26 (1991) · Zbl 0850.76606
[13] de Groot, S. R.; Mazur, P., Non-equilibrium Thermodynamics (1962), North-Holland: North-Holland Amsterdam · Zbl 1375.82003
[14] Shavaliyev, M. Sh., Transport phenomena in the Barnett approximation in multicomponent gaseous mixtures, Izv Akad. Nauk SSSR MZhG., 1, 126-137 (1974) · Zbl 0307.76044
[15] Waldman, L.; Vestner, H., Non-equilibrium thermodynamics of the gas kinetic boundary-value problem, Physica, 99A, 1, 1-33 (1979)
[16] Roddoskin, A. B.; Yushkanov, A. A.; Yalamov, Yu. I., The problem of the thermophoresis of moderately large aerosol particles, Zh. Tekh. Fiz., 50, 1, 158-161 (1980)
[17] Zhdanov, V. M.; Roldughin, V. I., The moment method and rarefied gas flow in channels. General relations, Physica, 184A, 1/2, 169-186 (1992)
[18] Bedeaux, D.; Hermans, L. J.F.; Ytrehus, T., Slow evaporation and condensation, Physica, 169A, 2, 263-280 (1990)
[19] Derjaguin, B. V.; Bakanov, S. P.; Kurgin, Yu. S., The kinetics of the evaporation of liquid drops coated with an insoluble film of impurity, Kolloid. Zh., 23, 3, 262-271 (1961)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.