Conditions on Thermocapillary Surface with Consideration of Liquid Evaporation and Transfer Coefficient Temperature Dependence
Abstract
Convective flows of fluids under action of a cocurrent gas flux and gas related evaporation effects are actively investigated nowadays analytically, numerically and experimentally. The problem of mathematical modeling of convective processes with evaporation is extremely complicated. Formulation of boundary conditions on the interface between liquid and gas-vapor mixture is a crucial aspect here. In this paper, generalized kinematic, dynamic and energy conditions on the thermocapillary interface are presented. The interface conditions are formulated with consideration of transfer coefficient temperature dependence under a hypothesis that free surface energy is identified with a surface tension coefficient, Stokes’ law is used for incompressible fluid, heat and vapor fluxes are derived from Fourier and Fick laws, and latent heat of evaporation is a jump of inner potential energy. Continuity of temperature and tangential velocities on the interface is assumed, and evaporation mass flux is obtained from kinetic theory.
DOI 10.14258/izvasu(2016)1-18
Downloads
Metrics
References
Белова И.В. Численные исследования напряжений в твердой фазе в процессе кристаллизации: дисс. . . . канд. физ-мат. наук. — Новосибирск, 1990.
Гончарова О.Н. Математическая модель формирования сферических оболочек в условиях кратковременной невесомости // Динамика сплошной среды. — 1987. — № 82.
Гончарова О.Н., Пухначёв В.В. Диффузионное приближение в задаче формирования сферических микробаллонов в условиях кратковременной невесомости // Моделирование в механике. — 1990. — № 4 (21).
Гончарова О.Н. Глобальная разрешимость задачи о формировании сферических микробаллонов // Динамика сплошной среды. — 1993. — № 106.
Das K.S., Ward C.A. Surface thermal capacity and its effects on the boundary conditions at fluid-fluid interfaces // Phys. Rev. E. — 2007. — V. 75, 065303.
Кузнецов В.В. Условия переноса тепла и массы на границе раздела жидкость-газ при диффузионном испарении // Journal of Siberian Federal University. — 2010. — № 3 (2).
Кузнецов В.В. Тепломассообмен на поверхности раздела жидкость-пар // Механика жидкости и газа. — 2011. — № 5.
Гончарова О.Н. Моделирование течений в условиях тепло- и массопереноса на границе раздела // Известия Алтайского. гос. ун-та. — 2012. — № 73 (1/2).
Iorio C.S., Goncharova O.N., Kabov O.A. Study of evaporative convection in an open cavity under shear stress flow // Microgravity Sci.Technol. — 2009. — V. 21 (1).
Iorio C.S., Goncharova O.N., Kabov O.A. Heat and mass transfer control by evaporative thermal pattering of thin liquid layers // Computational Thermal Sci. — 2011. — V. 3 (4).
Овсянников Л.В. Введение в механику сплошных сред. — Новосибирск, 1976. — Ч. 1 ; 1977. — Ч. 2.
Серрин Дж. Математические основы классической механики жидкости. — М., 1963.
Седов Л.И. Введение в механику сплошной среды. — М., 1962.
Гончарова О.Н. О единственности решения двумерной нестационарной задачи для уравнений свободной конвекции с вязкостью, зависящей от температуры // Дифференциальные уравнения. — 2002. — Т. 38. № 3.
Андреев В.К., Гапоненко Ю.В., Гончарова О.Н., Пухначёв В.В. Современные математические модели конвекции. — М., 2008.
Haase R. Thermodynamics of irreversible processes. — Mineola NY, 1990.
Bedeaux D., Hermans L.J.F., Ytrehus T. Slow evaporation and condensation // Physica A. — 1990. — V. 169.
Colinet P., Lebon G., Iorio C.S., Legros J.C. Interfacial nonequilibrium and Benard-Marangoni instability of a liquid-vapor system // Phys. Rev. E. — 2003. — V. 68.
Ghez R. A generalized Gibbsian surface // Surface sciences. — 1966. — V. 4.
Dufay R., Prigogine I. Surface tension and adsorption. — New York, 1966.
De Groot S.R., Mazur P. Non-equilibrium thermodynamics : 2nd, edn. — Amsterdam, 1962.
Haut B., Colinet P. Surface-tension-driven instability of a liquid layer evaporating into an inert gas // J. of Colloid and Interface Science. — 2005. — № 285.
De Groot S.R., Mazur P. Non-equilibrium thermodynamics. — Amsterdam, 1962.
Prigogine I., Dufay R. Chemical thermodynamics. — London ; New York, 1954.
Oron A., Davis S.H., Bankoff S.G. Longscale evolution of thin liquid films // Reviews of Modern Physics. — 1997. — V. 69 (3).
Мирзаде Ф.Х. Волновая неустойчивость слоя расплавленного металла, образующегося при интенсивных лазерных воздействиях // ЖТФ. — 2005. — Т. 75 (8).
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
