phone +7 (3412) 91 60 92

Archive of Issues


Germany; Russia Jena; Omsk
Year
2016
Volume
26
Issue
2
Pages
194-206
<<
>>
Section Mathematics
Title Boundary conditions and heat resistance at the moving solid-liquid interface
Author(-s) Buchbinder G.L.a, Galenko P.K.b
Affiliations Omsk State Universitya, University of Jenab
Abstract Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases taken at the interface and the quantities characterizing the interfacial surface such as surface temperature and surface heat flux. Introduction of the surface temperature as an independent variable, allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on interface velocity is considered. It is shown that the thermal resistance leads to non-linearity in solidification kinetics, namely, in “velocity-undercooling” relation. The conditions of the steady-state motion of the planar interface are found.
Keywords crystallization, Kapitza resistance, interface, boundary conditions
UDC 51-72, 531
MSC 74A50
DOI 10.20537/vm160205
Received 23 May 2016
Language Russian
Citation Buchbinder G.L., Galenko P.K. Boundary conditions and heat resistance at the moving solid-liquid interface, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 194-206.
References
  1. Langer J.S. Instabilities and pattern formation in crystal growth, Review of Modern Physics, 1980, vol. 52, pp. 1-28.
  2. Galenko P.K., Danilov D.A. Hyperbolic self-consistent problem of heat transfer in rapid solidification of supercooled liquid, Physics Letters A, 2000, vol. 278, issue 3, pp. 129-138.
  3. Kapitza P.L. Investigation of the mechanism of heat transfer in helium II, Zh. Eksp. Teor. Fiz., 1941, vol. 11, no. 1, pp. 1-31 (in Russian).
  4. Ghasemi H., Ward C.A. Mechanism of sessile water droplet evaporation: Kapitza resistance at the solid-liquid interface, The Journal of Physical Chemistry C, 2011, vol. 15, pp. 21311-21319.
  5. Palmieri B., Ward C.A., Dejmek M. Effects of nonlinear interfacial kinetics and interfacial thermal resistance in planar solidification, Physical Review E, 2012, vol. 86, 051605 (14 p).
  6. Brener E.A., Temkin D.E. Onsager approach to the one-dimensional solidification problem and its relation to the phase-field description, Physical Review E, 2012, vol. 85, 031601 (5 p).
  7. Castaing B., Nozieres P. Transmission of sound at the liquid-solid interface of helium: a new probe of melting kinetics, Journal de Physique, 1980, vol. 41, pp. 701-706.
  8. Bedeaux D., Albano A.M., Mazur P. Boundary conditions and non-equilibrium thermodynamics, Physica A, 1976, vol. 82, pp. 438-462.
  9. Zielinska B.J.A., Bedeaux D.A. Hydrodynamic theory for fluctuations around equilibrium of a liquid-vapour interface, Physica A, 1982, vol. 112, pp. 265-286.
  10. Waldmann L. Non-equilibrium thermodynamics of boundary conditions, Z. Naturforschung, 1967, vol. 22 a, pp. 1269-1280.
  11. Kjelstrup S., Bedeaux D. Non-equilibrium thermodynamics of heterogeneous system, Series on Advances in Statistical Mechanics, vol. 16, Singapore: World Scientific Publ., 2008, 425 p.
  12. Caroli B., Caroli C., Roulet B. Non-equilibrium thermodynamics of the solidification problem, Journal of Crystal Growth, 1984, vol. 66, pp. 575-585.
  13. De Groot S.R., Mazur P. Non-equilibrium thermodynamics, Amsterdam: North-Holland, 1969, 510 p.
  14. Umantsev A. Thermal effects of phase transformations: A review, Physica D, 2007, vol. 235, pp. 1-14.
  15. Umantsev A.R., Roytburd A.L. Nonisothermal relaxation in a nonlocal medium, Sov. Phys. Solid State, 1988, vol. 30, pp. 651-655.
  16. Karma A., Rappel W.J. Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys. Rev. E, 1998, vol. 57, pp. 4323-4349.
  17. Patashinskii A.Z., Chertkov M.V. The movement of the phase transition front with large undercooling, Fiz. Tverd. Tela, 1990, vol. 32, pp. 509-513 (in Russian).
  18. Swartz E.T., Pohl R.O. Thermal boundary resistance, Review of Modern Physics, 1989, vol. 61, pp. 605-668.
  19. Chen J., Zhang G., Li B. Thermal contact resistance across nanoscale silicon dioxide and silicon interface, J. Appl. Phys., 2012, vol. 112, 064319 (5 p).
  20. Bassler B.T., Hofmeister W.H.. Bayuzick R.J. The solidification velocity of pure nickel, Materials Science and Engineering: A, 2003, vol. 342, pp. 80-92.
  21. Chan W.-L., Averback R.S., Cahill D.G., Ashkenazy Y. Solidification velocities in deeply undercooled silver, Phys. Rev. Lett., 2009, vol. 102, 095701 (4 p).
  22. Herlach D.M., Non-equilibrium solidification of undercooled metallic melts, Metals, 2014, vol. 102, pp. 196-234.
Full text
<< Previous article
Next article >>