Coarse-grained description of thermo-capillary flow

Physics of Fluids

Volumn 8, Issue 3, 1996, Pages 660-669

  Jasnow, David ^a   Viñals, Jorge ^b,c  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

^c FAMU FSU COLLEGE OF ENGINEERING   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FLOW; NAVIER-STOKES EQUATIONS; THERMO;

EID: 0029673822     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.868851     Document Type: Article

References (39)

1. P. C. Hohenberg and B. I. Halperin, "Theory of dynamic critical phenomena," Rev. Mod. Phys. 49, 435 (1977).
2. E. D. Siggia, B. I. Halperin, and P. C. Hohenberg, "Renormalization-group treatment of the critical dynamics of the binary-fluid and gas-liquid transitions," Phys. Rev. B 13, 2110 (1976).
3. A. Onuki and K. Kawasaki, "Nonequilibrium steady state of critical fluids under shear flow: A renormalization group approach," Ann. Phys. 121, 456 (1979).
4. A. Onuki, K. Yamazaki, and K. Kawasaki, "Light scattering by critical fluids under shear flow," Ann. Phys. 131, 217 (1981).
5. E. Helfand and G. H. Fredrickson, "Large fluctuations in polymer solutions under shear," Phys. Rev. Lett. 62, 2468 (1989).
6. M. Doi, in Lecture Notes in Physics, edited by A. Onuki and K. Kawasaki (Springer-Verlag, Berlin, 1990), Vol. 52, p. 100.
7. K. Kawasaki and T. Ohta, "Kinetics of fluctuations for systems undergoing phase transitions - Interfacial approach," Physica A 118, 175 (1983).
8. T. Koga and K. Kawasaki, "Spinodal decomposition in binary fluids: Effects of hydrodynamic interactions," Phys. Rev. A 44, R817 (1991).
9. J. D. Gunton, M. San Miguel, and P. S. Sahni, in Kinetics of First Order Phase Transitions, Vol. 8 of Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, London, 1983).
10. L. Landau and E. Lifshitz, Statistical Mechanics, Part 1 (Pergamon, New York, 1980).
11. H. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971).
12. D. Jasnow, "Critical phenomena at inerfaces," Rep. Prog. Phys. 47, 1059 (1984).
13. D. Jasnow, in Renormalization Group Theory of Interfaces, Vol. 10 of Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, London, 1986).
14. J. Rowlinson and B. Widom, Molecular Theory of Capillarity (Clarendon Press, Oxford, 1982).
15. M. E. Gurtin, D. Polignone, and J. Viñals, "Two-phase binary fluids and immiscible fluids described by an order parameter," Math. Models Methods Appl. Sci. 6, (1996).
16. L. K. Antanovskii, "A phase field model of capillarity," Phys. Fluids 7, 747 (1995).
17. J. Langer, in Chance and Matter, Les Mouches Summer School, edited by J. V. J. Souletie and R. Stora (North-Holland, Amsterdam, 1986).
18. G. Caginalp, in Applications of Field Theory to Statistical Mechanics, Vol. 216 of Lecture Notes in Physics, edited by L. Garrido (Springer-Verlag, Berlin, 1985), p. 216.
19. G. Caginalp and P. C. Fife, "Phase field methods for interfacial boundaries," Phys. Rev. B 33, 7792 (1986).
20. We ignore for the time being thermal fluctuations and possible renormalizations due to them.
21. C. Peskin, "Numerical analysis of blood flow in the heart," J. Comput. Phys. 25, 220 (1977).
22. J. Hyman, "Numerical methods for tracking interfaces," Physica D 12, 396 (1984).
23. C. W. Hirt and B. D. Nichols, "Volume of fluid (vof) method for the dynamics of free boundaries," J. Comput. Phys. 39, 201 (1981).
24. S. O. Unverdi and G. Trygvasson, "A front-tracking method for viscous, incompressible, multi-fluid flows," J. Comput. Phys. 100, 25 (1992).
25. Q. Shi and H. Haj-Hariri, in Proceedings of the 32nd Aerospace Sciences Meeting (AIAA, Washington, 1994), Paper No. AIAA 94-0834.
26. In this case one may introduce an entropy functional instead of a free energy functional along the lines described in Refs. 27 and 28.
27. S.-L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, "Thermodynamicaily-consistent phasefield models for solidification," Physica D 69, 189 (1993).
28. H. W. Alt and I. Pawlow, "A mathematical model of dynamics of nonisothermal phase separation," Physica D 59, 389 (1992).
29. D. Boyanovsky, D. Jasnow, J. Llambías, and S. Takakura, "Statics and dynamics of an interface in a temperature gradient," Phys. Rev. E 51, 5453 (1995).
30. P. Bjorstad, W. W. Coughran, Jr., H. S. Greenside, D. J. Rose, and N. L. Schryer, Elliptic Problem Solvers II (Academic Press, New York, 1984).
31. R. Chella and J. Viñals, "Mixing of a two-phase fluid by cavity flow," Phys. Rev. E (in press).
32. N. Young, J. Goldstein, and J. Block, "'The motion of bubbles in a vertical temperature gradient," J. Fluid Mech. 6, 350 (1959).
33. R. S. Subramanian, in Transport Processes in Bubbles, Drops and Particles, edited by R. P. Chhabraand and D. DeKee (Hemisphere, Washington, DC, 1990), pp. 1-42.
34. Note that one can show for Model H, by using similar arguments as in deriving the tangential and normal surface forces in Section II above, that for weak temperature gradients the velocity is proportional to both the gradient and the radius, independent of the spatial dimensionality.
35. J. Llambías, A. Shinozaki, and D. Jasnow, in Proceedings of the 2nd Microgravity Fluid Physics Conference (NASA, Cleveland, 1994), pp. 207-212, NASA Conference Publication 3276.
36. V. Zakharov, V. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer-Verlag, New York, 1992), Chap. 1.
37. J. Serrin, in Mathematical Principles of Classical Fluid Mechanics, Vol. VIII/1 of Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1959), pp. 125-263, section 14-15.
38. B. Felderhof, "Dynamics near the diffuse gas-liquid interface near the critical point," Physica 48, 541 (1970).
39. L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959).