A diffuse-interface description of internal waves in a near-critical fluid

Physics of Fluids

Volumn 9, Issue 7, 1997, Pages 1870-1879

  Anderson, D M ^a   McFadden, G B ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTERFACES-FLUID; MODELLING-MATHEMATICAL; TWO-PHASE FLOW(GAS/LIQUID); WAVES INTERNAL;

EID: 0030804661     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869309     Document Type: Article

References (56)

1. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).
2. P. C. Hohenberg and M. Barmatz, "Gravity effects near the gas-liquid critical point," Phys. Rev. A 6, 289 (1972).
3. M. R. Moldover, J. V. Sengers, R. W. Gammon, and R. J. Hocken, "Gravity effects in fluids near the gas-liquid critical point," Rev. Mod. Phys. 51, 79 (1979).
4. R. F. Berg, M. J. Lyell, G. B. McFadden, and R. G. Rehm, "Internal wave in xenon near the critical point," Phys. Fluids 8, 1464 (1996).
5. M. Sh. Giterman, "Study of the critical state of a liquid using gravitational waves," Sov. Phys. Dokl. 12, 1141 (1968).
6. V. D. Khait, "On gravitational waves in a gas the critical point for the gas-liquid transition," Sov. Phys. JETP 30, 177 (1970).
7. M. Sh. Giterman and V. A. Shteinberg, "Internal gravitational waves and convective instability in liquids," Mekh. Zhi. Gosta 7, 55 (1972); English translation in Fluid Dyn 7, 238 (1972).
8. M. Sh. Giterman and V. A. Shteinberg, "Internal gravitational waves and convective instability in liquids," Mekh. Zhi. Gosta 7, 55 (1972); English translation in Fluid Dyn 7, 238 (1972).
9. 3," Phys. Rev. B 2, 4523 (1970).
10. J. W. Cahn and J. E. Hilliard, "Free energy of a nonuniform system. I. Interfacial free energy," J. Chem. Phys. 28, 258 (1958).
11. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, New York, 1995).
12. J. S. Rowlinson and B. Widom, Molecular Theory of Capillary (Clarendon, Oxford, 1989).
13. G. Cagunalp. "Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations," Phys. Rev. A 39, 5997 (1989).
14. R. Kobayashi, "Modeling and numerical simultions of dendritic crystal growth," Physica D 63, 410 (1993).
15. S.-L. Wang, and R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, "Thermodynamically-consistent phase-field models for solidification," Physica D 69, 189 (1993).
16. A. A. Wheeler, B. T. Murray, and R. J. Schaefer, "Computation of dendrites using a Phase-field model," Physica D 66, 243 (1993).
17. R. J. Braun, G. B. McFadden, and S. R. Coriell, "Morphological instability in phase-field models of solidification," Phys. Rev. E 49, 4336 (1994).
18. J. A. Warren and W. J. Boettinger, "Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method," Acta. Metall. Mat. 43, 689 (1995).
19. J. W. Cahn and S. M. Allen, "A microscopic theory for domain wall motion and its experimental verification in Fe-Al alloy domain growth kinetics," J. Phys. Paris Colloque C7, C7-51 (1977).
20. R. J. Braun, J. W. Cahn, G. B. McFadden, and A. A. Wheeler, "Anisotropy of interfaces in an ordered alloy: A multiple-order-parameter model," Philos. Trans. R. Soc. London, (in press).
21. M. Fixman, "Transport coefficients in the gas critical region," J. Chem. Phys. 47, 2808 (1967).
22. B.U. Felderhof, "Dynamics of the diffuse gas-liquid interface near the critical point," Physica 48, 541 (1970).
23. K. Kawasaki, "Kinetic equations and time correlation functions of critical fluctuations," Ann. Phys. 61, 1 (1970).
24. J. S. Langer and L. A. Turski, "Hydrodynamic model of the condensation of a vapor near its critical point," Phys. Rev. A 8, 3230 (1973).
25. B. I. Halperin, P C. Hobenberg, and E. D. Siggia, "Renormalizationgroup calculations of divergent transport coefficients at critical points," Phys. Rev. Lett. 32, 1289 (1974).
26. L. de Sobrino, "Some thermodynamic and stability properties of a fluid with gradient dependent free energy," Can J. Phys. 54, 105 (1976).
27. 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).
28. P. C. Hohenberg ang B. I. Halperin, "Theory of dynamic phenomena," Rev. Mod. Phys. 49, 435 (1977).
29. A. Onuki and K. Kawasaki, "Nonequilibrium steady state of critical fluids under shear flow: A renormalization group approach," Ann. Phys. 121, 456 (1979).
30. A. Onuki, K. Yamazaki, and K. Kawasaki, "Light scattering by critical fluids under shear flow," Ann. Phys. 131, 217 (1981).
31. J. E. Dunn and J. B. Serrin, "On the thermomechanics of interstitial working," Arch. Rat. Mech. 88, 95 (1985).
32. V. N. Starovoitov, "Model of the motion of a two-component liquid with allowance of capillary forces," J. Appl. Mech. Tech. Phys. 35, 891 (1994).
33. L. K. Antanovskii, "A phase-field model of capillarity," Phys. Fluids 7, 747 (1995).
34. M. E. Gurtin, D. Polignone, and J. Viñals, "Two-phase binary fluids and immiscible fluids described by an order parameter," Math. Mod. Methods Appl. Sci. 6, 815 (1996).
35. R. Chella and J. Viñals, "Mixing of a two-phase fluid by cavity flow," Phys. Rev. E 53, 3832 (1996).
36. D. Jasnow and J. Viñals, "Coarse-grained description of thermo-capillary flow," Phys. Fluids 8, 660 (1996).
37. D. Jacqmin, "An energy approach to the continuum surface tension method," in Proceedings of the 34th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, 1996.
38. P. Seppecher, "Moving contact lines in the Cahn-Hilliard theory," Int. J. Eng. Sci. 34, 977 (1996).
39. B. T. Nadiga and S. Zaleski, "Investigations of a two-phase fluid model," submitted to Eur. J. Mech. B Fluids.
40. J. Lowengrub and L. Truskinovsky, "Cahn-Hilliard fluids and topological transition," submitted to Proc. R. Soc. London A.
41. J. U. Brackbill, D. B. Kothe, and C. Zemach, "A continuum method for modeling surface tension," J. Comput. Phys. 100, 335 (1992).
42. S. O. Unverdi and G. Tryggvason, "A front-tracking method for viscous, incompressible, multi-fluid flows," J. Comput. Phys. 100, 25 (1992).
43. S. O. Unverdi and G. Tryggvason, "Computations of multi-fluid flows," Physica D 60, 70 (1992).
44. J. A. Sethian, Level Set Methods (Cambridge University Press, Cambridge, 1996).
45. D. J. Korteweg, "Sur la forme que prennent les équations du mouvements des fluids si l'on tient compte des forces capillaires causées par des variations de densité considérables mais continues et sur la théorie de la capillarité dans l'hypothèse d'une variation continue de la densité," Arch. Néerl. Sci. Exactes Nat. Ser. II 6, 1 (1901).
46. H. T. Davis and L. E. Scriven, "Stress and structure in fluid interfaces," Adv. Chem. Phys. 49, 357 (1982).
47. E. C. Aifantis and J. B. Serrin, "The mechanical theory of fluid interfaces and Maxwell's rule," J. Colloid. Interface Sci. 96, 517 (1983).
48. E. C. Aifantis and J. B. Serrin, "Equilibrium solutions in the mechanical theory of fluid microstructures," J. Colloid. Interface Sci. 96, 530 (1983).
49. J. W. Cahn, "Critical point wetting," J. Chem. Phys. 66, 3667 (1977).
50. A. A. Wheeler, G. B. McFadden, and W. J. Boettinger, "Phase-field model for solidification of a eutectic alloy," Proc. R. Soc. London Ser. A 452, 495 (1996).
51. D. M. Anderson and G. B. McFadden, "A diffuse-interface description of fluid systems," NISTIR 5887, National Institute of Standards and Technology, Gaithersburg, MD 20899, August 1996.
52. H. B. Callen, Thermodynamics and an Introduction to Thermostatics (Wiley, New York, 1985).
53. J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1978).
54. H. B. Keller, Numerical Solution of Two Point Boundary Value Problems, Regional Conference Series in Applied Mathematics (SIAM, Philadelphia, 1976), Vol. 24.
55. M. R. Scott and H. A. Watts, "Computational solution of linear two-point boundary value problems via orthonormalization" SIAM J. Num. Anal. 14, 40 (1977).
56. S. Fisk and B, Widom, "Structure and free energy of the interface between fluid phases in equilibrium near the critical point," J. Chem. Phys. 50, 3219 (1969).