Diffuse-Interface Modeling of Fluid Systems: References

The following is a list of references related to modeling fluid interfaces using diffuse-interface theory. It is the bibliography from the paper "Diffuse-Interface Models in Fluid Mechanics" (Anderson, McFadden and Wheeler) in Ann. Rev. Fluid Mech. 30 (1998) 139-165.
1. Abraham FF. 1979. On the thermodynamics, structure and phase stability of the nonuniform fluid state. Phys. Rep. 53:93-156.

2. Affouf M, Caflisch RE. 1991. A numerical study of Riemann problem solutions and stability for a system of viscous conservation laws of mixed type. SIAM J. Appl. Math. 51:605-34.

3. Aifantis EC, Serrin JB. 1983a. The mechanical theory of fluid interfaces and Maxwell's rule. J. Colloid Int. Sci. 96:517-29.

4. Aifantis EC, Serrin JB. 1983b. Equilibrium solutions in the mechanical theory of fluid microstructures, J. Colloid Int. Sci. 96:530-47.

5. Anderson DM, McFadden GB. 1996. A diffuse-interface description of fluid systems. NIST Int. Rep. 5887, National Institute of Standards and Technology, Gaithersburg, MD.

6. Anderson DM, McFadden GB. 1997. A diffuse-interface description of internal waves in a near-critical fluid. Phys. Fluids 9:1870-79

7. Antanovskii LK. 1995. A phase-field model of capillarity. Phys. Fluids 7:747-53.

8. Antanovskii LK. 1996. Microscale theory of surface tension. Phys. Rev. E 54:6285-90.

9. Batchelor GK. 1967. An Introduction to Fluid Dynamics, Cambridge: Cambridge University Press.

10. Bearman RJ, Kirkwood JG. 1958. Statistical mechanics of transport processes. XI. Equations of transport in multicomponent systems. J. Chem. Phys. 28:136-145.

11. Berg RF, Lyell MJ, McFadden GB, Rehm RG. 1996. Internal waves in xenon near the critical point. Phys. Fluids 8:1464-75.

12. Blinowski A. 1973a. On the surface behavior of gradient-sensitive liquids. Arch. Mech. 25:259-68.

13. Blinowski A. 1973b. On the order of magnitude of the gradient-of-density dependent part of an elastic potential in liquids. Arch. Mech. 25:833-49.

14. Blinowski A. 1974. Droplets and layers in the gradient model of a capillary liquid. Arch. Mech. 26:953-63.

15. Blinowski A. 1975. Gradient description of capillary phenomena in multicomponent fluids. Arch. Mech. 27:273-92.

16. Blinowski A. 1979. On two phenomenological models of capillary phenomena. Arch. Mech. 31:423-30.

17. Bongiorno V, Scriven LE, \& Davis HT. 1976. Molecular theory of fluid interfaces. J. Coll. Int. Sci. 57:462-75.

18. Brackbill JU, Kothe DB, Zemach C. 1992. A continuum method for modeling surface tension. J. Comp. Phys. 100:335-54.

19. Braun RJ, McFadden GB, Coriell SR. 1994. Morphological instability in phase-field models of solidification. Phys. Rev. E 49:4336-52.

20. Caginalp G. 1985. Surface tension and supercooling in solidification theory. In Applications of Field Theory to Statistical Mechanics, ed.~L Garrido, 216-226 Berlin: Springer-Verlag.

21. Caginalp G. 1986. An analysis of a phase field model of a free boundary. Arch. Rat. Mech. Anal. 92:205-45.

22. Caginalp G. 1989. Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. Phys. Rev. A 39:5887-96.

23. Cahn JW. 1961. On spinodal decomposition. Acta Metall. 9:795-801.

24. Cahn JW, Hilliard JE. 1958. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28:258-67.

25. Callen HB. 1985. Thermodynamics and an Introduction to Thermostatics, New York: Wiley.

26. Carslaw HS, Jaeger JC. 1959. Conduction of Heat in Solids, Oxford: Clarendon.

27. Chang YC, Hou TY, Merriman B, Osher S. 1996. A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comp. Phys. 124:449-64 (1996).

28. Chella R, Viñals J. 1996. Mixing of a two-phase fluid by cavity flow. Phys. Rev. E 53:3832-40.

29. Davis HT, Scriven LE. 1982. Stress and structure in fluid interfaces. Adv. Chem. Phys. 49:357-454.

30. Davis SH. 1983. Contact-line problems in fluid mechanics. J. Appl. Mech. 50:977-82.

31. de Sobrino L. 1976. Some thermodynamic and stability properties of a fluid with gradient dependent free energy. Can. J. Phys. 54:105-17.

32. de Sobrino L. 1985. Note on capillary waves in the gradient theory of interfaces. Can. J. Phys. 63:1132-33.

33. de Sobrino L, Peternelj J. 1982. Thermal fluctuations in the interface of an inhomogeneous fluid. Can. J. Phys. 60:137-53.

34. de Sobrino L, Peternelj J. 1985. On capillary waves in the gradient theory of interfaces. Can. J. Phys. 63:131-34.

35. Delhaye JM. 1974. Jump conditions and entropy sources in two-phase systems. Local instant formulation. Int. J. Multiphase Flow 1:395-409.

36. Dell'Isola F, Gouin H, Rotoli G. 1996. Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations. Eur. J. Mech. B/Fluids 15:545-68.

37. Dell'Isola F, Gouin H, Seppecher P. 1995. Radius and surface tension of microscopic bubbles by second gradient theory. C. R. Acad. Sci. Paris 320:211-16.

38. Dell'Isola F, Kosinski W. 1993. Deduction of thermodynamic balance laws for bidimensional nonmaterial directed continua modelling interphase layers. Arch. Mech. 45:333-59.

39. Drazin PG, Reid WH. 1981. Hydrodynamic Stability, Cambridge: Cambridge University Press.

40. Dunn JE. 1986. Interstitial working and a nonclassical continuum thermodynamics. In New Perspectives in Thermodynamics, ed. J Serrin. Berlin: Springer.

41. Dunn JE, Serrin JB. 1985. On the thermomechanics of interstitial working. Arch. Rat. Mech. Anal. 88:95-133.

42. Dussan V. EB. 1979. On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11:371-400.

43. Dussan V. EB, Davis SH. 1974. On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65:71-95.

44. Felderhof BU. 1970. Dynamics of the diffuse gas-liquid interface near the critical point. Physica 48:541-60.

45. Fixman M. 1967. Transport coefficients in the gas critical region. J. Chem. Phys. 47:2808-18.

46. Galdi P, Joseph DD, Preziosi L, Rionero S. 1991. Mathematical problems for miscible, incompressible fluids with Korteweg stresses. Eur. J. Mech. B/Fluids 10(3):253-67.

47. Gibbs JW. 1876. On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 3:108-248; 3:343-524, 1878. Reprinted in The Scientific Papers of J. Willard Gibbs, pp. 55-371. London: Longmans, Green, and Co, 1906.

48. Goldstein H. 1980. Classical Mechanics, Reading, MA, USA: Addison-Wesley.

49. Gurtin ME, Polignone D, Viñals J. 1996. Two-phase binary fluids and immiscible fluids described by an order parameter. Mathematical Models and Methods in Applied Sciences, 6:815.

50. Halperin BI, Hohenberg PC, Siggia ED. 1974. Renormalization-group calculations of divergent transport coefficients at critical points. Phys. Rev. Lett. 32:1289-92.

51. Helfand E, Fredrickson GH. 1989. Large fluctuations in polymer solutions under shear. Phys. Rev. Lett. 62:2468-71.

52. Hilliard JE. 1970. Spinodal decomposition. In Phase Transformations, ed. HI Aaronson. Metals Park, Ohio: American Society of Metals.

53. Hirt CW, Nichols BD. 1981. Volume of fluid (VOF) methods for the dynamics of free boundaries. J. Comp. Phys. 39:201-25.

54. Hohenberg PC, Halperin BI. 1977. Theory of dynamic critical phenomena. Rev. Mod. Phys. 49:435-79.

55. Huh C, Scriven LE. 1971. Hydrodynamic model of steady movement of a solid/liquid/ fluid contact line. J. Coll. Int. Sci. 35:85-101.

56. Hyman JM. 1984. Numerical methods for tracking interfaces. Physica D 12:396-407.

57. Irving JH, Kirkwood JG. 1950. The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18:817-829.

58. Jacqmin D. 1996. An energy approach to the continuum surface tension method. AIAA 96-0858. In Proceedings of the 34th Aerospace Sciences Meeting and Exhibit. Reno: American Institute of Aeronautics and Astronautics.

59. Jasnow D, Viñals J. 1996. Coarse-grained description of thermo-capillary flow. Phys. Fluids 8:660-69.

60. Joseph DD. 1990. Fluid dynamics of two miscible liquids with diffusion and gradient stresses. Eur. J. Mech., B/Fluids 9:565-96.

61. Joseph DD, Huang A, Hu H. 1996. Non-solenoidal velocity effects and Korteweg stresses in simple mixtures of incompressible liquids. Physica D 97:104-25.

62. Juric D, Tryggvason G. 1995. A front-tracking method for liquid-vapor phase change. In Advances in Numerical Modeling of Free Surface and Interfacial Fluid Dynamics, ed. PE Raad, TT Huang, G Tryggvason, FED-Vol. 234:141-48. New York: ASME.

63. Juric D, Tryggvason G. 1996. Direct numerical simulations of flows with phase change. AIAA 96-0857. In Proceedings of the 34th Aerospace Sciences Meeting and Exhibit. Reno: American Institute of Aeronautics and Astronautics.

64. Kawasaki K. 1970. Kinetic equations and time correlation functions of critical fluctuations. Ann. Phys. 61:1-56.

65. Kittel C, Kroemer H. 1980. Thermal Physics, New York: Freeman.

66. Kobayashi R. 1993. Modeling and numerical simulations of dendritic crystal growth. Physica D 63:410-23.

67. Korteweg DJ. 1901. Sur la forme que prennent les équations du mouvements des fluides 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'hypothése d'une variation continue de la densité. Arch. Néerl. Sci. Exactes Nat. Ser. II 6:1-24.

68. Lamb H. 1932. Hydrodynamics, Cambridge: Cambridge University Press.

69. Landau LD, Lifshitz EM. 1959. Fluid Mechanics, New York: Pergamon Press.

70. Langer JS. 1986. Models of pattern formation in first-order phase transitions. In Directions in Condensed Matter Physics, ed. G Grinstein, G Mazenko, 165-86. Philadelphia: World Scientific.

71. Langer JS, Turski LA. 1973. Hydrodynamic model of the condensation of a vapor near its critical point. Phys. Rev. A 8:3230-43.

72. Lighthill J. 1978. Waves in Fluids, Cambridge: Cambridge University Press.

73. Lowengrub J, Truskinovsky L. 1997. Cahn-Hilliard fluids and topological transitions. submitted to Proc. Roy. Soc. London A (1997).

74. Maxwell JC. 1876. Capillary Action. In Encyclopaedia Britannica (9th edition). Reprinted in The Scientific Papers of James Clerk Maxwell, vol.~2, pp. 541-591. New York: Dover, 1952.

75. Mulder W, Osher S, Sethian JA. 1992. Computing interface motion in compressible gas dynamics. J. Comp. Phys. 100:209-28.

76. Nadiga BT, Zaleski S. 1996. Investigations of a two-phase fluid model. European J. of Mech. B: Fluids. 15:885-896.

77. Nobari MR, Jan YJ, Tryggvason G. 1996. Head-on collision of drops-a numerical investigation. Phys. Fluids 8:29-42.

78. Onuki A. 1989. Elastic effects in the phase transition of polymer solutions under shear flow. Phys. Rev. Lett. 62:2472-75.

79. Onuki A, Kawasaki K. 1979. Nonequilibrium steady state of critical fluids under shear flow: a renormalization group approach. Ann. Phys. 121:456-528.

80. Onuki A, Yamazaki K, Kawasaki K. 1981. Light scattering by critical fluids under shear flow. Ann. Phys. 131:217-42.

81. Osher S, Sethian JA. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 79:12-49.

82. Poisson SD. 1831. Nouvelle Theorie de l'action capillaire, Paris: Bachelier.

83. Lord Rayleigh. 1892. On the theory of surface forces.-II. Compressible fluids. Phil. Mag. 33:209-220.

84. Rowlinson JS. 1979. Translation of J.D. van der Waals' the thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J. Stat. Phys. 20:197-244.

85. Rowlinson JS, Widom B. 1989. Molecular Theory of Capillarity, Oxford: Clarendon.

86. Seppecher P. 1996. Moving contact lines in the Cahn-Hilliard theory. Int. J. Engng. Sci. 34(9):977-92.

87. Sethian JA. 1996. Level Set Methods, Cambridge: Cambridge University Press.

88. Siggia ED, Halperin BI, Hohenberg PC. 1976. Renormalization-group treatment of the critical dynamics of the binary-fluid and gas-liquid transitions. Phys. Rev. B 13:2110-23.

89. Stanley HE. 1971. Introduction to Phase Transitions and Critical Phenomena, Oxford: Oxford University Press.

90. Starovoitov VN. 1994. Model of the motion of a two-component liquid with allowance of capillary forces. J. Appl. Mech. Techn. Phys. 35:891-97.

91. Sussman M, Smerka P, Osher S. 1994. A level set approach for computing solutions to incompressible two-phase flow. J. Comp. Phys. 114:146-59.

92. Truskinovsky, L. 1993. Kinks versus shocks. In Shock Induced Transitions and Phase Structures in General Media, IMA Series in Math. and its Appl. ed. JE Dunn, R Fosdick, M Slemrod, 52:185-229. New York: Springer-Verlag.

93. Tsai W, Yue DKP. 1996. Computation of nonlinear free-surface flows. Ann. Rev. Fluid Mech. 28:249-78.

94. Turski LA, Langer JS. 1980. Dynamics of a diffuse liquid-vapor interface. Phys. Rev. A 22:2189-95.

95. Unverdi SO, Tryggvason G. 1992a. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comp. Phys. 100:25-37.

96. Unverdi SO, Tryggvason G. 1992b. Computations of multi-fluid flows. Physica D 60:70-83.

97. van der Waals JD. 1893. Verhandel. Konink. Akad. Weten. Amsterdam (Sect. 1), vol. 1, No. 8 (Dutch); Transl. Ostwald, 1894, Thermodynamische theorie der kapillarität unter voraussetzung stetiger dichteänderung. Z. Phys. Chem. 13:657-725 (German); Transl. Anonymous, 1895, Arch. Néerl. 28:121-201 (French). Transl. JS Rowlinson, 1979, Translation of J.D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous density variation''. J. Stat. Phys. 20:197-244 (From Dutch, German, French)

98. Wang SL, Sekerka RF, Wheeler AA, Murray BT, Coriell SR, et al. 1993. Thermodynamically-consistent phase-field models for solidification. Physica D 69:189-200.

99. Warren JA, Boettinger WJ. 1995. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta. metall. mater. 43:689-703.

100. Warren JA, Murray BT. 1996. Ostwald ripening and coalescence of a binary alloy in two dimensions using a phase-field model. Modell. Simul. Mater. Sci. Eng. 4:215-29.

101. Weatherburn CE. 1925. Differential invariants in geometry of surfaces, with applications to mathematical physics. Quarterly J. Mathematics 50:230-69.

102. Wheeler AA, McFadden GB, Boettinger WJ. 1996. Phase-field model for solidification of a eutectic alloy. Proc. Roy. Soc. London A 452:495-525.

103. Wheeler AA, Murray BT, Schaefer RJ. 1993. Computation of dendrites using a phase-field model. Physica D 66:243-62.

104. Yang AJM, Fleming III PD, Gibbs JH. 1976. Molecular theory of surface tension. J. Chem. Phys. 64:3732-47.

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