Free access
Issue
ESAIM: M2AN
Volume 37, Number 5, September-October 2003
Page(s) 741 - 753
DOI http://dx.doi.org/10.1051/m2an:2003042
Published online 15 November 2003
  1. D.M. Anderson, G.B. McFadden and A.A. Wheeler, Diffuse interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1998) 139-165. [CrossRef]
  2. L.K. Antanovskii, Microscale theory of surface tension. Phys. Rev. E 54 (1996) 6285-6290. [CrossRef]
  3. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial Free Energy. J. Chem. Phys. 28 (1958) 258-267. [CrossRef]
  4. D. Joseph and M. Renardy, Fundamentals of two-fluid dynamics, Vol. II. Springer, New York (1992).
  5. D.J. Korteweg, Sur la forme que prennent les équations du mouvement des fluides si l'on tient compte des forces capillaires causées par des variations de densité considérables mais connues 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 (1901) 1-24.
  6. O.A. Ladyzhenskaya, Mathematical theory of viscous incompressible flow. Gordon and Breach (1963).
  7. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Gauthier-Villars, Paris (1969).
  8. J. Pojman, N. Bessonov, R. Texier, V. Volpert and H. Wilke, Numerical simulations of transient interfacial phenomena in miscible fluids, in Proceedings AIAA, Reno, USA (January 2002).
  9. J. Pojman, Y. Chekanov, J. Masere, V. Volpert, T. Dumont and H. Wilke, Effective interfacial tension induced convection in miscible fluids, in Proceedings of the 39th AIAA Aerospace Science Meeting, Reno, USA (January 2001).
  10. P. Petitjeans, Une tension de surface pour les fluides miscibles. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 673-679.
  11. R. Temam, Navier-Stokes equations. Theory and numerical analysis. North-Holland Publishing Co., Amsterdam-New York, Stud. Math. Appl. 2 (1979).
  12. R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM (1983).
  13. J.S. Rowlinson, Translation of J.D. van der Waals' ``The thermodynamic theory of capillarity under hypothesis of a continuous variation of density''. J. Statist. Phys. 20 (1979) 197. [CrossRef] [MathSciNet]
  14. V. Volpert, J. Pojman and R. Texier-Picard, Convection induced by composition gradients in miscible liquids. C. R. Acad. Sci. Paris Sér. I Math. 330 (2002) 353-358.

Recommended for you