Marangoni-driven singularities via mean-curvature flow

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 24, 2010, Pages

  Krechetnikov, Rouslan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952941244     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/24/242001     Document Type: Article

References (39)

1. Fernandez J and Homsy G M 2004 Chemical reaction-driven tip-streaming phenomena in a pendant drop Phys. Fluids 16 2548-55
2. Krechetnikov R and Homsy G M 2004 On physical mechanisms in chemical reaction-driven tip-streaming Phys. Fluids 16 2556-66
3. Krechetnikov R and Homsy G M 2004 On a new surfactant-driven fingering phenomenon in a Hele-Shaw cell J. Fluid Mech. 509 103-24
4. Fernandez J, Krechetnikov R and Homsy G M 2005 Experimental study of a new surfactant-driven fingering phenomenon in a Hele-Shaw cell J. Fluid Mech. 527 197-216
5. Taylor G I 1934 The formation of emulsions in definable fields of flow Proc. R. Soc. A 146 501-23
6. de Bruijn R A 1993 Tipstreaming of drops in simple shear flows Chem. Eng. Sci. 48 277-84
7. Bentley B J and Leal L G 1986 An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows J. Fluid Mech. 167 241-83
8. Eggleton C D, Tsai T-M and Stebe K J 2001 Tip streaming from a drop in the presence of surfactants Phys. Rev. Lett. 87 048302
9. Sethian J A and Chopp D L 1994 Physics and geometry of flow under curvature: singularity formation, minimal surfaces, geodesics, and surface tension Motion by Mean Curvature: Proc. Intl Conf. ed G Buttazzo and A Visintin (New York: de Gruyter) pp 168-85
10. Mullins W W 1956 Two-dimensional motion of idealized grain boundaries J. Appl. Phys. 27 900-4
11. Newmann J von 1952 Metal interfaces American Society for Testing Materials (Cleveland, OH: Chemical Rubber Company) p 108
12. Cardoso V, Dias O J C and Gualtieri L 2008 The return of the membrane paradigm? Black holes and strings in the water tap Int. J. Mod. Phys. D 17 505-11
13. Sethian J A 1990 Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws J. Differ. Geom. 31 131-61
14. Osher S and Sethian J A 1988 Fronts propasgating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 12-49
15. Sethian J A 1996 Level Set Methods (Cambridge: Cambridge University Press)
16. Xu J-J, Li Z, Lowengrub J and Zhao H 2006 A level-set method for interfacial flows with surfactant J. Comput. Phys. 212 590-616
17. Grayson M A 1989 A short note on the evolution of a surface by its mean curvature Duke Math. J. 58 555-8
18. Gage M and Hamilton R S 1986 The heat equation shrinking convex plane curves J. Differ. Geom. 23 69-96
19. Huisken G 1984 Flow by mean curvature of convex surfaces into spheres J. Differ. Geom. 20 237-66
20. Huisken G 1990 Asymptotic behavior for singularities of the mean curvature flow J. Differ. Geom. 31 285-99
21. Rayleigh L 1890 Measurements of the amount of oil necessary in order to check the motions of camphor upon water Proc. R. Soc. 47 364-7
22. Darcy H 1856 Les Fontaines Publiques de la Ville de Dijon (Paris: Dalmont)
23. Homsy G M 1987 Viscous fingering in porous media Annu. Rev. Fluid Mech. 19 271-311
24. Joseph D, Funada T and Wang J 2007 Potential Flows of Viscous and Viscoelastic Liquids (Cambridge: Cambridge University Press)
25. Batchelor G K 1967 An Introduction to Fluid Mechanics (Cambridge: Cambridge University Press)
26. Brackbill J U, Kothe D B and Zemach C 1992 A continuum method for modeling surface tension J. Comput. Phys. 100 335-54
27. Stone A 1994 Evolutionary existence proofs for the pendant drop and n-dimensional catenary problems Pac. J. Math. 164 147-78
28. Smale S 1980 Smooth solutions of the heat and wave equations Comment. Math. Helvetici 55 1-12
29. Folland G B 1995 Introduction to Partial Diferential Equations (Princeton, NJ: Princeton University Press)
30. McOwen R C 2003 Partial Differential Equations (Englewood Cliffs, NJ: Prentice Hall)
31. Sedov L I 1961 Similarity and Dimensional Methods in Mechanics (New York: Academic)
32. Barenblatt G I 1996 Scaling, Self-Similarity and Intermediate Asymptotics (Cambridge: Cambridge University Press)
33. Drazin P and Riley N 2006 The Navier-Stokes Equations: A Classification of Flows and Exact Solutions (Cambridge: Cambridge University Press)
34. Hou T Y, Lowengrub J S and Shelley M J 1994 Removing the stiffness from interfacial flows with surface tension J. Comput. Phys. 114 312-38
35. Pismen L M 2004 Diffuse-interface effects near a cusp singularity on a free surface Phys. Rev. E 70 051604
36. Kawasaki K and Kawakatsu T 1990 Continuum theory of an immiscible binary fluid mixture with a surfactant Physica A 164 549-63
37. Wheeler A A 2006 Phase-field theory of edges in an anisotropic crystal Proc. R. Soc. A 462 3363-84
38. Voigt A 2005 Dynamics of evolving surfaces with small corner energy regularization Nonlinear Anal. 63 e1179-84
39. Landau L D and Lifshitz E M 1987 Fluid Mechanics (Oxford: Butterworth-Heinemann)