Surface folding of viscoelastic fluids: Finite elasticity membrane model

European Journal of Applied Mathematics

Volumn 15, Issue 4, 2004, Pages 385-408

  Podgorski, T ^a,b   Belmonte, A ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12944317100     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792504005601     Document Type: Article

References (28)

1. ARUN KUMAR, K. & GRAHAM, M. D. (2000) Buckling instabilities in models of viscoelastic free surface flows. J. Non-Newtonian Fluid Mech. 89, 337-351.
2. BIRD, R. B., ARMSTRONG, R. C. & HASSAGER, O. (1987) Dynamics of Polymeric Liquids, vol. 1, 2nd ed. Wiley-Interscience.
3. CHEN, Y.-J. & STEEN, P. H. (1997) Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245-267.
4. CLANET, C. & QUÉRÉ, D. (2002) Onset of menisci. J. Fluid Mech. 460, 131-149.
5. COURANT, R. & HILBERT, D. (1962) Methods of Mathematical Physics, volume 2. Wiley-Interscience, 1962.
6. DE GENNES, P. G. (1985) Wetting: Statics and dynamics. Rev. Mod. Phys. 57, 827-863.
7. DUFFY, B. R. & MOFFATT, H. K. (1995) Flow of a viscous trickle on a slowly varying incline. Chem. Eng. J. 60, 141-146.
8. ELGSAETER, A., STOKKE, B. T., MIKKELSEN, A. & BRANTON, D. (1986) The molecular basis of erythrocyte shape. Science, 234, 1217-1223.
9. FOREST, M. G. & WANG, Q. (1990) Change-of-type behavior in viscoelastic free jets. J. Theor. Comput. Fluid Mech. 2, 1-25.
10. GELFAND, U. M. & FOMIN, S. V. (1963) Calculus of Variations. Dover.
11. GREEN, A. E. & ADKINS, J. E. (1960) Large Elastic Deformations. Oxford University Press.
12. HARLEN, O. G., HINCH, E. J. & RALLISON, J. M. (1992) Birefringent pipes: the steady flow of a dilute polymer solution near a stagnation point. J. Non-Newtonian Fluid Mech. 44, 229-265.
13. HARLEN, O. G., RALLISON, J. M. & CHILCOTT, M. D. (1990) High-Deborah number flows of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 34(3), 319-349.
14. HASSAGER, O. (1979) Negative wake behind bubbles in non-Newtonian liquids. Nature, 279, 402-403.
15. KAMPAS, F. (1998) Iterative solution of highly non-linear equations using Mathematica. 1998 Worldwide Mathematica Conference.
16. LIU, Y., LIAO, T. & JOSEPH, D. D. (1995) A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid. J. Fluid Mech. 304, 321-342.
17. MIDDLEMAN, S. (1995) Modeling Axisymmetric Flows: Dynamics of films, jets, and drops. Academic Press.
18. PODGORSKI, T. & BELMONTE, A. (2002) Surface folds during the penetration of a viscoelastic fluid by a sphere. J. Fluid Mech. 460, 337-348.
19. RASMUSSEN, H. K. & HASSAGER, O. (1999) Three-dimensional simulations of viscoelastic instability in polymeric filaments. J. Non-Newtonian Fluid Mech. 82, 189-202.
20. REHAGE, H. & HOFFMANN, H. (1991) Viscoelastic surfactant solutions: model systems for rheological research. Molecular Phys. 74, 933-973.
21. RENARDY, M. (2000) Wall boundary layers for Maxwell liquids. Arch. Rational Mech. Anal. 152, 93-102.
22. SEIFERT, U., BERNDL, K. & LIPOWSKY, R. (1991) Shape transformations of vesicles - phase diagram for spontaneous curvature and bilayer coupling models. Phys. Rev. A, 44, 1182-1202.
23. SMOLKA, L. B. & BELMONTE, A. (2003) Drop pinch-off and filament dynamics of wormlike micellar fluids. J. Non-Newtonian Fluid Mech. 115, 1-25.
24. SPIEGELBERG, S. H. & MCKINLEY, G. H. (1996) Stress relaxation and elastic decohesion of viscoelastic polymer solutions in extensional flow. J. Non-Newtonian Fluid Mech. 67, 49-76.
25. STONE, H. A., LIMAT, L., WILSON, S. K., FLESSELLES, J.-M. & PODGORSKI, T. (2002) Corner singularity of a contact line moving on a poorly wetting substrate. C. R. Acad. Sci. (Paris) IV, 3, 103-110.
26. TAYLOR, G. I. & MICHAEL, D. H. (1973) On making holes in a sheet of fluid. J. Fluid Mech. 58, 625-639.
27. YAO, M. & MCKINLEY, G. H. (1998) Numerical simulations of extensional deformations of viscoelastic liquid bridges in filament stretching devices. J. Non-Newtonian Fluid Mech. 74, 47-88.
28. YOUNG, T. (1805) An essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. 95, 65-87.