Pinch-off singularities in rotating Hele-Shaw flows at high viscosity contrast

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 5, 2009, Pages

  Alvarez Lacalle, E ^a   Casademunt, J ^b   Eggers, J ^c  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FORCE; CENTER OF ROTATION; CIRCULAR DROPS; HELE-SHAW CELLS; INITIAL CONDITIONS; NUMERICAL SIMULATION; PINCHOFF; ROTATING HELE-SHAW CELLS; ROTATING HELE-SHAW FLOWS; VISCOSITY CONTRAST;

AIR LUBRICATION; CENTRIFUGATION; COMPUTER SIMULATION; NUMERICAL METHODS; ROTATIONAL FLOW;

ROTATION;

EID: 71449127317     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.056306     Document Type: Article

References (23)

1. J. Eggers, Rev. Mod. Phys. 69, 865 (1997). 10.1103/RevModPhys.69.865
2. M. Moseler and U. Landman, Science 289, 1165 (2000). 10.1126/science.289. 5482.1165
3. J. Eggers, Phys. Rev. Lett. 89, 084502 (2002). 10.1103/PhysRevLett.89. 084502
4. A. Oron, S. H. Davis, and S. G. Bankoff, Rev. Mod. Phys. 69, 931 (1997). 10.1103/RevModPhys.69.931
5. G. Tryggvason and H. Aref, J. Fluid Mech. 154, 287 (1985). 10.1017/S0022112085001537
6. D. Bensimon, L. P. Kadanoff, S. Liang, B. I. Schraiman, and C. Tang, Rev. Mod. Phys. 58, 977 (1986). 10.1103/RevModPhys.58.977
7. J. Casademunt, Chaos 14, 809 (2004). 10.1063/1.1784931
8. L. Carrillo, F. X. Magdaleno, J. Casademunt, and J. Ortín, Phys. Rev. E 54, 6260 (1996). 10.1103/PhysRevE.54.6260
9. E. Alvarez-Lacalle, J. Casademunt, and J. Ortín, Phys. Rev. E 64, 016302 (2001). 10.1103/PhysRevE.64.016302
10. E. Alvarez-Lacalle, E. Pauné, J. Casademunt, and J. Ortín, Phys. Rev. E 68, 026308 (2003). 10.1103/PhysRevE.68.026308
11. W. W. Zhang and J. R. Lister, Phys. Fluids 11, 2454 (1999). 10.1063/1.870110
12. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, Phys. Rev. Lett. 70, 3043 (1993). 10.1103/PhysRevLett.70.3043
13. P. Constantin, T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, M. J. Shelley, and S.-M. Zhou, Phys. Rev. E 47, 4169 (1993). 10.1103/PhysRevE.47.4169
14. T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, and S.-M. Zhou, Phys. Rev. E 47, 4182 (1993). 10.1103/PhysRevE.47.4182
15. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, Phys. Rev. Lett. 75, 3665 (1995). 10.1103/PhysRevLett.75.3665
16. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, Phys. Fluids 10, 2701 (1998). 10.1063/1.869795
17. R. Almgren, Phys. Fluids 8, 344 (1996). 10.1063/1.869102
18. R. Almgren, A. Bertozzi, and M. Brenner, Phys. Fluids 8, 1356 (1996). 10.1063/1.868915
19. E. Alvarez-Lacalle, J. Casademunt, and J. Ortín, Phys. Fluids 16, 908 (2004). 10.1063/1.1644149
20. E. Alvarez-Lacalle, J. Ortín, and J. Casademunt, Phys. Rev. E 74, 025302 (R) (2006). 10.1103/PhysRevE.74.025302
21. R. Folch, E. Alvarez-Lacalle, J. Ortín, and J. Casademunt, Phys. Rev. E 80, 056305 (2009). 10.1103/PhysRevE.80.056305
22. J. Eggers and T. F. Dupont, J. Fluid Mech. 262, 205 (1994). 10.1017/S0022112094000480
23. Note that the linear growth of the vorticity with x in Eq. produces an apparent divergence of the integrals in Eq. 7 if considered separately and taken all the way to infinity. Note, however, that these would be naturally regularized for a closed (finite) interface and the two integrals in Eq. would cancel with each other the diverging part in the limit where the closure of the interface is taken to infinity.