The motion, stability and breakup of a stretching liquid bridge with a receding contact line

Journal of Fluid Mechanics

Volumn 666, Issue , 2011, Pages 554-572

  Qian, Bian ^a,b   Breuer, Kenneth S ^a  

^a Brown University   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

instability; liquid bridges

Indexed keywords

CONTACT ANGLE; FORECASTING; HYDROPHOBICITY; PLASMA STABILITY; ROLLING RESISTANCE; SURFACE CHEMISTRY;

DYNAMIC CONTACT ANGLE; DYNAMIC CONTACT LINE MODELS; DYNAMICAL EQUATION; HYDROPHOBIC SURFACES; LIQUID BRIDGE; NUMERICAL PREDICTIONS; QUASI STATIC ANALYSIS; RECEDING CONTACT LINES;

LIQUIDS;

COMPUTATIONAL FLUID DYNAMICS; DROPLET; EXPERIMENTAL STUDY; FLOW STABILITY; ONE-DIMENSIONAL MODELING; STABILITY ANALYSIS; SUBSTRATE;

EID: 79951650340     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010004611     Document Type: Article

References (38)

1. Aarts, D. G. A. L., Lekkerkerker, H. N. W., Guo, H., Wegdam, G. H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.
2. Bird, J. C., Mandre, S. & Stone, H. A. 2008 Short-time dynamics of partial wetting. Phys. Rev. Lett. 100, 234501.
3. Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739-805.
4. Deladi, S., Tas, N. R., Berenschot, J. W., Krijnen, G. J. M., de Boer, M. J., de Boer, J. H., Peter, M. & Elwenspoek, M. C. 2004 Micromachined fountain pen for atomic force microscope-based nanopatterning. Appl. Phys. Lett. 85, 5361-5363. (Pubitemid 40043578)
5. Dodds, S., da Silveira Carvalho, M. & Kumar, S. 2009 Stretching and slipping of liquid bridges near plates and cavities. Phys. Fluids 21, 092103.
6. Dussan V., E. B. 1979 On the spreading of liquid on the solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371-400. (Pubitemid 10412133)
7. Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 3458-3460.
8. Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262, 205-221. (Pubitemid 280656)
9. Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293-310. (Pubitemid 129657831)
10. Frankel, I. & Weihs, D. 1985 Stability of a capillaryjet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289-307. (Pubitemid 15527660)
11. Gillette, R. D. & Dyson, D. C. 1971 Stability of fluid interfaces of revolution between equal solid circular plates. Chem. Engng J. 2, 44-54.
12. Ginger, D. S., Zhang, H. & Mirkin, C. A. 2004 The evolution of dip-pen nanolithography. Angew. Chem. 43, 30-45. (Pubitemid 38063469)
13. Liao, Y. C., Franses, E. I. & Basaran, O. A. 2006 Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer. Phys. Fluids 18, 022101.
14. Lide, D. R. (Ed.) 2010 CRC Handbook of Chemistry and Physics. Internet Version 2010. URL http://hbcpnetbase.com/
15. Mason, G. C. 1970 An experimental determination of the stable length ofcylindrical liquid bubbles. J. Colloid Interface Sci. 32, 172-176.
16. Meseguer, J. 1984 Stability of slender, axisymmetric liquid bridges between unequal disks. J. Cryst. Growth 67, 141-143.
17. Meseguer, J. & Sanz, A. 1985 Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges. J. Fluid Mech. 153, 83-101. (Pubitemid 15494030)
18. Moldovan, N., Kim, K.-H. & Espinosa, H. D. 2006 Design and fabrication of a novel microfluidic nanoprobe. J. Microelectromech. Syst. 15, 204-213. (Pubitemid 43210804)
19. Müller, U. R. & Nicolau, D. V. 2004 Microarray Technology and Its Application. Springer.
20. Myshkis, A. D., Babskii, V. G., Slobozhanin, N. D. Kopachevskii L. A. & Tyuptsov, A. D. 1987 Low-Gravity Fluid Mechanics. Springer.
21. Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931-980.
22. Panditaratne, J. C. 2003 Deflection of microjets induced by asymmetric heating and related free surface flows with moving contact lines. PhD thesis, Purdue University.
23. Papageorgiou, D. T. 1995 Analytical description of the breakup of liquid jets. J. Fluid Mech. 301, 109-132.
24. Perales, J. M., Meseguer, J. & Martinez, I. 1991 Minimum volume stability limits for axisymmetric liquid bridges subject to steady axial acceleration. J. Cryst. Growth 110, 855-861. (Pubitemid 21715457)
25. Plateau, J. 1863 Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity. Annual Report of the Board of Regents of the Smithsonian Institution, p. 207. Washington: Smithsonian Institution.
26. Qian, B., Loureiro, M., Gagnon, D. A., Tripathi, A. & Breuer, K. S. 2009 Micron-scale droplet deposition on a hydrophobic surface using a retreating syringe. Phys. Rev. Lett. 102, 164502.
27. Rayleigh, Lord 1878 On the instability ofjets. Proc. Lond. Math. Soc. 10, 4-13.
28. Russo, M. J. & Steen, P. H. 1986 Instability of rotund capillary bridges to general disturbances, experiment and theory. J. Colloid Interface Sci. 113, 154-163.
29. Sanz, A. & Martinez, I. 1983 Minimum volume for a liquid bridge between equal disks. J. Colloid Interface Sci. 93, 235-240.
30. Slobozhanin, L. A. & Alexander, J. I. D. 1998 Combined effect of disk inequality and axial gravity on axisymmetric liquid bridge stability. Phys. Fluids 10, 2473-2488. (Pubitemid 128597759)
31. Slobozhanin, L. A., Alexander, J. I. D. & Resnick, A. H. 1997 Bifurcation of the equilibrium states of a weightless liquid bridge. Phys. Fluids 9, 1893-1905. (Pubitemid 127636059)
32. Slobozhanin, L. A. & Perales, J. M. 1993 Stability of liquid bridges between equal disks in an axial gravity field. Phys. Fluids A 5, 1305-1314.
33. Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 1473-1484. (Pubitemid 10414577)
34. Thoroddesen, S. T., Takehara, K. & Etoh, T. G. 2005 The coalescence speed of a pendent and a sessile drop. J. Fluid Mech. 527, 85-114.
35. Villanueva, W., Sjödahl, J., Stjernström, M., Roeraade, J. & Amberg, G. 2007 Microdroplet deposition under a liquid medium. Langmuir 23, 1171-1177.
36. Wilson, S. K., Hunt, R. & Duffy, B. R. 2000 The rate of spreading in spin coating. J. Fluid Mech. 413, 65-88.
37. Yildirim, O. E. & Basaran, O. A. 2001 Deformation and breakup ofstretching bridges of Newtonian and shear-thinning liquids: comparison of one-and two-dimensional models. Chem. Engng Sci. 56, 211-233. (Pubitemid 32285998)
38. Zhang, X., Padgett, R. S. & Basaran, O. A. 1996 Nonlinear deformation and breakup ofstretching liquid bridges. J. Fluid Mech. 329, 207-245. (Pubitemid 126454303)