Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

Physics of Fluids

Volumn 21, Issue 7, 2009, Pages

  Young, Y N ^a   Booty, M R ^a   Siegel, M ^a   Li, J ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; NAVIER STOKES EQUATIONS; SOLUBILITY; SURFACE ACTIVE AGENTS; VISCOSITY; VISCOUS FLOW;

ADSORPTION-DESORPTION KINETICS; DIFFUSION-CONTROLLED REGIME; INSOLUBLE SURFACTANTS; LONG WAVE MODELS; SOLUBLE SURFACTANTS; SURFACTANT SOLUBILITY; SURFACTANT-FREE; THREAD FORMATION;

FIGHTER AIRCRAFT;

EID: 70350716588     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3176462     Document Type: Article

References (51)

1. S. L. Anna, N. Bontoux, and H. A. Stone, "Formation of dispersions using 'flow focusing' in microchannels," Appl. Phys. Lett. APPLAB0003-6951 82, 364 (2003). 10.1063/1.1537519
2. O. Ozen, N. Aubry, D. T. Papageorgiou, and P. G. Petropolous, "Monodisperse drop formation in square microchannels," Phys. Rev. Lett. PRLTAO0031-9007 96, 144501 (2006). 10.1103/ PhysRevLett.96.144501
3. T. Thorsen, R. Roberts, F. Arnold, and S. Quake, "Coherent pattern formation in a non-equilibrium microfluidic device," Phys. Rev. Lett. PRLTAO0031-9007 86, 4163 (2001). 10.1103/PhysRevLett.86.4163
4. O. A. Basaran, "Small-scale free surface flows with breakup: Drop formation and emerging applications," AIChE J. AICEAC0001-1541 48, 1842 (2002). 10.1002/aic.690480902
5. J. Eggers, "Nonlinear dynamics and breakup of free-surface flows," Rev. Mod. Phys. RMPHAT0034-6861 69, 865 (1997). 10.1103/ RevModPhys.69.865
6. D. Quere, "Fluid coating on a fiber," Annu. Rev. Fluid Mech. ARVFA30066-4189 31, 347 (1999). 10.1146/annurev.fluid.31.1.347
7. H. A. Stone, "Dynamics of drop deformation and breakup in viscous fluids," Annu. Rev. Fluid Mech. ARVFA30066-4189 26, 65 (1994). 10.1146/annurev.fl.26.010194.000433
8. Lord Rayleigh, "On the instability of jets," Proc. London Math. Soc. PLMTAL0024-6115 s1-10, 4 (1878). 10.1112/plms/s1-10.1.4
9. Lord Rayleigh, "On the stability of a cylinder of viscous liquid under capillary force," Philos. Mag. PMHABF1478-6435 34, 145 (1892).
10. S. Tomotika, "On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid," Proc. R. Soc. London, Ser. A PRLAAZ0950-1207 150, 322 (1935). 10.1098/rspa.1935.0104
11. M. P. Brenner, J. R. Lister, and H. A. Stone, "Pinching threads, singularities and the number 0.0304...," Phys. Fluids PHFLE61070-6631 8, 2827 (1996). 10.1063/1.869086
12. J. Eggers and T. F. Dupont, "Drop formation in a one-dimensional approximation of the Navier-Stokes equation," J. Fluid Mech. JFLSA70022-1120 262, 205 (1994). 10.1017/S0022112094000480
13. D. T. Papageorgiou, "On the breakup of viscous liquid threads," Phys. Fluids PHFLE61070-6631 7, 1529 (1995). 10.1063/ 1.868540
14. P. Doshi, I. Cohen, W. W. Zhang, M. Siegel, P. Howell, O. A. Basaran, and S. R. Nagel, "Persistence of memory in drop breakup: The breakdown of universality," Science SCIEAS0036-8075 302, 1185 (2003). 10.1126/science.1089272
15. J. Eggers, "Theory of drop formation," Phys. Fluids PHFLE61070-6631 7, 941 (1995). 10.1063/1.868570
16. J. R. Lister and H. Stone, "Capillary breakup of a viscous thread surrounded by another viscous fluid," Phys. Fluids PHFLE61070-6631 10, 2758 (1998). 10.1063/1.869799
17. A. Sierou and J. R. Lister, "Self-similar solutions for viscous capillary pinch-off," J. Fluid Mech. JFLSA70022-1120 497, 381 (2003). 10.1017/S0022112003006736
18. R. Suryo, P. Doshi, and O. A. Basaran, "Non-self-similar, linear dynamics during pinch-off of a hollow annular jet," Phys. Fluids PHFLE61070-6631 16, 4177 (2004). 10.1063/1.1793631
19. W. W. Zhang and J. R. Lister, "Similarity solutions for capillary pinch-off in fluids of differing viscosity," Phys. Rev. Lett. PRLTAO0031-9007 83, 1151 (1999). 10.1103/PhysRevLett.83.1151
20. G. I. Taylor, "The formation of emulsions in definable fields of flow," Proc. R. Soc. London, Ser. A PRLAAZ0950-1207 146, 501 (1934). 10.1098/rspa.1934.0169
21. M. R. Booty and M. Siegel, "Steady deformation and tip-streaming of a slender bubble with surfactant in extensional flow," J. Fluid Mech. JFLSA70022-1120 544, 243 (2005). 10.1017/S0022112005006622
22. R. A. DeBruijn, "Tipstreaming of drops in simple shear flows," Chem. Eng. Sci. CESCAC0009-2509 48, 277 (1993). 10.1016/ 0009-2509(93)80015-I
23. C. D. Eggleton, T.-M. Tsai, and K. J. Stebe, "Tip streaming from a drop in the presence of surfactants," Phys. Rev. Lett. PRLTAO0031-9007 87, 048302 (2001). 10.1103/PhysRevLett.87.048302
24. S. L. Anna and H. C. Mayer, "Microscale tipstreaming in a microfluidic flow focusing device," Phys. Fluids PHFLE61070-6631 18, 121512 (2006). 10.1063/1.2397023
25. P. T. McGough and O. A. Basaran, "Repeated formation of fluid threads in breakup of a surfactant-covered jet," Phys. Rev. Lett. PRLTAO0031-9007 96, 054502 (2006). 10.1103/PhysRevLett.96.054502
26. S. Hansen, G. W. M. Peters, and H. E. H. Meijer, "The effect of surfactant on the stability of a fluid filament embedded in a viscous fluid," J. Fluid Mech. JFLSA70022-1120 382, 331 (1999). 10.1017/ S0022112098003991
27. M.-L. E. Timmermans and J. R. Lister, "The effect of surfactant on the stability of a liquid thread," J. Fluid Mech. JFLSA70022-1120 459, 289 (2002). 10.1017/S0022112002008224
28. S. Whitaker, "Studies of the drop-weight method for surfactant solutions: III. Drop stability, the effect of surfactants on the stability of a column of liquid," J. Colloid Interface Sci. JCISA50021-9797 54, 231 (1976). 10.1016/0021-9797(76)90303-9
29. B. Ambravaneswaran and O. A. Basaran, "Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges," Phys. Fluids PHFLE61070-6631 11, 997 (1999). 10.1063/1.869972
30. S. Kwak and C. Pozrikidis, "Effect of surfactants on the instability of a liquid thread or annular layer. Part I. Quiescent fluids," Int. J. Multiphase Flow IJMFBP0301-9322 27, 1 (2001). 10.1016/S0301-9322(00)00011-2
31. Y.-C. Liao, E. I. Franses, and O. A. Basaran, "Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer," Phys. Fluids PHFLE61070-6631 18, 022101 (2006). 10.1063/1.2166657
32. M. Hameed, M. Siegel, Y.-N. Young, J. Li, M. R. Booty, and D. T. Papageorgiou, "Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid," J. Fluid Mech. JFLSA70022-1120 594, 307 (2008). 10.1017/S0022112007009032
33. G. I. Taylor, Proceedings of the 11th International Congress of Theoretical Applied Mechanics, Munich, 1964 (Springer Verlag, Heidelberg, 1964), pp. 790-796.
34. S. S. Sadhal and R. E. Johnson, "Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant: Exact solution," J. Fluid Mech. JFLSA70022-1120 126, 237 (1983). 10.1017/S0022112083000130
35. C. M. Z. He and Z. Dagan, "The size of stagnant caps of bulk soluble surfactants on interfaces of translating fluid droplets," J. Colloid Interface Sci. JCISA50021-9797 146, 442 (1991). 10.1016/ 0021-9797(91)90209-Q
36. Y. Liao and J. B. McLaughlin, "Bubble motion in aqueous surfactant solutions," J. Colloid Interface Sci. JCISA50021-9797 224, 297 (2000). 10.1006/jcis.2000.6741
37. Y. Liao, J. Wang, R. J. Nunge, and J. B. McLaughlin, "Comment on 'Bubble motion in aqueous surfactant solutions'," J. Colloid Interface Sci. JCISA50021-9797 272, 498 (2004). 10.1016/ j.jcis.2004.01.015
38. R. Palaparthi, D. T. Papageorgiou, and C. Maldarelli, "Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles," J. Fluid Mech. JFLSA70022-1120 559, 1 (2006). 10.1017/S0022112005007019
39. Y. Wang, D. T. Papageorgiou, and C. Maldarelli, "Increased mobility of a surfactant retarded bubble at high bulk concentrations," J. Fluid Mech. JFLSA70022-1120 390, 251 (1999). 10.1017/S0022112099005157
40. W. J. Milliken and L. G. Leal, "The influence of surfactant on the deformation and breakup of a viscous drop: The effect of surfactant solubility," J. Colloid Interface Sci. JCISA50021-9797 166, 275 (1994). 10.1006/jcis.1994.1296
41. R. A. Johnson and A. Borhan, "Stability of the shape of a surfactant-laden drop translating at low Reynolds number," Phys. Fluids PHFLE61070-6631 12, 773 (2000). 10.1063/1.870334
42. M. Muradoglu and G. Tryggvason, "A front-tracking method for computation of interfacial flows with soluble surfactants," J. Comput. Phys. JCTPAH0021-9991 227, 2238 (2008). 10.1016/j.jcp.2007.10.003
43. J. Zhang, D. M. Eckmann, and P. S. Ayyaswamy, "A front tracking method for a deformable intravascular bubble in a tube with soluble surfactant," J. Comput. Phys. JCTPAH0021-9991 214, 366 (2006). 10.1016/j.jcp.2005.09.016
44. R. G. M. van der Sman and S. van der Graaf, "Diffuse interface model of surfactant adsorption onto flat and droplet interfaces," Rheol. Acta RHEAAK0035-4511 46, 3 (2006). 10.1007/s00397-005-0081-z
45. F. Jin, N. R. Gupta, and K. J. Stebe, "The detachment of a viscous drop in a viscous solution in the presence of a soluble surfactant," Phys. Fluids PHFLE61070-6631 18, 022103 (2006). 10.1063/1.2172003
46. C. H. Chang and E. Franses, "Adsorption dynamics of surfactants at the air/water interface: A critical review of mathematical models, data, and mechanisms," Colloids Surf., A CPEAEH0927-7757 100, 1 (1995). 10.1016/0927-7757(94)03061-4
47. J. Donea and A. Huerta, Finite Element Methods for Flow Problems (Wiley, New York, 2003).
48. P. K. Notz, A. U. Chen, and O. A. Basaran, "Satellite drops: Unexpected dynamics and change of scaling during pinch-off," Phys. Fluids PHFLE61070-6631 13, 549 (2001). 10.1063/1.1343906
49. E. D. Wilkes, S. D. Phillips, and O. A. Basaran, "Computational and experimental analysis of dynamics of drop formation," Phys. Fluids PHFLE61070-6631 11, 3577 (1999). 10.1063/1.870224
50. J. Li, M. Hesse, J. Ziegler, and A. W. Woods, "An arbitrary Lagrangian Eulerian method for moving-boundary problems and its application to jumping over water," J. Comput. Phys. JCTPAH0021-9991 208, 289 (2005). 10.1016/j.jcp.2005.02.016
51. J. Li, "The effect of an insoluble surfactant on the skin friction of a bubble," Eur. J. Mech. B/Fluid 25, 59 (2006). 10.1016/ j.euromechflu.2005.04.002