Nonlinear dynamics and breakup of compound jets

Physics of Fluids

Volumn 18, Issue 8, 2006, Pages

  Suryo, Ronald ^a   Doshi, Pankaj ^a   Basaran, Osman A ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DEFORMATION; DROP BREAKUP; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FLUID DYNAMICS; GALERKIN METHODS; INTEGRATION; REYNOLDS NUMBER; ROTATIONAL FLOW; SURFACE TENSION; VISCOSITY;

COMPOUND JETS; RECIRCULATING FLOWS; TEMPORAL ANALYSIS;

JETS;

ALGORITHMS; DEFORMATION; DROP BREAKUP; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FLUID DYNAMICS; GALERKIN METHODS; INTEGRATION; JETS; REYNOLDS NUMBER; ROTATIONAL FLOW; SURFACE TENSION; VISCOSITY;

EID: 33748264556     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2245377     Document Type: Article

References (95)

1. D. H. Michael, "Meniscus stability," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fl.13.010181.001201 13, 189 (1981).
2. J. Eggers, "Nonlinear dynamics and breakup of free-surface flows," Rev. Mod. Phys. RMPHAT0034-686110.1103/RevModPhys.69.865 69, 865 (1997).
3. C. H. Hertz and B. Hermanrud, "A liquid compound jet," J. Fluid Mech. JFLSA70022-112010.1017/S0022112083001329 131, 271 (1983).
4. J. M. Kendall, "Experiments on annular liquid jet instability and on the formation of liquid shells," Phys. Fluids PFLDAS0031-917110.1063/1.865595 29, 2086 (1986).
5. K. Masters, Spray Drying Handbook, 4th ed. (Wiley, New York, 1985).
6. C. W. Park, "Extensional flow of a 2-phase fiber," AIChE J. AICEAC0001-1541 36, 1997 (1990).
7. A. M. Gañán-Calvo and J. M. Gordillo, "Perfectly monodisperse microbubbling by capillary flow focusing," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.87.274501 87, 274501 (2001).
8. I. G. Loscertales, A. Barrero, I. Guerrero, R. Cortijo, M. Marquez, and A. M. Gañán-Calvo, "Micro/nano encapsulation via electrified coaxial liquid jets," Science SCIEAS0036-807510.1126/ science.1067595 295, 1695 (2002).
9. J. M. Gordillo, Z. Cheng, A. M. Gañán-Calvo, M. Márquez, and D. A. Weitz, "A new device for the generation of microbubbles," Phys. Fluids PHFLE61070-663110.1063/1.1737739 16, 2828 (2004).
10. C. Berkland, E. Pollauf, D. W. Pack, and K. Kim, "Uniform double-walled polymer microspheres of controllable shell thickness," J. Controlled Release JCREEC0168-3659 96, 101 (2004).
11. A. S. Utada, E. Lorenceau, D. R. Link, P. D. Kaplan, H. A. Stone, and D. A. Weitz, "Monodisperse double emulsions generated from a microcapillary device," Science SCIEAS0036-807510.1126/ science.1109164 308, 537 (2005).
12. F. Savart, "Mémoire sur la constitution des veines liquides lancèes par des orifices circulaires en mince paroi," Ann. Chim. Phys.ACPHAA0365-1444 53, 337 (1833).
13. J. Plateau, "Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity," in Annual Report of the Board of Regents of the Smithsonian Institution, Washington, DC, 1863, pp. 270-283.
14. L. Rayleigh, "On the instability of jets," Proc. London Math. Soc. PLMTAL 10, 4 (1879).
15. L. Rayleigh, "On the capillary phenomena of jets," Proc. R. Soc. LondonPRSLAZ0370-1662 19, 71 (1879).
16. L. Rayleigh, "On the instability of a cylinder of viscous liquid under capillary force," Philos. Mag. PHMAA40031-8086 34, 145 (1892).
17. L. Rayleigh, "On the instability of cylindrical fluid surfaces," Philos. Mag. PHMAA40031-8086 34, 177 (1892).
18. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961).
19. S. Tomotika, "On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 150, 322 (1935).
20. R. M. Christiansen and A. N. Hixson, "Breakup of a liquid jet in a denser liquid," Ind. Eng. Chem. IECHAD0019-786610.1021/ie50570a036 49, 1017 (1957).
21. C. A. Miller and L. E. Scriven, "The oscillations of a fluid droplet immersed in another fluid," J. Fluid Mech. JFLSA70022-112010.1017/S0022112068000832 32, 417 (1968).
22. J. B. Keller, S. L. Rubinov, and Y. O. Tu, "Spatial instability of a jet," Phys. FluidsPFLDAS0031-917110.1063/1.1694264 16, 2052 (1973).
23. S. J. Leib and M. E. Goldstein, "Convective and absolute instability of a viscous jet," Phys. Fluids PFLDAS0031-917110.1063/ 1.866000 29, 952 (1986).
24. S. J. Leib and M. E. Goldstein, "The generation of capillary instabilities on a liquid jet," J. Fluid Mech.JFLSA70022-112010.1017/S0022112086000472 168, 479 (1986).
25. S. A. Berger, "Initial-value stability analysis of a liquid jet," SIAM J. Appl. Math. SMJMAP0036-139910.1137/0148057 48, 973 (1988).
26. R. J. Donnelly, "Experiments on capillary instability of a liquid jet," Proc. R. Soc. London, Ser. APRLAAZ1364-5021 290, 547 (1966).
27. E. F. Goedde and M. C. Yuen, "Experiments on liquid jet instability," J. Fluid Mech. JFLSA70022-1120 40, 495 (1970).
28. M.-C. Yuen, "Non-linear capillary instability of a liquid jet," J. Fluid Mech. JFLSA70022-1120 33, 151 (1968).
29. A. H. Nayfeh, "Nonlinear stability of a liquid jet," Phys. Fluids PFLDAS0031-917110.1063/1.1693025 13, 841 (1970).
30. P. Lafrance, "Nonlinear breakup of a laminar liquid jet," Phys. FluidsPFLDAS0031-917110.1063/1.861168 18, 428 (1975).
31. J. Eggers, "Universal pinching of 3D axisymmetric free-surface flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.71.3458 71, 3458 (1993).
32. K. C. Chaudhary and L. G. Redekopp, "The nonlinear capillary instability of a liquid jet. Part 1. Theory," J. Fluid Mech. JFLSA70022-112010.1017/S0022112080002108 96, 257 (1980).
33. D. F. Rutland and G. J. Jameson, "Non-linear effect in capillary instability of liquid jets," J. Fluid Mech. JFLSA70022-1120 46, 267 (1971).
34. K. C. Chaudhary and T. Maxworthy, "The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behavior before droplet formation," J. Fluid Mech. JFLSA70022-112010.1017/ S002211208000211X 96, 275 (1980).
35. O. A. Basaran, "Small-scale free surface flows with breakup: Drop formation and emerging applications," AIChE J. AICEAC0001-154110.1002/aic.690480902 48, 1842 (2002).
36. M. Orme and E. P. Muntz, "The manipulation of capillary stream breakup using amplitude-modulated disturbances: A pictorial and quantitative representation," Phys. Fluids A PFADEB0899-821310.1063/ 1.857612 2, 1124 (1990).
37. A. Kalaaji, B. Lopez, P. Attané, and A. Soucemarianadin, "Breakup length of forced liquid jets," Phys. Fluids PHFLE61070-663110.1063/1.1593023 15, 2469 (2003).
38. N. N. Mansour and T. S. Lundgren, "Satellite formation in capillary jet breakup," Phys. Fluids A PFADEB0899-821310.1063/1.857613 2, 1141 (1990).
39. N. Ashgriz and F. Mashayek, "Temporal analysis of capillary jet breakup," J. Fluid Mech. JFLSA70022-112010.1017/S0022112095002667 291, 163 (1995).
40. O. A. Basaran, "Nonlinear oscillations of viscous liquid drops," J. Fluid Mech. JFLSA70022-112010.1017/S002211209200199X 241, 169 (1992).
41. T.-Y. Chen and J. Tsamopoulos, "Nonlinear dynamics of capillary bridges: Theory," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112093002526 255, 373 (1993).
42. C. P. Lee and T. G. Wang, "A theoretical model for the annular jet instability," Phys. FluidsPFLDAS0031-917110.1063/1.865594 29, 2076 (1986).
43. J. Shen and X. Li, "Instability of an annular viscous liquid jet," Acta Mech. AMHCAP0001-597010.1007/BF01170402 114, 167 (1996).
44. F. Chen, J. Tsaur, F. Durst, and S. K. Das, "On the axisymmetry of annular jet instabilities," J. Fluid Mech.JFLSA70022-112010.1017/ S002211200300497X 488, 355 (2003).
45. C. Mehring and W. Sirignano, "Axisymmetric capillary waves on thin annular liquid sheets. I. Temporal stability," Phys. FluidsPHFLE61070-663110.1063/1.870393 12, 1417 (2000).
46. C. Mehring and W. A. Sirignano, "Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development," Phys. Fluids PHFLE61070-663110.1063/1.870394 12, 1440 (2000).
47. A. Sanz and J. Meseguer, "One-dimensional linear analysis of the compound jet," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112085003093 159, 55 (1985).
48. S. Radev and V. Shkadov, "On a stability of two-layer capillary jet," Theor Appl. Mech. ZZZZZZ0285-6042 16, 68 (1985).
49. S. Radev and B. Tchavadorov, "Linear capillary instability of compound jets," Int. J. Multiphase FlowIJMFBP0301-9322 14, 67 (1988).
50. V. Y. Shkadov and G. M. Sisoev, "Instability of a two layer capillary jet," Int. J. Multiphase FlowIJMFBP0301-932210.1016/ 0301-9322(95)00073-9 22, 363 (1996).
51. A. Chauhan, C. Maldarelli, D. S. Rumschitzki, and D. Papageorgiou, "Temporal and spatial instability of an inviscid compound jet," Rheol. Acta RHEAAK0035-451110.1007/BF00396508" 35, 567 (1996).
52. A. Chauhan, C. Maldarelli, D. Papageorgiou, and D. S. Rumschitzki, "Temporal instability of compound threads and jets," J. Fluid Mech. JFLSA70022-112010.1017/S0022112000001282 420, 1 (2000).
53. A. Chauhan, C. Maldarelli, D. T. Papageorgiou, and D. S. Rumschitzki, "The absolute instability of an inviscid compound jet," J. Fluid Mech.JFLSA70022-1120 549, 81 (2006).
54. J. R. Richards, A. N. Beris, and A. M. Lenhoff, "Steady laminar-flow of liquid-liquid jets at high Reynolds-number," Phys. Fluids A PFADEB0899-821310.1063/1.858847 5, 1703 (1993).
55. J. R. Richards, A. M. Lenhoff, and A. N. Beris, "Dynamics breakup of liquid-liquid jets," Phys. Fluids PHFLE61070-663110.1063/ 1.868154 6, 2640 (1994).
56. J. R. Richards, A. N. Beris, and A. M. Lenhoff, "Drop formation in liquid-liquid systems before and after jetting," Phys. Fluids PHFLE61070-663110.1063/1.868710 7, 2617 (1995).
57. J. R. Richards and G. F. Scheele, "Measurement of laminar jet velocity distributions in liquid-liquid systems using flash photolysis," Chem. Eng. Commun. CEGCAK0098-6445 36, 73 (1985).
58. H. Yu and G. F. Scheele, "Laminar jet contraction and velocity distribution in immiscible liquid-liquid systems," Int. J. Multiphase Flow IJMFBP0301-9322 2, 153 (1975).
59. X. Zhang, "Dynamics of growth and breakup of viscous pendant drops into air," J. Colloid Interface Sci. JCISA50021-979710.1006/ jcis.1998.6047 212, 107 (1999).
60. X. Zhang, "Dynamics of drop formation in viscous flows," Chem. Eng. Sci. CESCAC0009-250910.1016/S0009-2509(99)00027-5 54, 1759 (1999).
61. E. D. Wilkes, S. D. Phillips, and O. A. Basaran, "Computational and experimental analysis of dynamics of drop formation," Phys. Fluids PHFLE61070-663110.1063/1.870224 11, 3577 (1999)
62. A. U. Chen, P. K. Notz, and O. A. Basaran, "Computational and experimental analysis of pinch-off and scaling," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.88.174501 88, 174501 (2002).
63. D. R. Webster and E. K. Longmire, "Jet pinch-off and drop formation in immiscible liquid-liquid systems," Exp. Fluids EXFLDU0723-486410.1007/s003480000134 30, 47 (2001).
64. E. K. Longmire, T. L. Norman, and D. L. Gefroh, "Dynamics of pinch-off inliquid/liquid jets with surface tension," Int. J. Multiphase Flow IJMFBP0301-932210.1016/S0301-9322(01)00030-1 27, 1735 (2001).
65. W. W. Zhang and J. R. Lister, "Similarity solutions for capillary pinch-off in fluids of differing viscosity," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.83.1151 83, 1151 (1999).
66. J. R. Lister and H. A. Stone, "Capillary breakup of a viscous thread surrounded by another viscous fluid," Phys. Fluids PHFLE61070-663110.1063/1.869799 10, 2758 (1998).
67. I. Cohen, M. P. Brenner, J. Eggers, and S. R. Nagel, "Two fluid drop snap-off problem: Experiments and theory," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.83.1147 83, 1147 (1999).
68. I. Cohen and S. R. Nagel, "Testing for scaling behavior dependence on geometrical and fluid parameters in the two fluid drop snap-off problem," Phys. Fluids PHFLE61070-663110.1063/1.1409369 13, 3533 (2001).
69. D. Leppinen and J. R. Lister, "Capillary pinch-off in inviscid fluids," Phys. FluidsPHFLE61070-663110.1063/1.1537237 15, 568 (2003).
70. 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 SCIEAS0036-807510.1126/ science.1089272 302, 1185 (2003).
71. A. Sierou and J. R. Lister, "Self-similar solutions for viscous capillary pinch-off," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112003006736 497, 381 (2004).
72. M. Chacha, S. Radev, L. Tadrist, and R. Occelli, "Numerical treatment of the instability and the breakup of a liquid capillary column in a bounded immiscible phase," Int. J. Multiphase Flow IJMFBP0301-9322 23, 377 (1997).
73. B. Tchavdarov, P. D. Minev, and S. Radev, "Numerical analysis of compound jet disintegration," Comput. Methods Appl. Mech. Eng. CMMECC0045-7825 118, 121 (1994).
74. R. V. Craster, O. K. Matar, and D. T. Papageorgiou, "Pinchoff and satellite formation in compound viscous threads," Phys. Fluids PHFLE61070-663110.1063/1.1611879 15, 3409 (2003).
75. R. V. Craster, O. K. Matar, and D. T. Papageorgiou, "On compound liquid threads with large viscosity contrasts," J. Fluid Mech. JFLSA70022-1120 533, 95 (2005).
76. G. Strang and G. J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1973).
77. L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering (John Wiley & Sons, New York, 1982).
78. P. Huyakorn, C. Taylor, R. Lee, and P. Gresho, "Comparison of various mixed-interpolation finite-elements in velocity-pressure formulation of Navier-Stokes equations," Comput. Fluids CPFLBI0045-793010.1016/0045-7930(78)90004-X 6, 25 (1978).
79. P. M. Gresho, R. L. Lee, and R. L. Sani, "On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions," in Recent Advances in Numerical Methods in Fluids, edited by C. Taylor and K. Morgan (Pineridge, Swansea, U. K., 1980), Vol. 1, Chap. 2, pp. 27-79.
80. K. N. Christodoulou and L. E. Scriven, "Discretization of free surface flows and other moving boundary problems," J. Comput. Phys. JCTPAH0021-999110.1016/0021-9991(92)90273-2 99, 39 (1992).
81. P. K. Notz, A. U. Chen, and O. A. Basaran, "Satellite drops: Unexpected dynamics and change of scaling during pinch-off," Phys. Fluids PHFLE61070-663110.1063/1.1343906 13, 549 (2001).
82. P. K. Notz and O. A. Basaran, "Dynamics and breakup of a contracting liquid filament," J. Fluid Mech. JFLSA70022-1120 512, 223 (2004).
83. R. Suryo, P. Doshi, and O. A. Basaran, "Non-self-similar, linear dynamics during pinch-off of a hollow annular jet," Phys. FluidsPHFLE61070-663110.1063/1.1793631 16, 4177 (2004).
84. P. Hood, "Frontal solution program for unsymmetric matrices," Int. J. Numer. Methods Eng.IJNMBH0029-598110.1002/nme.1620100209 10, 379 (1976).
85. T. S. Lundgren and N. N. Mansour, "Oscillations of drops in zero gravity with weak viscous effects," J. Fluid Mech. JFLSA70022-112010.1017/S0022112088003076 194, 479 (1988).
86. T. W. Patzek, R. E. Benner, O. A. Basaran, and L. E. Scriven, "Nonlinear oscillations of inviscid free drops," J. Comput. Phys. JCTPAH0021-999110.1016/0021-9991(91)90010-I 97, 489 (1991).
87. A. Chauhan, C. Maldarelli, D. S. Rumschitzki, and D. Papageorgiou, "An experimental investigation of the convective instability of a jet," Chem. Eng. Sci. CESCAC0009-250910.1016/S0009-2509(03)00076-9 58, 2421 (2003).
88. X. D. Shi, M. P. Brenner, and S. R. Nagel, "A cascade of structure in a drop falling from a faucet," Science SCIEAS0036-8075 265, 219 (1994).
89. D. M. Henderson, W. G. Pritchard, and L. B. Smolka, "On the pinch-off of a pendant drop of viscous fluid," Phys. Fluids PHFLE61070-663110.1063/1.869435 9, 3188 (1997).
90. O. A. Basaran and D. W. DePaoli, "Nonlinear oscillations of pendant drops," Phys. Fluids PHFLE61070-663110.1063/1.868120 6, 2923 (1994).
91. E. D. Wilkes and O. A. Basaran, "Forced oscillations of pendant (sessile) drops," Phys. Fluids PHFLE61070-663110.1063/1.869276 9, 1512 (1997).
92. S. Whitaker, Introduction to Fluid Mechanics (Krieger, New York, 1992).
93. L. G. Leal, Laminar Flow and Convective Transport Processes, in Butterworth-Heinemann Series in Chemical Engineering (Butterworth-Heinemann, Boston, 1992).
94. R. Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover, New York, 1962).
95. C. E. Weatherburn, Differential Geometry of Three Dimensions (Cambridge University Press, Cambridge, 1927).