Drop dynamics in an oscillating extensional flow at finite Reynolds numbers

Physics of Fluids

Volumn 17, Issue 2, 2005, Pages 1-13

  Li, Xiaoyi ^a   Sarkar, Kausik ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DEFORMATION; DROP BREAKUP; FINITE DIFFERENCE METHOD; FLUID DYNAMICS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATIONS; REYNOLDS NUMBER; SURFACE TENSION; VISCOUS FLOW;

DROP DYNAMICS; OSCILLATING EXTENSIONAL FLOW; VISCOUS DROP;

DROP FORMATION;

DROPLET; EXTENSIONAL FLOW; FLUID DYNAMICS; OSCILLATING FLOW; REYNOLDS NUMBER;

EID: 22544469511     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1844471     Document Type: Article

References (41)

1. C. L. Tucker III and P. Moldenaers, "Microstructural evolution in polymer blends," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/ annurev.fluid.34.082301.144051 34, 177 (2002).
2. G. K. Batchelor, "The stress system in a suspension of force-free particles," J. Fluid Mech.JFLSA70022-1120 41, 545 (1970).
3. G. I. Taylor, "The viscosity of a liquid containing small drops of another liquid," Proc. R. Soc. London, Ser. APRLAAZ0950-1207 138, 41 (1932).
4. G. I. Taylor, "The formation of emulsions in definable fields of flow," Proc. R. Soc. London, Ser. APRLAAZ0950-1207 146, 501 (1934).
5. R. G. Cox, "The deformation of a drop in general time-dependent fluid flow," J. Fluid Mech.JFLSA70022-1120 37, 601 (1969).
6. C. E. Chaffey and H. Brenner, "A second order theory for shear deformation of drops," J. Colloid Interface Sci.JCISA50021-979710.1016/0021-9797(67)90229-9 24, 258 (1967).
7. A. Acrivos and T. S. Lo, "Deformation and breakup of a single slender drop in an extensional flow," J. Fluid Mech.JFLSA70022-1120 86, 641 (1978).
8. E. J. Hinch and A. Acrivos, "Long slender drops in a simple shear flow," J. Fluid Mech.JFLSA70022-1120 98, 305 (1980).
9. D. V. Khakhar and J. M. Ottino, "Deformation and breakup of slender drop in linear flows," J. Fluid Mech.JFLSA70022-1120 166, 265 (1986).
10. M. R. Kennedy, C. Pozrikidis, and R. Skalak, "Motion and deformation of liquid drops and the rheology of dilute emulsions in simple shear flow," Comput. FluidsCPFLBI0045-793010.1016/ 0045-7930(94)90040-X 23, 251 (1994).
11. M. Loewenberg and E. J. Hinch, "Numerical simulation of a concentrated emulsion in shear flow," J. Fluid Mech.JFLSA70022-1120 321, 395 (1996).
12. A. Z. Zinchenco and R. H. Davis, "Shear flow of highly concentrated emulsions of deformable drops by numerical simulations," J. Fluid Mech.JFLSA70022-112010.1017/S0022112001007042 455, 21 (2002).
13. H. P. Grace, "Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems," Chem. Eng. Commun.CEGCAK0098-6445 14, 225 (1982).
14. B. J. Bentley and L. G. Leal, "An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows," J. Fluid Mech.JFLSA70022-1120 167, 241 (1986).
15. S. Guido, M. Minale, and P. L. Maffettone, "Drop shape dynamics under shear-flow reversal," J. Rheol.JORHD20148-605510.1122/ 1.1315310 44, 1385 (2000).
16. A. S. Almusallam, R. G. Larson, and M. J. Solomon, "A constitutive model for the prediction of ellipsoidal droplet shapes and stresses in immiscible blends," J. Rheol.JORHD20148-605510.1122/1.1287288 44, 1055 (2000).
17. P. L. Maffettone and M. Minale, "Equations of change for ellipsoidal drops in viscous flow," J. Non-Newtonian Fluid Mech.JNFMDI0377-025710.1016/S0377-0257(98)00065-2 78, 227 (1998).
18. M. Bousmina, "Rheology of polymer blends: Linear model for viscoelastic emulsions," Rheol. ActaRHEAAK0035-451110.1007/ s003970050157 38, 73 (1999).
19. N. E. Jackson and C. L. Tucker III, "A model for large deformation of an ellipsoidal droplet with interfacial tension," J. Rheol.JORHD20148-605510.1122/1.1562152 47, 659 (2003).
20. S. Ramaswamy and L. G. Leal, "A note on inertial effects in the deformation of Newtonian drops in uniaxial extensional flow," Int. J. Multiphase FlowIJMFBP0301-932210.1016/S0301-9322(96)00079-1 23, 561 (1997).
21. I. S. Kang and L. G. Leal, "Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number I. finite-difference scheme and its application to the deformation of a bubble in uniaxial straining flow," Phys. FluidsPFLDAS0031-917110.1063/1.866207 30, 1929 (1987).
22. I. S. Kang and L. G. Leal, "Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number II. deformation of a bubble in biaxial straining flow," Phys. Fluids APFADEB0899-821310.1063/1.857439 1, 644 (1989).
23. Y. Y. Renardy and V. Cristini, "Effects of inertia on drop breakup under shear," Phys. FluidsPHFLE61070-663110.1063/1.1331321 13, 7 (2001).
24. Y. Renardy, V. Cristini, and J. Li, "Drop fragmentation distribution under shear with inertia," Int. J. Multiphase FlowIJMFBP0301-932210.1016/S0301-9322(02)00022-8 28, 1125 (2002).
25. R. Cavallo, S. Guido, and M. Simeone, "Drop deformation under small-amplitude oscillatory shear flow," Rheol. ActaRHEAAK0035-451110.1007/s00397-002-0245-z 42, 1 (2003).
26. W. Yu and M. Bousmina, "Modeling of oscillatory shear flow of emulsions under small and large deformation fields," J. Rheol.JORHD20148-605510.1122/1.1517303 46, 1401 (2002).
27. S. Wannaborworn, M. R. Mackley, and Y. Renardy, "Experimental observation and matching numerical simulation for the deformation and breakup of immiscible drops in oscillatory shear," J. Rheol.JORHD20148-605510.1122/1.1501960 46, 1279 (2002).
28. J. F. Palierne, "Linear rheology of viscoelastic emulsions with interfacial tension," Rheol. ActaRHEAAK0035-4511 29, 204 (1990).
29. K. Sarkar and W. R. Schowalter, "Deformation of a two-dimensional drop at non-zero Reynolds number in time-periodic extensional flows: numerical simulation," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112001004025 436, 177 (2001).
30. K. Sarkar and W. R. Schowalter, "Deformation of a two-dimensional viscous drop in time-periodic extensional flows: Analytical treatment," J. Fluid Mech.JFLSA70022-112010.1017/S0022112001004013 436, 207 (2001).
31. I. S. Kang and L. G. Leal, "Bubble dynamics in time-periodic straining flows," J. Fluid Mech.JFLSA70022-1120 218, 41 (1990).
32. F. Risso and J. Fabre, "Oscillations and breakup of a bubble immersed in a turbulent field," J. Fluid Mech.JFLSA70022-112010.1017/S0022112098002705 372, 323 (1998).
33. H. A. Stone, "Dynamics of drop deformation and breakup in viscous fluids," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/ annurev.fluid.26.1.65 26, 65 (1994).
34. H. A. Stone, B. J. Bentley, and L. G. Leal, "An experimental study of transient effects in the breakup of viscous drops," J. Fluid Mech.JFLSA70022-1120 173, 131 (1986).
35. G. Tryggvason, B. Bunner, O. Ebrat, and W. Taubar, "Computation of multiphase flows by a finite difference front tracking method. I. Multi-fluid flows," 29th Computational Fluid Dynamics Lecture Series 1998-03 (Von Karman Institute of Fluid Dynamics, Sint-Genesius-Rode, Belgium, 1998).
36. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Taubar, J. Han, S. Nas, and Y. J. Jan, "A front-tracking method for the computations of multiphase flow," J. Comput. Phys.JCTPAH0021-999110.1006/jcph.2001.6726 169, 708 (2001).
37. K. Sarkar and W. R. Schowalter, "Deformation of a two-dimensional viscoelastic drop at non-zero Reynolds number in time-periodic extensional flows," J. Non-Newtonian Fluid Mech.JNFMDI0377-025710.1016/S0377-0257(00)00156-7 95, 315 (2000).
38. J. T. Davies and E. K. Rideal, Interfacial Phenomena (Academic, New York, 1963).
39. S. Guido and M. Villone, "Three-dimensional shape of a drop under simple shear flow," J. Rheol.JORHD20148-605510.1122/1.550942 42, 395 (1998).
40. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987).
41. J. Blawzdziewicz, V. Cristini, and M. Loewenberg, "Multiple stationary states for deformable drops in linear Stokes flow," Phys. FluidsPHFLE61070-663110.1063/1.1562162 15, L37 (2003).