Numerical investigation of the rheology of a dilute emulsion of drops in an oscillating extensional flow

Journal of Non-Newtonian Fluid Mechanics

Volumn 128, Issue 2-3, 2005, Pages 71-82

  Li, Xiaoyi ^a   Sarkar, Kausik ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

Complex modulus; Excess stress; Front tracking; Loss modulus; Oscillating extension; Rheology; Storage modulus; Viscoelastic

Indexed keywords

DEFORMATION; DROP FORMATION; EMULSIONS; FINITE DIFFERENCE METHOD; INTERFACES (MATERIALS); OSCILLATIONS; RELAXATION PROCESSES; STRESS ANALYSIS; VISCOUS FLOW;

BACHELOR'S FORMULA; DILUTE EMULSIONS; DROP-DROP INTERACTIONS; OSCILLATING EXTENSIONAL FLOW; VISCOUS DROPS;

RHEOLOGY;

EMULSION; NON-NEWTONIAN FLUID; OSCILLATING FLOW; RHEOLOGY; VISCOELASTICITY;

EID: 22544439328     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2005.04.001     Document Type: Article

References (48)

1. C.L. Tucker III P. Moldenaers Microstructural evolution in polymer blends Ann. Rev. Fluid Mech. 34 2002 177-210
2. S. Wannaborworn M.R. Mackley Y. Renardy Experimental observation and matching numerical simulation for the deformation and breakup of immiscible drops in oscillatory shear J. Rheol. 46 5 2002 1279-1293
3. R. Cavallo S. Guido M. Simeone Drop deformation under small-amplitude oscillatory shear flow Rheol. Acta 42 2003 1-9
4. W. Yu M. Bousmina Modeling of oscillatory shear flow of emulsions under small and large deformation fields J. Rheol. 46 6 2002 1401-1418
5. W. Yu M. Bousmina M. Grmela J. Palierne C. Zhou Quantitative relationship between rheology and morphology in emulsions J. Rheol. 46 6 2002 1381-1399
6. B.J. Bentley L.G. Leal An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows J. Fluid Mech. 167 1986 241-283
7. G.I. Taylor The formation of emulsions in definable fields of flow Proc. R. Soc. A 146 1934 501-523
8. R.G. Cox The deformation of a drop in general time-dependent fluid flow J. Fluid Mech. 37 1969 601-623
9. N.A. Frankel A. Acrivos The constitutive equations for a dilute emulsion J. Fluid Mech. 44 1970 65-78
10. D. Barthes-Biesel A. Acrivos The rheology of suspensions and its relation to phenomenological theories for non-Newtonian fluids Int. J. Multiphase Flow 1 1973 1-24
11. J.M. Rallison Note on the time-dependent deformation of a viscous drop which is almost spherical J. Fluid Mech. 98 1980 625-633
12. A. Acrivos T.S. Lo Deformation and breakup of a single slender drop in an extensional flow J. Fluid Mech. 86 1978 641-672
13. E.J. Hinch A. Acrivos Long slender drops in a simple shear flow J. Fluid Mech. 98 1980 305-328
14. D.V. Khakhar J.M. Ottino Deformation and breakup of slender drops in linear flows J. Fluid Mech. 166 1986 185-265
15. H.A. Stone Dynamics of drop deformation and breakup in viscous fluids Ann. Rev. Fluid Dyn. 26 1994 65-102
16. M. Doi T. Ohta Dynamics and rheology of complex interfaces Int. J. Chem. Phys. 95 1991 1242-1248
17. G.K. Batchelor The stress system in a suspension of force-free particles J. Fluid Mech. 41 3 1970 45-570
18. J. Mellema M.W.M. Willemse Effective viscosity of dispersions approached by a statistical continuum method Physica A 122A 1983 286-312
19. A. Onuki Viscosity enhancement by domains in phase-separating fluids near the critical points: Proposal of critical rheology Phys. Rev. A 35 12 1987 5149-5155
20. A.S. Almusallam R.G. Larson M.J. Solomon Comprehensive constitutive model for immiscible blends of Newtonian polymers J. Rheol. 48 2 2004 319-384
21. H.M. Lee O.O. Park Rheology and dynamics of immiscible polymer blends J. Rheol. 38 5 1994 1405-1425
22. G.W.M. Peters S. Hansen H.E.H. Meijer Constitutive modeling of dispersive mixtures J. Rheol. 45 2001 659-689
23. P.L. Maffettone M. Minale Equations of change for ellipsoidal drops in viscous flow J. Non-Newtonian Fluid Mech. 78 1998 227-241
24. S. Guido M. Villone Three-dimensional shape of a drop under simple shear flow J. Rheol. 42 2 1998 395-415
25. Y.T. Hu A. Lips Transient and steady state three-dimensional drop shapes and dimensions under planar extensional flow J. Rheol. 47 2 2003 349-369
26. T. Jansseune J. Mewis P. Moldenaers M. Minale P.L. Maffettone Rheology and rheological morphology determination in immiscible two-phase polymer model blends J. Non-Newtonian Fluid Mech. 93 2000 153-165
27. T. Jansseune I. Vinckier P. Moldenaers J. Mewis Transient stresses in immiscible model polymer blends during start-up flows J. Non-Newtonian Fluid Mech. 99 2001 167-181
28. E.D. Wetzel C.L. Tucker III Area tensors for modeling microstructure during laminar liquid-liquid mixing Int. J. Multiphase Flow 25 1999 35-61
29. E.D. Wetzel C.L. Tucker III Droplet deformation in dispersions with unequal viscosities and zero interfacial tension J. Fluid Mech. 426 2001 199-228
30. N.E. Jackson C.L. Tucker III A model for large deformation of an ellipsoidal droplet with interfacial tension J. Rheol. 47 3 2003 659-682
31. Y. Wu A.Z. Zinchenko R.H. Davis Ellipsoidal model for deformable drops and application to non-Newtonian emulsion flow J. Non-Newtonian Fluid Mech. 102 2002 281-298
32. W. Yu M. Bousmina Ellipsoidal model for droplet deformation in emulsions J. Rheol. 47 4 2003 1011-1039
33. M.R. Kennedy C. Pozrikidis R. Skalak Motion and deformation of liquid drops and the rheology of dilute emulsions in simple shear flow Comput. Fluids 23 1994 251-278
34. V. Cristini C.W. Macosko T. Jansseune A note on transient stress calculation via numerical simulations J. Non-Newtonian Fluid Mech. 105 2002 177-187
35. M. Loewenberg E.J. Hinch Numerical simulation of a concentrated emulsion in shear flow J. Fluid Mech. 321 1996 395-419
36. A.Z. Zinchenko R.H. Davis Shear flow of highly concentrated emulsions of deformable drops by numerical simulations J. Fluid Mech. 455 2002 21-62
37. R. Scardovelli S. Zaleski Direct numerical simulation of free-surface and interfacial flow Ann. Rev. Fluid Dyn. 31 1999 567-603
38. J.A. Sethian P. Smereca Level set methods for fluid interfaces Ann. Rev. Fluid Dyn. 35 2003 341-372
39. G. Tryggvason, B. Bunner, O. Ebrat, 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, 1998.
40. K. Sarkar W.R. Schowalter Deformation of a two-dimensional drop at non-zero Reynolds number in time-periodic extensional flows: Numerical simulation J. Fluid Mech. 436 2001 177-206
41. K. Sarkar W.R. Schowalter Deformation of a two-dimensional viscous drop in time-periodic extensional flows: Analytical treatment J. Fluid Mech. 436 2001 207-230
42. K. Sarkar 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. 95 2000 315-342
43. X. Li, K. Sarkar, Drop dynamics in an oscillating extensional flow at finite Reynolds numbers, Phys. Fluids 17, 027103 (2005).
44. J.G. Oldroyd The elastic and viscous properties of emulsions and suspensions Proc. R. Soc. A218 1953 122-132
45. J.G. Oldroyd The effect of interfacial stabilizing films on the elastic and viscous properties of emulsions Proc. R. Soc. A232 1955 567-577
46. M. Bousmina Effect of interfacial tension on linear viscoelastic behavior of immiscible polymer blends Rheol. Acta 38 1999 251-254
47. W. Yu M. Bousmina C. Zhou C.L. Tucker Theory for drop deformation in viscoelastic systems J. Rheol. 48 2 2004 417-438
48. P.L. Maffettone F. Greco Ellipsoidal drop model for single drop dynamics with non-Newtonian fluids J. Rheol. 48 1 2004 83-100