Effect of overall drop deformation on flow-induced coalescence at low capillary numbers

Physics of Fluids

Volumn 18, Issue 1, 2006, Pages

  Baldessari, Fabio ^a   Leal, L Gary ^b  

^a University of California   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Capillarity; Deformation; Drops; External flows; Film flow; Flow simulation; Two phase flow; Viscosity

Indexed keywords

CAPILLARITY; COLLOIDS; COMPUTER SIMULATION; DEFORMATION; DROP BREAKUP; VAN DER WAALS FORCES; VISCOSITY;

DROP DEFORMATION; EXTERNAL FLOWS; FLOW SIMULATION;

TWO PHASE FLOW;

CAPILLARITY; COLLOIDS; COMPUTER SIMULATION; DEFORMATION; DROP BREAKUP; TWO PHASE FLOW; VAN DER WAALS FORCES; VISCOSITY;

EID: 33645655108     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2158427     Document Type: Article

References (49)

1. S. Lyu, F. S. Bates, and C. W. Macosko, " Competitive roles of block copolymer during polymer blending: Suppression of coalescence and reduction of interfacial tension, " Abstr. Pap. - Am. Chem. Soc. 218, 595 (1999). 8xa ACSRAL 0065-7727
2. S. Lyu, T. D. Jones, F. S. Bates, and C. W. Macosko, " Role of block copolymers on suppression of droplet coalescence, " Macromolecules 35, 7845 (2002). mml MAMOBX 0024-9297 10.1021/ma020754t
3. S. P. Lyu, F. S. Bates, and C. W. Macosko, " Modeling of coalescence in polymer blends, " AIChE J. 48, 7 (2002). aic AICEAC 0001-1541 10.1002/aic.690480103
4. S. P. Lyu, F. S. Bates, and C. W. Macosko, " Coalescence in polymer blends during shearing, " AIChE J. 46, 229 (2000). aic AICEAC 0001-1541 10.1002/aic.690460203
5. M. Maric and C. W. Macosko, " Block copolymer compatibilizers for polystyrene/poly(dimethylsiloxane) blends, " J. Polym. Sci., Part B: Polym. Phys. 40, 346 (2002). bpp JPBPEM 0887-6266
6. C. W. Macosko, " Morphology development and control in immiscible polymer blends, " Macromol. Symp. 149, 171 (2000). msy MSYMEC 1022-1360 10.1002/1521-3900(200001)149:1<171::AID-MASY171> 3.0.CO;2-8
7. B. E. Burkhart, P. V. Gopalkrishnan, S. D. Hudson, A. M. Jamieson, M. A. Rother, and R. H. Davis, " Droplet growth by coalescence in binary fluid mixtures, " Phys. Rev. Lett. 87, 098304 (2001). prl PRLTAO 0031-9007 10.1103/PhysRevLett.87.098304
8. H. Yang, C. C. Park, Y. T. Hu, and L. G. Leal, " The coalescence of two equal-sized drops in a two-dimensional linear flow, " Phys. Fluids 13, 1087 (2001). phf PHFLE6 1070-6631 10.1063/1.1358873
9. C. C. Park, Ph.D. thesis, University of California, Santa Barbara, 2002.
10. J. W. Ha, Y. Yoon, and L. G. Leal, " The effect of compatibilizer on the coalescence of two drops in flow, " Phys. Fluids 15, 849 (2003). phf PHFLE6 1070-6631 10.1063/1.1555803
11. Y. T. Hu, D. J. Pine, and L. G. Leal, " Drop deformation, breakup, and coalescence with compatibilizer, " Phys. Fluids 12, 484 (2000). phf PHFLE6 1070-6631 10.1063/1.870254
12. A. K. Chesters, "The modeling of coalescence processes in fluid liquid dispersions - a review of current understanding," Chem. Eng. Res. Des. 69, 259 (1991). 8q3 CERDEE 0263-8762
13. S. G. Yiantsios and R. H. Davis, " Close approach and deformation of two viscous drops due to gravity and van der Waals forces, " J. Colloid Interface Sci. 144, 412 (1991). jci JCISA5 0021-9797
14. H. Wang and R. H. Davis, " Droplet growth due to Brownian, gravitational, or thermocapillary motion and coalescence in dilute dispersions, " J. Colloid Interface Sci. 159, 108 (1993). jci JCISA5 0021-9797 10.1006/jcis.1993.1302
15. It is difficult to perform head-on collision experiments at capillary numbers larger than approximately 0.01 in the four-roll mill that is used in our lab. For larger Ca, the drops collide and are maintained via an active control system in the head-on configuration for a very long period of time, but eventually rotate out of the plane of the flow and separate (Ref. 8). We do not know at this stage whether this behavior at large Ca is due to limitations of the flow control scheme, or is due to inhibited coalescence due to the increasing importance of the re-circulating flow within the drops (Ref. 16), as originally suggested by Loewenberg (Ref. 17).
16. L. G. Leal, " Flow induced coalescence of drops in viscous fluid (Fluid Dynamics Prize lecture), " Phys. Fluids 16, 1833 (2004). phf PHFLE6 1070-6631 10.1063/1.1701892
17. M. B. Nemer, X. Chen, D. H. Papadopoulos, J. Blawzdziewicz, and W. Loewenberg, " Hindered and enhanced coalescence of drops in Stokes flow, " Phys. Rev. Lett. 92, 114501 (2004). prl PRLTAO 0031-9007 10.1103/PhysRevLett.92.114501
18. R. H. Davis, J. A. Schonberg, and J. M. Rallison, " The lubrication force between two viscous drops, " Phys. Fluids A 1, 77 (1989). pfa PFADEB 0899-8213 10.1063/1.857525
19. M. A. Rother, A. Z. Zinchenko, and R. H. Davis, " Buoyancy-driven coalescence of slightly deformable drops, " J. Fluid Mech. 346, 117 (1997). jfl JFLSA7 0022-1120 10.1017/S002211209700623X
20. S. G. Yiantsios and R. H. Davis, " On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface, " J. Fluid Mech. 217, 547 (1990). jfl JFLSA7 0022-1120
21. For a detailed description of the experimental protocol, see Yang et al; (Ref. 8) and Park (Ref. 9).
22. D. C. Tretheway, M. Muraoka, and L. G. Leal, " Experimental trajectories of two drops in planar extensional flow, " Phys. Fluids 11, 971 (1999). phf PHFLE6 1070-6631 10.1063/1.869969
23. M. A. Rother, A. Z. Zinchenko, and R. H. Davis, " A three-dimensional boundary-integral algorithm for thermocapillary motion of deformable drops, " J. Colloid Interface Sci. 245, 356 (2002). jci JCISA5 0021-9797 10.1006/jcis.2001.8002
24. A. Z. Zinchenko, M. A. Rother, and R. H. Davis, " A novel boundary-integral algorithm for viscous interaction of deformable drops, " Phys. Fluids 9, 1493 (1997). phf PHFLE6 1070-6631 10.1063/1.869275
25. A. Z. Zinchenko, M. A. Rother, and R. H. Davis, " Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm, " J. Fluid Mech. 391, 249 (1999). jfl JFLSA7 0022-1120 10.1017/S0022112099005285
26. V. Cristini, J. Blawzdziewicz, and M. Loewenberg, " An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence, " J. Comput. Phys. 168, 445 (2001). jct JCTPAH 0021-9991 10.1006/jcph.2001.6713
27. M. Loewenberg and E. J. Hinch, " Collision of two deformable drops in shear flow, " J. Fluid Mech. 338, 299 (1997). jfl JFLSA7 0022-1120 10.1017/S0022112097005016
28. M. Loewenberg and E. J. Hinch, " Numerical simulation of a concentrated emulsion in shear flow, " J. Fluid Mech. 321, 395 (1996). jfl JFLSA7 0022-1120
29. S. Abid and A. K. Chesters, " The drainage and rupture of partially mobile films between colliding drops at constant approach velocity, " Int. J. Multiphase Flow 20, 613 (1994). iny IJMFBP 0301-9322 10.1016/0301-9322(94)90033-7
30. A. Saboni, C. Gourdon, and A. K. Chesters, " Drainage and rupture of partially mobile films during coalescence in liquid-liquid systems under a constant interaction force, " J. Colloid Interface Sci. 175, 27 (1995). jci JCISA5 0021-9797 10.1006/jcis.1995.1425
31. I. B. Bazhlekov, A. K. Chesters, and F. N. van de Vosse, " The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops, " Int. J. Multiphase Flow 26, 445 (2000). iny IJMFBP 0301-9322 10.1016/S0301-9322(99)00032-4
32. V. Cristini, J. Blawzdziewicz, and M. Loewenberg, " Near-contact motion of surfactant-covered spherical drops, " J. Fluid Mech. 366, 259 (1998). jfl JFLSA7 0022-1120 10.1017/S0022112098001359
33. D. S. Valkovska and K. D. Danov, " Influence of ionic surfactants on the drainage velocity of thin liquid films, " J. Colloid Interface Sci. 241, 400 (2001). jci JCISA5 0021-9797
34. H. Wang, A. Z. Zinchenko, and R. H. Davis, " The collision rate of small drops in linear flow-fields, " J. Fluid Mech. 265, 161 (1994). jfl JFLSA7 0022-1120
35. A. Z. Zinchenko, " Calculation of close interaction between drops, with internal circulation and slip effect taken into account, " J. Appl. Math. Mech. 45, 564 (1981). jlm JAMMAR 0021-8928
36. A. Z. Zinchenko, " The slow asymmetric motion of two drops in a viscous medium, " J. Appl. Math. Mech. 44, 30 (1980). jlm JAMMAR 0021-8928
37. A. Z. Zinchenko, " Calculation of hydrodynamic interaction between drops at low Reynolds-numbers, " J. Appl. Math. Mech. 42, 1046 (1978). jlm JAMMAR 0021-8928
38. A. Z. Zinchenko and R. H. Davis, " Collision rates of spherical drops or particles in a shear-flow at arbitrary Peclet numbers, " Phys. Fluids 7, 2310 (1995). phf PHFLE6 1070-6631 10.1063/1.868745
39. A. Z. Zinchenko, " Calculation of the effectiveness of gravitational coagulation of drops with allowance for internal circulation, " J. Appl. Math. Mech. 46, 58 (1982). jlm JAMMAR 0021-8928
40. M. A. Rother and R. H. Davis, " The effect of slight deformation on droplet coalescence in linear flows, " Phys. Fluids 13, 1178 (2001). phf PHFLE6 1070-6631 10.1063/1.1358871
41. F. Baldessari, Ph.D. thesis, University of California, Santa Barbara, 2004.
42. The details of the full two drops calculation will be given in a subsequent publication and are presented in Baldessari (Ref. 41).
43. W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989).
44. C. C. Park, F. Baldessari, and L. G. Leal, " Study of molecular weight effects on coalescence: Interface slip layer, " J. Rheol. 47, 911 (2003). jor JORHD2 0148-6055 10.1122/1.1579686
45. G. Reiter, A. Sharma, A. Casoli, M. O. David, R. Khanna, and P. Auroy, " Thin film instability induced by long-range forces, " Langmuir 15, 2551 (1999). lan LANGD5 0743-7463 10.1021/la981470y
46. G. Reiter, A. Sharma, R. Khanna, A. Casoli, and M.-O. David, " The strength of long-range forces across thin liquid films, " J. Colloid Interface Sci. 214, 126 (1999). jci JCISA5 0021-9797 10.1006/ jcis.1999.6158
47. D. Bhatt, J. Newman, and C. J. Radke, " Molecular simulation of disjoining-pressure isotherms for free aqueous thin films, " J. Phys. Chem. B 107, 13076 (2003). bfk JPCBFK 1089-5647
48. D. Bhatt, J. Newman, and C. J. Radke, " Molecular simulation of disjoining-pressure isotherms for free liquid, Lennard-Jones thin films, " J. Phys. Chem. B 106, 6529 (2002). bfk JPCBFK 1089-5647 10.1021/ jp0202136
49. E. Schaffer and U. Steiner, " Acoustic instabilities in thin polymer films, " Eur. Phys. J. E 8, 347 (2002). 9fm EPJSFH 1292-8941 10.1140/epje/i2002-10018-0