Hydrodynamic assist and the dynamic contact angle in the coalescence of liquid drops

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 71, Issue 5, 2006, Pages 740-767

  Decent, S P ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Coalescence; Hydrodynamic assist; Interface formation

Indexed keywords

HYDRODYNAMIC ASSIST; INTERFACE FORMATION; LIQUID DROPS;

CONTACT ANGLE; DIFFERENTIAL EQUATIONS; DROP FORMATION; HYDRODYNAMICS; LIQUIDS; REYNOLDS NUMBER; SURFACE TENSION; VISCOSITY OF LIQUIDS;

COALESCENCE;

EID: 33749611763     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxl005     Document Type: Article

References (49)

1. Ahn, K., Link, D., Griffiths, A. & Weitz, D. (2005) Enzyme-inhibitor assay using microdroplets. Bull. Am. Phys. Soc., 50, 1291.
2. Anna, S. & Mayer, H. (2005) A microfluidic tensiometer. Bull. Am. Phys. Soc., 50, 986.
3. Bedeaux, D. (2003) Nonequilibrium thermodynamic description of the three phase contact line. J. Chem. Phys., 120, 3744-3748.
4. Beysens, D. A., Andrieu, C., Nikolayev, V. S. & Pomeau, Y. (2002) Coalescence of sessile drops. J. Fluid Mech., 453, 427-438.
5. Billingham, J. & King, A. C. (2005) Surface tension driven flow outside a slender wedge with an application to the inviscid coalescence of drops. J. Fluid Mech., 533, 193-221.
6. Blake, T. D., Bracke, M. & Shikhmurzaev, Y. D. (1999) Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys. Fluids, 11, 1995-2007.
7. Blake, T. D. & Shikhmurzaev, Y. D. (2002) Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci., 253, 196-202.
8. Boinovich, L. B. & Deryagin, B. V. (1987) Disjoining pressure of thin wetting films of heptane-pentanol solutions. Coll. J. USSR, 49, 549-552.
9. Chatterjee, D., Hetayothin, B., Wheeler, A., King, D. & Garrell, R. (2005) Transport of nonconductive and conductive droplets in a parallel plate array. Bull. Am. Phys. Soc., 50, 987.
10. Daneshbod, Y., Sterling, J. D. & Nadim, A. (2005) Analysis of drop shapes during electrowetting on a dielectric. Bull. Am. Phys. Soc., 50, 987.
11. Davies, J. T. & Rideal, E. K. (1963) Interfacial Phenomena, 2nd edn. London: Academic Press.
12. Decent, S. P., Sharpe, G., Shaw, A. J. & Suckling, P. M. (2006) The formation of a liquid-bridge during the coalescence of liquid drops. Int. J. Multiphase Flow (in press).
13. Deryagin, B. V. (1993) Strict thermodynamic theory of wetting capillary rise, and capillary condensation. Coll. J. Russ. Acad. Sci., 55, 669-671.
14. Deryagin, B. V. & Churaev, N. V. (1972) Isotherm of disjoining pressure of water films on quartz surface. Dokl. Akad. Nauk SSSR, 207, 572.
15. Deryagin, B. V. & Churaev, N. V. (1976) Definition of disjoining pressure and its importance in equilibrium and flow of thin-films. Coll. J. USSR, 38, 402-410.
16. Deryagin, B. V. & Levi, S. M. (1964) Film Coating Theory. London: Focal P.
17. Eggers, J. & Evans, R. (2004) Comment on "dynamic wetting by liquids of different viscosity" by T. D. Blake and Y. D. Shikhmurzaev. J. Colloid Interface Sci., 280, 537.
18. Hopper, R. W. (1984) Coalescence of two equal cylinders - exact results for creeping viscous plane flow driven by capillarity. J. Am. Ceram. Soc., 67, C262-C264.
19. Hopper, R. W. (1990) Plane Stokes flow driven by capillarity on a free surface. J. Fluid Mech., 213, 349-375.
20. Hopper, R. W. (1992) Stokes flow of a cylinder and half-space driven by capillarity. J. Fluid Mech., 243, 171-181.
21. Hopper, R. W. (1993) Coalescence of two viscous cylinders by capillarity: Part II, shape evolution. J. Am. Ceram. Soc., 76, 2953-2960.
22. Jayaratne, O. W. & Mason, B. J. (1964) The coalescence and bouncing of water drops at an air/water interface. Proc. R. Soc. Lond. A, 280, 545-565.
23. Jeong, J. T. & Moffatt, H. K. (1992) Free-surface cusps associated with flow at a low Reynolds number. J. Fluid Mech., 241, 1.
24. Keller, J. B., Milewski, P. A. & Vanden-Broeck, J. (2000) Wetting and merging driven by surface tension. Eur. J. Mech. B. Fluids, 19, 491.
25. Kerbage, C., Ahn, K., Hunt, T., Westervelt, R. & Weitz, D. (2005) Optical detection and magnetic manipulation of drops in microfluidic devices. Bull. Am. Phys. Soc., 50, 1291.
26. Krupenkin, T., Taylor, A., Kolodner, P., Pau, S., Lyons, A. & Hodes, M. (2005) Manipulating liquids on the tunable nanostructured surfaces. Bull. Am. Phys. Soc., 50, 986.
27. Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. & Zanetti, G. (1994) Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys., 113, 134-147.
28. Menchaca-Rocha, A., Martinez-Davalos, A., Nunez, R., Popinet, S. & Zaleski, S. (2001) Coalescence of liquid drops by surface tension. Phys. Rev. E, 63, 046309.
29. Monnier J. & Witomski P. (2004) Analysis of a local hydrodynamic model with Marangoni effect. J. Sci. Comput., 21, 369-403.
30. Partridge, L. (2002) Coalescence of two liquid volumes. M.Sc. Project, School of Mathematics and Statistics, University of Birmingham, Birmingham.
31. Pergamalis, H. (2002) Droplet impingement onto quiescent and moving liquid surfaces. Ph.D. Thesis, Mechanical Engineering Department, Imperial College of Science, Technology and Medicine, London.
32. Quake, S. (2005) Biological large scale integration. Bull. Am. Phys. Soc., 50, 652.
33. Richardson, S. (1997) Two-dimensional Stokes flows with time-dependant free surface boundaries driven by surface tension. Eur. J. Appl. Math., 8, 311.
34. Shaw, A. J. (2003) Coalescence of two liquid volumes: Topological transitions in their free surface flows. MPhil. Thesis, School of Mathematics and Statistics, The University of Birmingham, Birmingham.
35. Shikhmurzaev, Y. D. (1993) The moving contact line on a smooth solid surface. Int. J. Multiphase Flow, 19, 589-610.
36. Shikhmurzaev, Y. D. (1994) Mathematical modelling of wetting hydrodynamics. Fluid Dyn. Res., 13, 45-64.
37. Shikhmurzaev, Y. D. (1996) Dynamic contact angles in gas-liquid-solid systems and flow in vicinity of moving contact line. AIChE J., 42, 601.
38. Shikhmurzaev, Y. D. (1997a) Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech., 334, 211-249.
39. Shikhmurzaev, Y. D. (1997b) Spreading of drops on solid surfaces in a quasi-static regime. Phys. Fluids, 9, 266.
40. Shikhmurzaev, Y. D. (1998) On cusped interfaces. J. Fluid Mech., 359, 313-328.
41. Shikhmurzaev, Y. D. (2000) Coalescence and capillary breakup of liquid volumes. Phys. Fluids, 12, 2386-2396.
42. Shikhmurzaev, Y. D. (2002) On metastable regimes of dynamic wetting. J. Phys. Condens. Matter, 14, 319-330.
43. Shikhmurzaev, Y. D. (2005a) Capillary breakup of liquid threads: A singularity-free solution. IMA J. Appl. Math., 70, 880-907.
44. Shikhmurzaev, Y. D. (2005b) Macroscopic mechanism of rupture of free liquid films. C. R. Mec., 333, 205-210.
45. Shikhmurzaev, Y. D. (2005c) Fluid dynamics with transitions in the topology of the flow domain: Breakup of jets and rupture of films. Dokl. Phys., 50, 40-43.
46. Shikhmurzaev, Y. D. & Blake, T. D. (2004) Response to the comment on "dynamic wetting by liquids of different viscosity" by J. Eggers and R. Evans. J. Colloid Interface Sci., 280, 539-541.
47. Suckling, P. M. (2003) The impact and spreading of a drop on a surface. Ph.D. Thesis, School of Mathematics and Statistics, The University of Birmingham, Birmingham.
48. Tabeling, P., Willaime, H., Barbier, V. & Menetrier, L. (2005) Nonlinear phenomena in two-phase flows in microfluidic systems. Bull. Am. Phys. Soc., 50, 1291.
49. Zheng, B., Tice, J. & Ismagilov, R. (2005) Formation of droplets of different compositions in microfluidic channels and applications to protein crystallization. Bull. Am. Phys. Soc., 50, 1291.