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Droplet coalescence: drainage, film rupture and neck growth in ultralow interfacial tension systems

Published online by Cambridge University Press:  10 July 2008

DIRK G. A. L. AARTS  and
HENK N. W. LEKKERKERKER
DIRK G. A. L. AARTS
Affiliation:
Van't Hoff Laboratory, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
HENK N. W. LEKKERKERKER
Affiliation:
Van't Hoff Laboratory, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
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Abstract

We study the coalescence of a drop with its bulk phase in fluid–fluid demixing colloid–polymer mixtures. Such mixtures show behaviour analogous to molecular fluid–fluid systems, but the interfacial tension is between 105 to 107 times smaller than in the molecular case. Such an ultralow interfacial tension has several important consequences and offers significant advantages in the study of droplet coalescence. The coalescence process can be divided into three consecutive stages: (i) drainage of the continuous film between droplet and bulk phase, (ii) rupture of the film, and (iii) growth of the connection. These stages can be studied within a single experiment by optical microscopy thanks to the ultralow interfacial tension in colloid–polymer mixtures, which significantly changes the relevant characteristic length and time scales. The first stage is compared with existing theories on drainage, where we show several limiting theoretical cases. The experimental drainage curves of different colloid–polymer mixtures can be scaled and then show very similar behaviour. We observe that drainage becomes very slow and eventually the breakup of the film is induced by thermal capillary waves. The time it takes for a certain height fluctuation of the interface to occur, which turns out to be an important parameter for the kinetics of the process, can be directly obtained from experiment. During the third stage we observe that the radius of the connecting neck grows linearly with time both for gas bubbles and liquid droplets with an order of magnitude that is in good agreement with the capillary velocity. Finally, partially bleaching the fluorescent dye inside the liquid droplet reveals how the surface energy is transformed into kinetic energy upon coalescence. This opens the way for a more complete understanding of the hydrodynamics involved.

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Papers
Information
Journal of Fluid Mechanics , Volume 606 , 10 July 2008 , pp. 275 - 294
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Aarts, D. G. A. L. 2005 J. Phys. Chem. B 109, 7407.CrossRefGoogle Scholar
Aarts, D. G. A. L., Dullens, R. P. A. & Lekkerkerker, H. N. W. 2005 a New J. Phys. 7, 40.Google Scholar
Aarts, D. G. A. L., Dullens, R. P. A., Lekkerkerker, H. N. W., Bonn, D. & van Roij, R. 2004 a J. Chem. Phys. 120, 1973.CrossRefGoogle Scholar
Aarts, D. G. A. L. & Lekkerkerker, H. N. W. 2004 J. Phys.: Condens. Matter 16, S4231.Google Scholar
Aarts, D. G. A. L., Lekkerkerker, H. N. W., Guo, H., Wegdam, G. & Bonn, D. 2005 b Phys. Rev. Lett. 95, 164503.CrossRefGoogle Scholar
Aarts, D. G. A. L., Schmidt, M. & Lekkerkerker, H. N. W. 2004 b Science 304, 847.Google Scholar
Aarts, D. G. A. L., Schmidt, M., Lekkerkerker, H. N. W. & Mecke, K. R. 2005 c Adv. Solid State Phys.Google Scholar
Aarts, D. G. A. L., van der Wiel, J. H. & Lekkerkerker, H. N. W. 2003 J. Phys.: Condens. Matter 15, S245.Google Scholar
Asakura, S. & Oosawa, F. 1954 J. Chem. Phys. 22, 1255.Google Scholar
Becker, R. 1966 Theorie der Wärme. Springer.Google Scholar
Berry, G. C. 1966 J. Chem. Phys. 44, 4550.CrossRefGoogle Scholar
Bosma, G., Pathmamanoharan, C., de Hoog, E. H. A., Kegel, W. K., van Blaaderen, A. & Lekkerkerker, H. N. W. 2002 J. Colloid Interface Sci. 245, 292.Google Scholar
Brader, J. M. & Evans, R. 2000 Europhys. Lett. 49, 678.Google Scholar
Brader, J. M., Evans, R., Schmidt, M. & Löwen, H. 2002 J. Phys.: Condens. Matter 14, L1.Google Scholar
Brandes, A.E., Zhang, G.F. & Vivekanadan, J. 2004 J. Appl. Met. 43, 461.Google Scholar
Brown, A. H. & Hanson, C. 1967 Nature 214, 76.Google Scholar
Buff, F. P., Lovett, R. A. & Stillinger, F. H. 1965 Phys. Rev. Lett. 15, 621.CrossRefGoogle Scholar
Charles, G. E. & Mason, S.G. 1960 J. Colloid Sci. 15, 236.CrossRefGoogle Scholar
Chen, B. H., Payandeh, B. & Robert, M. 2000 Phys. Rev. E 62, 2369.Google Scholar
Chen, N., Kuhl, T., Tadmor, R., Lin, Q. & Israelachvili, J. N. 2004 Phys. Rev. Lett. 92, 024501.Google Scholar
Chi, B. K. & Leal, L. G. 1989 J. Fluid Mech. 201, 123.Google Scholar
De Gennes, P.G. 1979 Scaling Concepts in Polymer Physics. Cornell University Press.Google Scholar
Dickinson, E. & Walstra, P. 1993 Food Colloids and Polymers: Stability and Mechanical Properties. Cambridge: Royal Society of Chemistry.Google Scholar
Duchemin, L., Eggers, J. & Josserand, C. 2003 J. Fluid Mech. 487, 167.CrossRefGoogle Scholar
Eggers, J., Lister, J. R. & Stone, H. A. 1999 J. Fluid Mech. 401, 293.CrossRefGoogle Scholar
Frohn, A. & Roth, N. 2000 Dynamics of Droplets. Springer.CrossRefGoogle Scholar
Haeberlea, S. & Zengerle, R. 2007 Lab on a Chip 7, 1094.Google Scholar
Happel, J. & Brenner, H. 1986 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.Google Scholar
Hartland, S. 1967 Trans. Inst. Chem. Engrs 45, T102.Google Scholar
Hartland, S. 1968 J. Colloid Interface Sci. 26, 383.Google Scholar
Hartland, S. 1969 a Can. J. Chem. Engng 47, 221.Google Scholar
Hartland, S. 1969 b Chem. Engng Sci. 24, 987.CrossRefGoogle Scholar
Hartland, S. 1969 c Chem. Engng Sci. 24, 611.CrossRefGoogle Scholar
Hartland, S., Yang, B. & Jeelani, S. A. K. 1993 Chem. Engng Sci. 49, 1313.CrossRefGoogle Scholar
Helden, A. K., Jansen, J. W. & Vrij, A. 1980 J. Colloid Interface Sci. 77, 418.Google Scholar
de Hoog, E. H. A. 2001 Interfaces and crystallization in colloid-polymer suspensions. PhD thesis, Utrecht University.Google Scholar
de Hoog, E. H. A. & Lekkerkerker, H. N. W. 1999 J. Phys. Chem. B 103, 5274.CrossRefGoogle Scholar
de Hoog, E. H. A. & Lekkerkerker, H. N. W. 2001 J. Phys. Chem. B 105, 11636.CrossRefGoogle Scholar
Iancu, F. O. 2005 Droplet dynamics in a fluid environment. a mesoscopic simulation study. PhD thesis, Technical University Delft.Google Scholar
Israelachvili, J. N. 1992 Intermolecular and Surface Forces. Academic.Google Scholar
Jeffreys, G. V. & Hawksley, J. L. 1962 J. Appl. Chem. 12, 329.Google Scholar
Jeng, U. S., Esibov, L., Crow, L. & Steyerl, A. 1998 J. Phys.: Condens. Matter 10, 4955.Google Scholar
Jones, A. F. & Wilson, S. D. R. 1978 J. Fluid Mech. 87, 263.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Mandelstam, L. 1913 Ann. Phys. 41, 609–624.Google Scholar
Mechaca-Rocha, A., Martínez-Dávalos, A., Núñez, R., Popinet, S. & Zaleski, S. 2001 Phys. Rev. E 63, 046309.Google Scholar
Mohamed-Kassim, Z. & Longmire, E. K. 2003 Phys. Fluids 15, 3263.Google Scholar
Mohamed-Kassim, Z. & Longmire, E. K. 2004 Phys. Fluids 16, 2170.CrossRefGoogle Scholar
Moncho-Jorda, A., Rotenberg, B. & Louis, A. A. 2003 J. Chem. Phys. 119, 12667–12672.CrossRefGoogle Scholar
Nemer, M. B., Chen, X., Papadopoulos, D. H., Blawzdziewicz, J. & Loewenberg, M. 2004 Phys. Rev. Lett. 92, 114501.CrossRefGoogle Scholar
Nemer, M. B., Chen, X., Papadopoulos, D. H., Blawzdziewicz, J. & Loewenberg, M. 2007 J. Colloid Interface Sci. 308, 1.Google Scholar
Princen, H. M. & Mason, S. G. 1965 J. Colloid Sci. 20, 246.Google Scholar
Probstein, R. F. 2003 Physicochemical Hydrodynamics, section 10.2. John Wiley & Sons.Google Scholar
Reynolds, O. 1886 Phil. Trans. R. Soc. Lond. 177, 157.Google Scholar
Rowlinson, J. S. & Widom, B. 1982 Molecular Theory of Capillarity. Clarendon.Google Scholar
Scheludko, A. 1967 Adv. Colloid Interface Sci. 44, 391.Google Scholar
Schulze, H. J., Stöckelhuber, K. W. & Wenger, A. 2001 Colloids Surf. A 192, 61.Google Scholar
von Smoluchowski, M. 1916 Phys. Zeitschrift 17, 537.Google Scholar
Squires, T. M. & Quake, S. R. 2005 Rev. Mod. Phys. 77, 977.Google Scholar
Stone, H. A. 1994 Annu. Rev. Fluid Mech. 26, 65.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Annu. Rev. Fluid Mech. 36, 381.CrossRefGoogle Scholar
Thomson, J. J. & Newall, H. F. 1885 Proc. R. Soc. Lond. 39, 417.Google Scholar
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2005 J. Fluid Mech. 527, 85.Google Scholar
Verhaegh, N. A. M., van Duijneveldt, J. S., Dhont, J. K. G. & Lekkerkerker, H. N. W. 1996 Physica A 230, 409.CrossRefGoogle Scholar
de Villeneuve, V. W. A., Aarts, D. G. A. L. & Lekkerkerker, H. N. W. 2006 Colloids Surf. A 282–283, 61.Google Scholar
Vincent, B. 1990 Colloids Surf. 50, 241.Google Scholar
Vink, R. L. C. & Horbach, J. 2004 a J. Chem. Phys. 121, 3253.CrossRefGoogle Scholar
Vink, R. L. C. & Horbach, J. 2004 b J. Phys.: Condens. Matter 16, S3807.Google Scholar
Vliegenthart, G. A. & Lekkerkerker, H. N. W. 1997 Prog. Colloid Polym. Sci. 105, 27.Google Scholar
Vrij, A. 1966 Disc. Faraday Soc. 42, 23.Google Scholar
Vrij, A. 1976 Pure Appl. Chem. 48, 471.Google Scholar
Vrij, A. 1997 Physica A 235, 120.Google Scholar
Webb, R. H. 1996 Rep. Prog. Phys. 59, 427.Google Scholar
Wu, M., Cubaud, T. & Ho, C. 2004 Phys. Rev. E 16, L51.Google Scholar
Yao, W., Maris, J. H., Pennington, P. & Seidel, G. M. 2005 Phys. Rev. E 71, 016309.Google Scholar
Yiantsios, S. G. & Davis, R. H. 1990 J. Fluid Mech. 217, 547.Google Scholar