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A parametric study of the coalescence of liquid drops in a viscous gas

Published online by Cambridge University Press:  22 July 2014

James E. Sprittles Open the ORCID record for James E. Sprittles [Opens in a new window]  and
Yulii D. Shikhmurzaev
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Abstract

The coalescence of two liquid drops surrounded by a viscous gas is considered in the framework of the conventional model. The problem is solved numerically with particular attention paid to resolving the very initial stage of the process which only recently has become accessible both experimentally and computationally. A systematic study of the parameter space of practical interest allows the influence of the governing parameters in the system to be identified and the role of viscous gas to be determined. In particular, it is shown that the viscosity of the gas suppresses the formation of toroidal bubbles predicted in some cases by early computations where the gas’ dynamics was neglected. Focusing computations on the very initial stages of coalescence and considering the large parameter space allows us to examine the accuracy and limits of applicability of various ‘scaling laws’ proposed for different ‘regimes’ and, in doing so, reveal certain inconsistencies in recent works. A comparison with experimental data shows that the conventional model is able to reproduce many qualitative features of the initial stages of coalescence, such as a collapse of calculations onto a ‘master curve’ but, quantitatively, overpredicts the observed speed of coalescence and there are no free parameters to improve the fit. Finally, a phase diagram of parameter space, differing from previously published ones, is used to illustrate the key findings.

JFM classification

Drops and Bubbles: Breakup/coalescence Interfacial Flows (free surface): Capillary flows Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 753 , 25 August 2014 , pp. 279 - 306
Copyright
© 2014 Cambridge University Press 

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References

Aarts, D. G. A. L., Lekkerkerker, H. N. W., Guo, H., Wegdam, G. H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.Google Scholar
Derby, B. 2010 Inkjet printing of functional and structural materials: fluid property requirements, feature stability and resolution. Annu. Rev. Mater. Res. 40, 395–414.Google Scholar
Duchemin, L., Eggers, J. & Josserand, C. 2003 Inviscid coalescence of drops. J. Fluid Mech. 487, 167–178.CrossRefGoogle Scholar
Eddi, A., Winkels, K. G. & Snoeijer, J. H. 2013 Short time dynamics of viscous drop spreading. Phys. Fluids 25, 013102.CrossRefGoogle Scholar
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
Enright, R., Miljkovic, N., Al-Obeidi, A., Thompson, C. V. & Wang, E. N. 2012 Condensation on superhydrophobic surfaces: the role of local energy barriers and structure length scale. Langmuir 28, 14424–14432.Google Scholar
Hopper, R. W. 1984 Coalescence of two equal cylinders: exact results for creeping viscous plane flow driven by capillarity. J. Am. Ceram. Soc. 67, 262–264.CrossRefGoogle Scholar
Hopper, R. W. 1990 Plane Stokes flow driven by capillarity on a free surface. J. Fluid Mech. 213, 349–375.Google Scholar
Hopper, R. W. 1993a Coalescence of two viscous cylinders by capillarity: part 1. Theory. J. Am. Ceram. Soc. 76, 2947–2952.CrossRefGoogle Scholar
Hopper, R. W. 1993b Coalescence of two viscous cylinders by capillarity: part 2. Shape evolution. J. Am. Ceram. Soc. 76, 2953–2960.CrossRefGoogle Scholar
Menchaca-Rocha, A., Martínez-Dávalos, A., Núńez, R., Popinet, S. & Zaleski, S. 2001 Coalescence of liquid drops by surface tension. Phys. Rev. E 63, 046309.CrossRefGoogle ScholarPubMed
Oguz, H. N. & Prosperetti, A. 1989 Surface-tension effects in the contact of liquid surfaces. J. Fluid Mech. 203, 149–171.CrossRefGoogle Scholar
Paulsen, J. D. 2013 Approach and coalescence of liquid drops in air. Phys. Rev. E 88, 063010.Google Scholar
Paulsen, J. D., Burton, J. C. & Nagel, S. R. 2011 Viscous to inertial crossover in liquid drop coalescence. Phys. Rev. Lett. 106, 114501.CrossRefGoogle ScholarPubMed
Paulsen, J. D., Burton, J. C., Nagel, S. R., Appathurai, S., Harris, M. T. & Basaran, O. 2012 The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl Acad. Sci. USA 109, 6857–6861.CrossRefGoogle ScholarPubMed
Paulsen, J. D., Carmigniani, R., Kannan, A., Burton, J. C. & Nagel, S. R. 2014 Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5, 3182.Google Scholar
Richardson, S. 1992 Two-dimensional slow viscous flows with time-dependent free boundaries driven by surface tension. Eur. J. Appl. Maths 3, 193–207.CrossRefGoogle Scholar
Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.CrossRefGoogle Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012a Coalescence of liquid drops: different models versus experiment. Phys. Fluids 24, 122105.CrossRefGoogle Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012b The dynamics of liquid drops and their interaction with solids of varying wettabilities. Phys. Fluids 24, 082001.Google Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012c A finite element framework for describing dynamic wetting phenomena. Intl J. Numer. Meth. Fluids 68, 1257–1298.CrossRefGoogle Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2013 Finite element simulation of dynamic wetting flows as an interface formation process. J. Comput. Phys. 233, 34–65.Google Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2014a The coalescence of liquid drops in a viscous fluid: interface formation model. J. Fluid Mech. 751, 480–499.Google Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2014b Dynamics of liquid drops coalescing in the inertial regime. Phys. Rev. E 89, 063006.CrossRefGoogle ScholarPubMed
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2008 High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40, 257–285.Google Scholar
Thoroddsen, S. T. & Takehara, K. 2000 The coalescence cascade of a drop. Phys. Fluids 12, 1265–1267.Google Scholar
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2005 The coalescence speed of a pendent and sessile drop. J. Fluid Mech. 527, 85–114.CrossRefGoogle Scholar
Wu, M., Cubaud, T. & Ho, C. 2004 Scaling law in liquid drop coalescence driven by surface tension. Phys. Fluids 16, 51–54.CrossRefGoogle Scholar