Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-08T05:34:30.771Z Has data issue: false hasContentIssue false
  • English
  • Français

Separation-driven coalescence of droplets: an analytical criterion for the approach to contact

Published online by Cambridge University Press:  27 July 2009

ANN LAI ,
NICOLAS BREMOND  and
HOWARD A. STONE
ANN LAI
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
NICOLAS BREMOND
Affiliation:
UPMC Paris 06, ESPCI ParisTech, CNRS UMR 7195, 10 rue Vauquelin, 75005 Paris, France
HOWARD A. STONE*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent microfluidic experiments by Bremond, Thiam & Bibette (Phys. Rev. Lett., vol. 100, 2008, paper no. 024501), along with simulations by Yoon et al. (Phys. Fluid, vol. 19, 2007, paper no. 102102) and near-contact experiments and simulations by Manica et al. (Langmuir, vol. 24, 2008, pp. 1381–1390), have demonstrated that two droplets can coalesce as they are separating rather than upon their collision. We analyse the experimental microfluidic flow configuration for the approach to contact with a two-dimensional model: we apply a lubrication analysis followed by the method of domain perturbation to determine the droplet deformation as a function of time. We find the approximate shape for the deformed droplet at the time of contact. In particular, for droplets of radius R, moving apart according to h0(t) = h0(0) + αt2, where 2h0(t) is the separation distance, we define a non-dimensional parameter A=4CμR2α1/2/πγ[h0(0)]3/2, where μ is the viscosity of the continuous phase; γ is the interfacial tension; and C depends on the viscosity ratio between the droplets and the continuous phase. Our model suggests that there exists a critical value Acrit = 16/33/2 ≈ 3.0792, below which separation is unlikely to facilitate the coalescence of the droplets. The predictions are in good agreement with available experimental data.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 632 , 10 August 2009 , pp. 97 - 107
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aarts, D. G. A. L. & Lekkerkerker, H. N. W. 2008 Droplet coalescence: drainage, film rupture and neck growth in ultralow interfacial tension systems. J. Fluid Mech. 606, 275–294.CrossRefGoogle Scholar
Barthés-Biesel, D. & Acrivos, A. 1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1–21.CrossRefGoogle Scholar
Bremond, N., Thiam, A. R. & Bibette, J. 2008 Decompressing emulsion droplets favors coalescence. Phys. Rev. Lett. 100, 024501.CrossRefGoogle ScholarPubMed
Davis, R. H., Schonberg, J. A. & Rallison, J. M. 1989 The lubrication force between two viscous drops. Phys. Fluid A 1, 77–81.CrossRefGoogle Scholar
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in droplet coalescence. J. Fluid Mech. 87, 263–288.CrossRefGoogle Scholar
Leal, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.Google Scholar
Loewenberg, M. & Hinch, E. J. 1997 Collision of two deformable drops in shear flow. J. Fluid Mech. 338, 299–315.CrossRefGoogle Scholar
Manica, R., Conner, J. N., Clasohm, L. Y., Carnie, S. L., Horn, R. G., & Chan, D. Y. C. 2008 Transient responses of a wetting film to mechanical and electrical perturbations. Langmuir 24, 1381–1390.CrossRefGoogle ScholarPubMed
Nemer, M. B., Chen, X., Papadopoulos, D. H., Blawzdziewicz, J. & Loewenberg, M. 2004 Hindered and accelerated coalescence of drops in Stokes flow. Phys. Rev. Letters 92, 114501.CrossRefGoogle Scholar
Park, C.-W., Gorell, S. & Homsy, G. M. 1984 Two-phase displacement in Hele–Shaw cells: experiments on viscously driven instabilities. J. Fluid Mech. 141, 257–287.CrossRefGoogle Scholar
Park, C.-W. & Homsy, G. M. 1984 Two-phase displacement in Hele–Shaw cells: theory. J. Fluid Mech. 139, 291–308.CrossRefGoogle Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16, 45–66.CrossRefGoogle Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.CrossRefGoogle Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501–523.Google Scholar
Yoon, Y., Baldessari, F., Ceniceros, H. D. & Leal, L. G. 2007 Coalescence of two equal-sized deformable drops in an axisymmetric flow. Phys. Fluid 19, 102102.CrossRefGoogle Scholar
Yoon, Y., Borrell, M., Park, C. C. & Leal, L. G. 2005 Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow. J. Fluid Mech. 525, 355–379.CrossRefGoogle Scholar