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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: has@seas.harvard.edu
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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

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