Effect of overall drop deformation on flow-induced coalescence at low capillary numbers

Abstract

Comparison of recent experimental results for flow-induced drop coalescence ͓H. Yang, C. C. Park, Y. T. Hu et al., "The coalescence of two equal-sized drops in a two-dimensional linear flow," Phys. Fluids 13, 1087 ͑2001͔͒ with existing theory provides the motivation for an examination of the theory. Specifically, for head-on collisions, the experiments show a plateau in the dependence of drainage time versus capillary number at low capillary number that could not be explained by either the existing scaling analysis or the existing thin-film theory of the film drainage process previously described in the pioneering work of Davis and co-workers ͓S. G. Yiantsios and R. H. Davis, "Close approach and deformation of two viscous drops due to gravity and van der Waals forces," J. Colloid Interface Sci. 144, 412 ͑1991͒; R. H. Davis, J. A. Schonberg, and J. M. Rallison, "The lubrication force between two viscous drops," Phys. Fluids A 1, 77 ͑1989͒; M. A. Rother, A. Z. Zinchenko, and R. H. Davis, "Buoyancy-driven coalescence of slightly deformable drops," J. Fluid Mech. 346, 117 ͑1997͒; S. G. Yiantsios and R. H. Davis, "On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface," ibid. 217, 547 ͑1990͔͒. Both of these results indicate that the existing theories, while fundamentally correct in concept, are incomplete in providing a framework for a comprehensive explanation of the experimental results. In the present paper, we reexamine the thin-film theory of Davis et al. in the low capillary number limit. We find that a quasistatic model in which deformation is localized within the thin film is in general not sufficient to describe the leading-order asymptotic approximation of the flow-induced collision and coalescence of two slightly deformable drops at low capillary number. Instead, the overall deformation induced in the drops by the external flow plays a key role in determining the initial film thickness needed for numerical simulation of the thin-film dynamics via the existing theoretical framework. Also, we find that including retardation effects is important to be able to make quantitatively accurate predictions, especially at viscosity ratios below O͑1͒.

Colloidal behavior of nanoemulsions: Interactions, structure, and rheology

“…[54,55] Film drainage produces a significant hydrodynamic lubrication M A N U S C R I P T ACCEPTED MANUSCRIPT 4 force on the droplet surfaces, which tends to deform them before they come into contact, resulting in an increase in the interfacial area of the near-contacting surfaces. [56,57] This increased area can either promote or suppress surface contact depending on the relative magnitudes and ranges of attractive and repulsive forces between droplets. Nevertheless, it is the energetics of this surface deformation that leads to qualitatively different rates of coalescence for nanodroplets as compared to larger droplets, since the Laplace pressure, which scales as , resisting deformation is orders of magnitude larger for nanodroplets than for micron-scale droplets.…”

Theory of non-equilibrium force measurements involving deformable drops and bubbles

“…An alternate approach to treat hydrodynamic interactions is to solve the complete Stokes flow equations using direct numerical simulations [23][24][25][26]. Such methods have been used to study drop coalescence for capillary numbers in the range: Ca~0.001-0.1, where the computational time for a collision encounter can take over 100 h of CPU time.…”

Influence of drop size and superimposed mass transfer on coalescence in liquid/liquid dispersions – Test cell design for single drop investigations

“…Des., Elsevier, 2014, 92, 635-643 http://dx.doi.org/10.1016/j.cherd.2013 has been made modelling the film formation and drainage of two coalescing droplets (e.g. Abid and Chesters, 1994;Baldessari and Leal, 2006;Bozzano and Dente, 2011;Chen, 1985;Chesters, 1991;Danov et al, 1993;Eggers et al, 1999;Ivanov et al, 1999;Klaseboer et al, 2000;Lee and Hodgson, 1968;Marrucci, 1969;Toro-Mendoza and Petsev, 2010). Experimental studies of droplet-droplet coalescence can be classified by the used set-up.…”