DOI: 10.1063/1.2158427. Effect of overall drop deformation on flow-induced coalescence at low capillary numbers

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

10.1063/1.2158427

Crossref journal-article

AIP Publishing

Physics of Fluids (317)

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. Fluids13, 1087 (2001)] 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 (1991); R. H. Davis, J. A. Schonberg, and J. M. Rallison, “The lubrication force between two viscous drops,” Phys. Fluids A 1, 77 (1989); M. A. Rother, A. Z. Zinchenko, and R. H. Davis, “Buoyancy-driven coalescence of slightly deformable drops,” J. Fluid Mech. 346, 117 (1997); S. G. Yiantsios and R. H. Davis, “On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface,” J. Fluid Mech. 217, 547 (1990)]. 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 O(1).

Bibliography

Baldessari, F., & Leal, L. G. (2006). Effect of overall drop deformation on flow-induced coalescence at low capillary numbers. Physics of Fluids, 18(1).

Authors 2

Fabio Baldessari (first)
L. Gary Leal (additional)

References 46 Referenced 54

{'key': '2023062823132693800_c1', 'first-page': '595', 'article-title': 'Competitive roles of block copolymer during polymer blending: Suppression of coalescence and reduction of interfacial tension', 'volume': '218', 'year': '1999', 'journal-title': 'Abstr. Pap. - Am. Chem. Soc.'} / Abstr. Pap. - Am. Chem. Soc. / Competitive roles of block copolymer during polymer blending: Suppression of coalescence and reduction of interfacial tension (1999)
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10.1063/1.1358873 / Phys. Fluids / The coalescence of two equal-sized drops in a two-dimensional linear flow (2001)
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Dates

Type	When
Created	19 years, 6 months ago (Feb. 3, 2006, 6:06 p.m.)
Deposited	2 years, 1 month ago (June 28, 2023, 7:13 p.m.)
Indexed	3 weeks, 4 days ago (July 30, 2025, 6:45 a.m.)
Issued	19 years, 7 months ago (Jan. 1, 2006)
Published	19 years, 7 months ago (Jan. 1, 2006)
Published Online	19 years, 7 months ago (Jan. 20, 2006)
Published Print	19 years, 7 months ago (Jan. 1, 2006)

Funders 0

None

BibTeX

@article{Baldessari_2006, title={Effect of overall drop deformation on flow-induced coalescence at low capillary numbers}, volume={18}, ISSN={1089-7666}, url={http://dx.doi.org/10.1063/1.2158427}, DOI={10.1063/1.2158427}, number={1}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Baldessari, Fabio and Leal, L. Gary}, year={2006}, month=jan }

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