The capillary interaction between two vertical cylinders

Himantha Cooray, Pietro Cicuta, Dominic Vella

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27 Scopus citations


Particles floating at the surface of a liquid generally deform the liquid surface. Minimizing the energetic cost of these deformations results in an inter-particle force which is usually attractive and causes floating particles to aggregate and form surface clusters. Here we present a numerical method for determining the three-dimensional meniscus around a pair of vertical circular cylinders. This involves the numerical solution of the fully nonlinear Laplace-Young equation using a mesh-free finite difference method. Inter-particle force-separation curves for pairs of vertical cylinders are then calculated for different radii and contact angles. These results are compared with previously published asymptotic and experimental results. For large inter-particle separations and conditions such that the meniscus slope remains small everywhere, good agreement is found between all three approaches (numerical, asymptotic and experimental). This is as expected since the asymptotic results were derived using the linearized Laplace-Young equation. For steeper menisci and smaller inter-particle separations, however, the numerical simulation resolves discrepancies between existing asymptotic and experimental results, demonstrating that this discrepancy was due to the nonlinearity of the Laplace-Young equation. © 2012 IOP Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)284104
JournalJournal of Physics: Condensed Matter
Issue number28
StatePublished - Jun 27 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: We thank J Li and M Oettel for many useful discussions. This work is supported by a Developing World Education Fund Cambridge Scholarship made by Cambridge Commonwealth Trust, Overseas Research Students Awards Scheme (HC), by grant no. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST) (DV), and by the Marie Curie Training Network ITN-COMPLOIDS (FP7-PEOPLE-ITN-2008 no. 234810) (PC).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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