The Mathematical Institute, University of Oxford, Eprints Archive

The Capillary Interaction Between Two Vertical Cylinders

Cooray, H. and Cicuta, P. and Vella, D. (2011) The Capillary Interaction Between Two Vertical Cylinders. Journal of Physics: Condensed Matter . (Submitted)

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Abstract

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.
Good agreement is found between all three approaches (numerical, asymptotic and experimental) for large inter-particle separations and conditions such that the meniscus
slope remains small everywhere. 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 in these situations.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1472
Deposited By:Peter Hudston
Deposited On:22 Feb 2012 07:54
Last Modified:22 Feb 2012 07:54

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