A fluid-mechanical model of elastocapillary coalescence

Singh, Kiran; Lister, John R.; Vella, Dominic

A fluid-mechanical model of elastocapillary coalescence

Type

Article

Authors

Singh, Kiran
Lister, John R.
Vella, Dominic

KAUST Grant Number

KUK-C1-013-04

Online Publication Date

2014-03-25

Print Publication Date

2014-04

Date

2014-03-25

Abstract

© 2014 Cambridge University Press. We present a fluid-mechanical model of the coalescence of a number of elastic objects due to surface tension. We consider an array of spring-block elements separated by thin liquid films, whose dynamics are modelled using lubrication theory. With this simplified model of elastocapillary coalescence, we present the results of numerical simulations for a large number of elements, N = O(10

). A linear stability analysis shows that pairwise coalescence is always the most unstable mode of deformation. However, the numerical simulations show that the cluster sizes actually produced by coalescence from a small white-noise perturbation have a distribution that depends on the relative strength of surface tension and elasticity, as measured by an elastocapillary number K. Both the maximum cluster size and the mean cluster size scale like K

for small K. An analytical solution for the response of the system to a localized perturbation shows that such perturbations generate propagating disturbance fronts, which leave behind 'frozen-in' clusters of a predictable size that also depends on K. A good quantitative comparison between the cluster-size statistics from noisy perturbations and this 'frozen-in' cluster size suggests that propagating fronts may play a crucial role in the dynamics of coalescence.

Citation

Singh K, Lister JR, Vella D (2014) A fluid-mechanical model of elastocapillary coalescence. Journal of Fluid Mechanics 745: 621–646. Available: http://dx.doi.org/10.1017/jfm.2014.102.

Acknowledgements

KS and DV wish to acknowledge the support of the King Abdullah University of Science and Technology (KAUST; Award No. KUK-C1-013-04), and the John Fell Oxford University Press (OUP) Research Fund. JRL gratefully acknowledges support from Princeton University to cover a sabbatical visit during the Spring semester 2013, and we also acknowledge all of those involved in the Oxford-Princeton Collaboration 2013 that prompted some early stages of this work.