A fluid-mechanical model of elastocapillary coalescence

• Published in: Journal of fluid mechanics Vol. 745; pp. 621 - 646
• Main Authors: Singh, Kiran, Lister, John R., Vella, Dominic
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.04.2014
• Subjects: Applied sciences; Boundary lubrication; Capillarity; Clusters; Coalescence; Coalescing; Computer simulation; Dynamics; Electronics; Exact sciences and technology; Fluid mechanics; Mathematical models; Micro- and nanoelectromechanical devices (mems/nems); Perturbation methods; Propagation; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Surface tension; capillary flows; MEMS/NEMS; lubrication theory; Rinsing; Numerical simulation; Capillary flow; Manufacturing; Coalescence; Elastic deformation; Modeling; Microelectromechanical device
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.102

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, $N=O(10^4)$. 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 $K^{-1/2}$ 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.