弹性毛细血管聚结的流体力学模型
A fluid-mechanical model of elastocapillary coalescence
摘要：
我们提出了一个流体力学模型的聚结的一些弹性物体由于表面张力。我们考虑一个阵列的弹簧块元件分离的薄液膜，其动力学建模使用润滑理论。用这个简化的弹性毛细血管合并模型，我们提出了大量的元素，$N=O(10^4)$的数值模拟结果。线性稳定性分析表明，成对合并总是最不稳定的变形模式。然而，数值模拟表明，实际上产生的聚结从一个小的白噪声扰动的集群大小有一个分布，这取决于表面张力和弹性的相对强度，测量的弹性毛细数$K$。对于小的$K$，最大簇大小和平均簇大小都像$K^{-1/2}$那样缩放。一个本地化的扰动的系统的响应的分析解决方案表明，这种扰动产生传播的扰动前，留下的“冻结”集群的可预测的大小，也取决于$K$。一个很好的定量比较从嘈杂的扰动和这个'冻结'集群大小的集群大小的统计数据表明，传播战线可能发挥至关重要的作用，在动态的合并。
英文摘要：
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.
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