弹性Rayleigh-Plateau不稳定性：非线性状态的动力学选择
Elastic Rayleigh-Plateau instability: Dynamical selection of nonlinear states
摘要：
弹性水凝胶的细线容易受到表面不稳定性的影响，这让人想起液体射流的经典瑞利-高原不稳定性。在实验中观察到的最后的高度非线性状态是由毛细作用和大的弹性形变之间的竞争引起的。结合细长的分析和完全三维的数值模拟，我们提出了一个不稳定的neo-Hookean圆柱体受到毛细作用力的所有可能的形态的相图。有趣的是，对于较软的圆柱体，我们发现两种不同的配置，即圆柱体上的一个字符串和珠串的共存。它示出，对于一组给定的参数，最终的图案选择通过动态演化。为了捕捉这一点，我们计算色散关系，并确定动态选择的配置文件的特征波长。通过模拟证实了“细长”结果的有效性，这些结果与弹性和粘弹性线的实验结果一致。
英文摘要：
A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are observed in experiments arise from a competition between capillarity and large elastic deformations. Combining a slender analysis and fully three-dimensional numerical simulations, we present the phase map of all possible morphologies for an unstable neo-Hookean cylinder subjected to capillary forces. Interestingly, for softer cylinders we find the coexistence of two distinct configurations, namely, cylinders-on-a-string and beads-on-a-string. It is shown that for a given set of parameters, the final pattern is selected via a dynamical evolution. To capture this, we compute the dispersion relation and determine the characteristic wavelength of the dynamically selected profiles. The validity of the "slender" results is confirmed via simulations and these results are consistent with experiments on elastic and viscoelastic threads.
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