刚性圆柱体上软层涂层的Plateau-Rayleigh不稳定性
Plateau-Rayleigh instability of a soft layer coated on a rigid cylinder
AI总结：
本文通过线性稳定性分析，研究刚性圆柱上软层的Plateau-Rayleigh不稳定性，发现刚性芯显著提高临界弹性毛细数并稳定系统，且最快增长波长与芯半径无关。
摘要：
我们研究了涂覆在刚性圆柱体上的粘弹性软固体层的Plateau-Rayleigh不稳定性，即具有刚性芯的软纤维。使用线性稳定性分析检查不稳定性的起始。我们发现，增加刚性圆柱体的半径会降低最快增长模式的增长率。对于每个刚性圆柱体半径，存在一个临界弹性毛细数，低于该数时所有波长的扰动都是稳定的。对于具有厚刚性圆柱芯的软纤维，其临界值可以比完全软纤维（无刚性芯）的临界值大几个数量级，这突显了刚性芯对系统的强稳定作用。增加粘弹性材料的松弛时间尺度也会减缓扰动的增长，但对临界弹性毛细数没有影响。有趣的是，对于纯弹性情况，最快增长模式的波长与刚性圆柱体的半径无关。
英文摘要：
We study the Plateau-Rayleigh instability of a viscoelastic soft solid layer coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of instability is examined using a linear stability analysis. We find that increasing the rigid cylinder radius reduce the growth rate of the fastest growing mode. For each rigid cylinder radius, a critical elastocapillary number is found below which all wavelengths of disturbances are stable. The critical value for a soft fibre with a thick rigid cylindrical core can be several orders of magnitudes larger than that for a totally soft fibre (no rigid core), which highlights the strong stabilizing effect of the rigid core on the system. Increasing the relaxation timescale of the viscoelastic material also slows down the growth of disturbance, but has no effect on the critical elastocapillary number. Interestingly, the wavelength of the fastest growing mode is independent of the rigid cylinder radius for the purely elastic case.
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