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On Plateau-Rayleigh Instability of a Cylinder of Viscous Liquid

机译：粘性液体圆柱的高原-瑞利不稳定性

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In 1892, in his classical work, L. Rayleigh considered the instability of a cylinder of viscous liquid under capillary force, the so-called Plateau-Rayleigh instability. In this work, in linear approximation, he obtained a dispersion equation describing the increment of this instability as a function of wavelength, the radius of cylinder, the mass density, surface tension, and viscosity of the liquid. Hundreds of authors referred to this work, but none of them used his dispersion equation in its complete form; they used only the asymptotic solutions of his equation for zero or infinitely large viscosities. A reason for this is, probably, that Rayleigh's writing is difficult and his dispersion equation is quite complex. Then, in 1961, S. Chandrasekhar, in his monograph, also considered the stability of a viscous cylindrical jet and obtained his dispersion equation which is also quite complex and differs from the one obtained by Rayleigh. As in the case of Rayleigh's dispersion equation, other works use only the asymptotic solution of Chandrasekhar's equation that corresponds to the case where the viscosity is very large in comparison to inertia. In this article, the author demonstrates that Chandrasekhar's dispersion equation is equivalent to Rayleigh's and then simplifies their dispersion equations to a form which can be easily solved numerically for arbitrary values of viscosity. He also presents a Mathematica code to calculate the maximum increment of the Plateau-Rayleigh instability for given parameters of the jet. To illustrate how the code works, he applies it to a cylindrical jet to estimate its breakup. (C) 2018 Society for Imaging Science and Technology.
机译：1892年，L。Rayleigh在他的经典著作中考虑了在毛细作用力下的粘性液体圆柱体的不稳定性，即所谓的Plateau-Rayleigh不稳定性。在这项工作中，他以线性近似的方式获得了一个色散方程，描述了这种不稳定性随波长，圆柱半径，质量密度，表面张力和液体粘度的变化。数以百计的作者提到了这项工作，但没有一个人完整地使用他的色散方程。他们只将他的方程的渐近解用于零或无限大的粘度。造成这种情况的原因可能是，Rayleigh的写作很困难，并且他的色散方程非常复杂。然后，在1961年，S。Chandrasekhar在他的专着中也考虑了粘性圆柱状射流的稳定性，并得出了他的色散方程，该方程也非常复杂，与Rayleigh获得的色散方程有所不同。与Rayleigh色散方程的情况一样，其他工作仅使用Chandrasekhar方程的渐近解，该解对应于与惯性相比粘度非常大的情况。在本文中，作者证明了Chandrasekhar的色散方程等效于Rayleigh的色散方程，然后将它们的色散方程简化为一种可以轻松数值求解任意粘度值的形式。他还提出了Mathematica代码，以计算给定射流参数时高原-瑞利不稳定性的最大增量。为了说明代码是如何工作的，他将其应用于圆柱射流以估计其破裂。 （C）2018年影像科学与技术学会。

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