2017/12/19 by Leonid Pekker, Pekker, Leonid
Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Fluid dynamics and aerodynamics studies #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.1712.07069
openalex publication_date 2017/12/19 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In 1982, in his classical work, L. Rayleigh considered the instability of a\ncylinder of viscous liquid under capillary force, the so-called\nPlateau-Rayleigh instability. In this work, in linear approximation, he\nobtained a dispersion equation describing the increment of this instability as\na function of wavelength, the radius of cylinder, the mass density, surface\ntension, and viscosity of the liquid. Hundreds of authors referred to this\nwork, but none of them used his dispersion equation in its complete form; they\nused only the asymptotic solutions of his equation for zero and infinitely\nlarge viscousities. A reason for this is, probably, that Rayleigh's writing is\nvery difficult and his dispersion equation is quite complex. Then, in 1961, S\nChandrasekhar, in his monograph, also considered the stability of a viscous\ncylindrical jet and obtained his dispersion equation which is also quite\ncomplex and differs from the one obtained by Rayleigh. As in the case of\nRayleigh's dispersion equation, other works use only the asymptotic solution of\nChandrasekhar's equation that corresponds to the case where the viscosity is\nvery large in comparison to inertia. In this paper, I demonstrate that\nChandrasekhar's dispersion equation is equivalent to Rayleigh's and then\nsimplify their dispersion equations to a form which can be easily solved\nnumerically for arbitrary values of viscosity. I also present Mathematica code\nto calculate the maximum increment of the Plateau-Rayleigh instability for\ngiven parameters of the jet. To illustrate how the code works, I apply it to a\ncylindrical jet to estimate its breakup.\n