Weakly nonlinear instability of a viscous liquid jet

Abstract

[EN] A weakly nonlinear stability analysis of an axisymmetric viscous liquid jet is performed. The calculation is based on a small-amplitude perturbation method and restricted to second order. Contrary to the inviscid jet and the planar viscous sheet cases studied by Yuen in 1968 [1] and Yang et al. in 2013 [2], respectively, a part of the solution results from a polynomial approximation of Bessel functions. Results on interface shapes for a small wave number and initial perturbation amplitude, four different Ohnesorge numbers, taking into account the approximate part or not, are used to predict the influence of liquid viscosity on satellite drop formation and evaluate the influence of the approximation. It is observed that the liquid viscosity has a retarding effect on satellite drop formation, in agreement with previous experimental and numerical work. In addition, it is found that the approximate terms can be reasonably ignored, providing a simpler viscous weakly nonlinear model for the description of the first nonlinearity growth in liquid jets. The present work replaces the ILASS 2016 paper [3] by the authors on the same subject.