3-D and 1-D dynamics of slender liquid jets: linear analysis with electric field and accuracy of 1-D models near the breakup

Abstract

In a previous paper [Phys. Fluids, vol. 6, 2676 (1994)], the authors derived four 1-D models (Lee, Cosserat, averaged, and parabolic models) for slender axisymmetric liquid jets from the Navier-Stokes equations. The error of these 1-D models was calculated for small perturbations, in the absence of electric field. Here, we extend the linear error analysis to both perfectly insulating liquid jets in a tangential electric field and perfectly conducting liquid jets in a radial electric field. The accuracy of these models for studying the breakup, when nonlinear effects are no longer negligible, is also tested in the absence of electric field. A comparison of numerical 3-D solutions with results from 1-D models is made. A formulation of the energy conservation in 1-D models allows identifying and correcting a numerical instability of the averaged model near the breakup. It also explains why the Cosserat model overestimates the breakup time for moderate or large viscosity. Good agreement between 1-D and 3-D numerical results is found.