Linear Stability Analysis of an Electrified Viscoelastic Liquid Jet

Abstract

A linear instability analysis method has been used to investigate the breakup of an electrified viscoelastic liquid jet. The liquid is assumed to be a dilute polymer solution modeled by the linear viscoelastic constitutive equation. As for its electric properties, the liquid is assumed to be of perfect electrical conductivity. The axisymmetric and nonaxisymmetric disturbance wave growth rate has been worked out by solving the dispersion equation of an electrified viscoelastic liquid jet, which was obtained by combining the linear instability model of an electrified Newtonian liquid jet with the linear viscoelastic model. The maximum growth rate and corresponding dominant wavenumbers have been observed. The electrical Euler number, non-Newtonian rheological parameters and some flow parameters have been tested for their influence on the instability of the electrified viscoelastic liquid jet. The results show that the disturbance growth rate of electrified viscoelastic liquid jets is higher than that of Newtonian ones for axisymmetric mode disturbance and almost the same for the nonaxisymmetric mode. The growth rate of the axisymmetric mode is greater than that of the nonaxisymmetric mode for large wavenumbers, and the trend is opposite in the small wavenumber range. The ratio of gas to liquid density, electrical Euler number, and elasticity number can accelerate the breakup of the electrified viscoelastic liquid jet for both modes. The increase of the time constant ratio, zero shear viscosity, and jet radius can decrease the growth rate of the axisymmetric mode; however, their effects on the nonaxisymmetric mode are different. As for the effect of surface tension and jet velocity, there is a critical value. The variation trend is opposite when the surface tension or jet velocity is larger or smaller than the critical value.