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Multiphase Flows

Linear Stability Analysis of an Electrified Viscoelastic Liquid Jet

[+] Author and Article Information
Li-jun Yang1

 School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, China, 100191yanglijun@buaa.edu.cn

Yu-xin Liu, Qing-fei Fu

 School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, China, 100191

1

Corresponding author.

J. Fluids Eng 134(7), 071303 (Jun 21, 2012) (13 pages) doi:10.1115/1.4006913 History: Received March 08, 2012; Revised May 15, 2012; Published June 21, 2012; Online June 21, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of liquid jet

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Figure 2

Variation of growth rate with wavenumber. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, σ = 0.03 kg/s2, Uz = 1 m/s, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, and λ1 = λ2 = 0 for Newtonian fluid.

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Figure 3

Effect of time constant ratio on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid μ0 = 0.008 kg/m·s, Uz = 1 m/s, σ = 0.03 kg/s2, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, λ1 = 0.01, and λ1 = λ2 = 0 for Newtonian fluid.

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Figure 4

Effect of elasticity number on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid μ0 = 0.008 kg/m·s, Uz = 1 m/s, σ = 0.03 kg/s2, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, λ2 = 0.001, and λ1 = λ2 = 0 for Newtonian fluid.

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Figure 5

Effect of gas-to-liquid density ratio on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, σ = 0.03 kg/s2, Uz = 1 m/s, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, and Q = 0.001, λ1 = λ2 = 0 for Newtonian fluid.

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Figure 6

Effect of electrical Euler number on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, σ = 0.03 kg/s2, Uz = 1 m/s, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, and Eu = 0.1, λ1 = λ2 = 0 for Newtonian fluid.

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Figure 7

Effect of surface tension on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, Uz = 1 m/s, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, and σ = 0.03 kg/s2, λ1 = λ2 = 0 for Newtonian fluid.

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Figure 8

Effect of jet velocity on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, σ = 0.03 kg/s2, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, and Uz = 1 m/s, λ1 = λ2 = 0 for Newtonian fluid.

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Figure 9

Effect of zero shear viscosity on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, σ = 0.03 kg/s2, Uz = 1 m/s, ρg = 1.2 kg/m3, R0 = 20 mm, R = 0.2 mm, ρl = 1000 kg/m3, V0 = 4000 V, and μ0 = 0.008 kg/m·s, λ1 = λ2 = 0 for Newtonian fluid.

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Figure 10

Effect of jet radius on the stability of electrified viscoelastic liquid jets. For viscoelastic fluid λ1 = 0.01, λ2 = 0.001, μ0 = 0.008 kg/m·s, σ = 0.03 kg/s2, Uz = 1 m/s, ρg = 1.2 kg/m3, R0 = 20 mm, ρl = 1000 kg/m3, V0 = 4000 V, and R = 0.2 mm, λ1 = λ2 = 0 for Newtonian fluid.

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