Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-22T12:06:04.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability of a viscous coflowing jet in a radial electric field

Published online by Cambridge University Press:  17 January 2008

FANG LI ,
XIE-YUAN YIN  and
XIE-ZHEN YIN
FANG LI
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, Chinaxzyin@ustc.edu.cn
XIE-YUAN YIN
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, Chinaxzyin@ustc.edu.cn
XIE-ZHEN YIN
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, Chinaxzyin@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 285 - 311
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Artana, G., Romat, H. & Touchard, G. 1998 Theoretical analysis of linear stability of electrified jets flowing at high velocity inside a coaxial electrode. J. Electrost. 43, 830–100.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Chen, F., Tsaur, J.-Y., Durst, F. & Das, S. K. 2003 On the axisymmetry of annular jet instabilities. J. Fluid Mech. 488, 355–367.CrossRefGoogle Scholar
Chen, J. N. & Lin, S. P. 2002 Instability of an annular jet surrounded by a viscous gas in a pipe. J. Fluid Mech. 450, 235–258.CrossRefGoogle Scholar
Chen, X. P., Jia, L. B., Yin, X. Z., Cheng, J. S. & Lu, J. 2005 Spraying modes in coaxial jet electrospray with outer driving liquid. Phys. Fluids 17, 032101.CrossRefGoogle Scholar
Elhefnawy, A. R. F., Agoor, B. M. H. & Elcoot, A. E. K. 2001 Nonlinear electrohydrodynamic stability of a finitely conducting jet under an axial electric field. Physica A 297, 368–388.CrossRefGoogle Scholar
Elhefnawy, A. R. F., Moatimid, G. M. & Elcoot, A. E. K. 2004 Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges. Z. Angew. Math. Phys. 55, 63–91.Google Scholar
García, F. J., González, H., Ramos, A. & Castellanos, A. 1997 Stability of insulating viscous jets under axial electric fields. J. Electrost. 40&41, 161–166.CrossRefGoogle Scholar
González, H., García, F. J. & Castellanos, A. 2003 Stability analysis of conducting jets under ac radial electric fields for arbitrary viscosity. Phys. Fluids 15, 395–407.CrossRefGoogle Scholar
Higuera, F. J. 2007 Stationary coaxial electrified jet of a dielectric liquid surrounded by a conductive liquid. Phys. Fluids 19, 012102.CrossRefGoogle Scholar
Huebner, A. L. & Chu, H. N. 1971 Instability and breakup of charged liquid jets. J. Fluid Mech. 49, 361–372.CrossRefGoogle Scholar
Li, F., Yin, X. Y. & Yin, X. Z. 2005 Linear instability analysis of an electrified coaxial jet. Phys. Fluids 17, 077104.CrossRefGoogle Scholar
Li, F., Yin, X. Y. & Yin, X. Z. 2006 Instability analysis of a coaxial jet under a radial electric field in the nonequipotential case. Phys. Fluids 18, 037101.CrossRefGoogle Scholar
Lim, D. W. & Redekopp, L. G. 1998 Absolute instability conditions for variable density, swirling jet flows. Eur. J. Mech. B/Fluids 17, 165–185.CrossRefGoogle Scholar
López-herrera, J. M., Barrero, A., López, A., Loscertales, I. G. & Márquez, M. 2003 Coaxial jets generated from electrified Taylor cones. Scaling laws. J. Aerosol Sci. 34, 535–552.CrossRefGoogle Scholar
López-herrera, J. M. & Gañán-calvo, A. M. 2004 A note on charged capillary jet breakup of conducting liquids: experimental validation of a viscous one-dimensional model. J. Fluid Mech. 501, 303–326.CrossRefGoogle Scholar
López-herrera, J. M., Gañán-calvo, A. M. & Perez-saborid, M. 1999 One-dimensional simulation of the breakup of capillary jets of conducting liquids. Application to E.H.D. spraying. J. Aerosol Sci. 30, 895–912.CrossRefGoogle Scholar
López-herrera, J. M., Riesco-chueca, P. & Gañán-calvo, A. M. 2005 Linear stability analysis of axisymmetric perturbations in imperfectly conducting liquid jets. Phys. Fluids 17, 034106.CrossRefGoogle Scholar
Loscertales, I. G., Barrero, A., Guerrero, I., Cortijo, R., Márquez, M. & Gañán-calvo, A. M. 2002 Micro/nano encapsulation via electrified coaxial liquid jets. Science 95, 1695–1698.CrossRefGoogle Scholar
Marin, A. G., Loscertales, I. G., Marquez, M. & Barrero, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.CrossRefGoogle ScholarPubMed
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111–146.CrossRefGoogle Scholar
Mestel, A. J. 1994 Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. 274, 93–113.CrossRefGoogle Scholar
Mestel, A. J. 1996 Electrohydrodynamic stability of a highly viscous jet. J. Fluid Mech. 312, 311–326.CrossRefGoogle Scholar
Meyer, J. & Weihs, D. 1987 Capillary instability of an annular liquid jet. J. Fluid Mech. 179, 531–545.CrossRefGoogle Scholar
Moatimid, G. M. 2003 Non-linear electrorheological instability of two streaming cylindrical fluids. J. Phys. A: Math. Gen. 36, 11343–11365.CrossRefGoogle Scholar
Saville, D. A. 1971 Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet. J. Fluid Mech. 48, 815–827.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.CrossRefGoogle Scholar
Shen, J. & Li, X. 1996 Instability of an annular viscous liquid jet. Acta Mech. 114, 167–183.CrossRefGoogle Scholar
Son, P. H. & Ohba, K. 1998 Theoretical and experimental investigations on instability of an electrically charged liquid jet. Intl J. Multiphase Flow 24, 605–615.CrossRefGoogle Scholar
Turnbull, R. J. 1992 On the instability of an electrostatically sprayed liquid jet. IEEE Trans. Ind. Appl. 28, 1432–1438.CrossRefGoogle Scholar
Turnbull, R. J. 1996 Finite conductivity effects on electrostatically sprayed liquid jets. IEEE Trans. Ind. Appl. 32, 837–843.CrossRefGoogle Scholar
Zakaria, K. 2000 Nonlinear instability of a liquid jet in the presence of a uniform electric field. Fluid Dyn. Res. 26, 405–420.CrossRefGoogle Scholar