We analytically investigate breakup phenomena of a viscous liquid column jet closely placed in a concentric sheath on which a static electric field is imposed.Taking account of a surrounding electric field of the jet, long wave nonlinear equations of the jet radius, velocity, and electric surface charge density are derived.These equations are numerically solved for the initial-boundary condition that a semi-spherical jet initially emanates from a nozzle exit. It is shown that there exist three types of breakup modes – jetting, spraying, and spinning – depending upon the parameters Λ (electric force/fluid inertial force) and Pe (convective current/conductive current). Then, critical curves are found in the Λ-Pe parameter space, across which the mode is transferred from the jetting to the spinning through the spraying with the increase of Λ and/or the decrease of Pe. In the transition from jetting to spraying mode, the produced drop size gradually decreases with the increase of Λ for larger Pe. On the other hand, there is a range of Λ where the drop size discontinuously decreases with increasing Λ for smaller Pe, which may lead to producing a satellite drop.
1. Li, D. and Xia, Y. Electrospinning of nanofibers: reinventing the wheel? Adv. Mater., 2004, 16, 1151–1170.
2. Castellanos, A. Electrohydrodynamics (Castellanos, A., ed.). Springer, Wien, 1998.
3. Lord Rayleigh. On the equilibrium of liquid conducting masses charged with electricity. Phil. Mag., 1882, 14, 184–186.
4. Taylor, G. I. Electrically driven jets. P. Roy. Soc. Lond. A Mat., 1969, 313, 453–475.
5. Cloupeau, M. and Prunet-Foch, B. Electrohydrodynamic spraying functioning modes: critical review. J. Aerosol Sci., 1994, 25, 1021–1036.
6. Fernández de la Mora, J. The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech., 2007, 39, 217–243.
7. Barrero, A. and Loscertales, I. G. Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech., 2007, 39, 89–106.
8. Collins, T. T., Jones, J. J., Harris, M. T., and Basaran, O. A. Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys., 2008, 4, 149–154.
9. Yoshinaga, T. and Iwai, T. Breakup of a liquid column jet in a static electric field. Theoretical and Applies Mechanics Japan, 2013, 62, 219–226.
10. Saville, D. A. Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech., 1997, 29, 27–64.
11. Melcher, J. R. and Warren, E. P. Electrohydrodynamics of a current-carrying semi-insulating jet. J. Fluid Mech., 1971, 47, 127–143.
12. Ganan-Calvo, A. M. On the theory of electrohydrodynamically driven capillary jets. J. Fluid Mech., 1997, 335, 165–188.
13. Hohman, M. M., Shin, M., Rutledge, G., and Brenner, M. P. Electrospinning and electrically forced jets. I. Stability theory. Phys. Fluids, 2001, 13, 2201–2220.
14. Yabe, T. and Aoki, T. A universal solver for hyperbolic equations by cubic-polynomial interpolation. I. One-dimensional solver. Comput. Phys. Commun., 1991, 66, 219–232.