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Whipping instability characterization of an electrified visco-capillary jet



The charged liquid micro-jet issued from a Taylor cone may develop a special type of non-axisymmetric instability, usually referred to in the literature as a whipping mode. This instability usually manifests itself as a series of fast and violent lashes of the charged jet, which makes its characterization in the laboratory difficult. Recently, we have found that this instability may also develop when the host medium surrounding the Taylor cone and the jet is a dielectric liquid instead of air. When the oscillations of the jet occur inside a dielectric liquid, their frequency and amplitude are much lower than those of the oscillations taking place in air. Taking advantage of this fact, we have performed a detailed experimental characterization of the whipping instability of a charged micro-jet within a dielectric liquid by recording the jet motion with a high-speed camera. Appropriate image processing yields the frequency and wavelength, among the other important characteristics, of the jet whipping as a function of the governing parameters of the experimental set-up (flow rate and applied electric field) and liquid properties. Alternatively, the results can be also written as a function of three dimensionless numbers: the capillary and electrical Bond numbers and the ratio between an electrical relaxation and residence time.


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Barrero, A., López-Herrera, J. M., Boucard, A., Loscertales, I. G. & Márquez, M. 2004 Steady cone-jet electrosprays in liquid insulator baths. J. Colloid Interface Sci. 272, 104108.
Barrero, A. & Loscertales, I. G. 2007 Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89106.
Bassett, E. B. 1894 Waves and jets in a viscous liquid. Am. J. Math. 16, 93110.
Bourrières, F. J. 1939 Sur un Phénomène d'Oscillation Auto-Entretenue en Mécanique des Fluides Réels, Publications Scientifiques et Techniques du Ministère de l'Air, vol. 147. Gauthier-Villars
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquids in cone-jet mode. J. Electrost. 22, 135159.
Díaz, J. E., Barrero, A., Márquez, M. & Loscertales, I. G. 2006 Controlled encapsulation of hydrophobic liquids in hydrophilic polymer nanofibers by co-electrospinning hydrophilic polymer nanofibers by co-electrospinning. Adv. Funct. Mater. 16, 21102116.
Doaré, O. & de Langre, E. 2002 The flow-induced instability of long hanging pipes. Eur. J. Mech. A 21, 857867.
Doshi, J. & Reneker, D. H. 1995 Electrospinning process and applications of electrospun fibers. J. Electrost. 35 (2–3), 151160.
Fernández De La Mora, J. & Loscertales, I. G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260, 155184.
Fridrikh, S. V., Yu, J. H., Brenner, M. P. & Rutledge, G. C. 2003 Controlling the fiber diameter during electrospinning. Phys. Rev. Lett. 90 (14), 144502.
Fridrikh, S. V., Yu, J. H., Brenner, M. P. & Rutledge, G. C. 2006 Nonlinear whipping behaviour of electrified fluid jets. In Polymeric Nanofibers (ed. Reneker, D. H. & Fong, H.), American Chemical Society Symposium Series, vol. 918, pp. 3655. American Chemical Society.
Gañán-Calvo, A. M., Dávila, J. & Barrero, A. 1997 Current and droplet size in the electrospraying of liquids: scaling laws. J. Aerosol Sci. 28 (2), 249275.
Hartman, R. P. A., Brunner, D. J., Camelot, D. M. A., Marijnissen, J. C. M. & Scarlett, B. 2000 Jet break-up in electrohydrodynamic atomization in the cone-jet mode. J. Aerosol Sci. 31 (1), 6595.
Higuera, F. J. 2006 Stationary viscosity-dominated electrified capillary jets. J. Fluid Mech. 558, 143152.
Higuera, F. J. 2010 Numerical computation of the domain of operation of an electrospray of a very viscous liquid. J. Fluid Mech. 648, 3552.
Hohman, M. M., Shin, M., Rutledge, G. & Brenner, M. P. 2001 a Electrospinning and electrically forced jets. Part I. Stability theory. Phys. Fluids 13 (8), 22012220.
Hohman, M. M., Shin, M., Rutledge, G. & Brenner, M. P. 2001 b Electrospinning and electrically forced jets. Part II. Applications. Phys. Fluids 13 (8), 22212236.
Jaeger, R., Bergshoef, M. M., Battle, C. M., Schönher, H. & Vansco, G. J. 1998 Electrospinning of ultrathin polymer fibers. Macromol. Symp. 127, 141150.
Lallave, M., Bedia, J., Ruiz-Rosas, R., Rodríguez-Mirasol, J., Cordero, T., Otero, J. C., Marquez, M., Barrero, A. & Loscertales, I. G. 2007 Filled and hollow carbon nanofibers by coaxial electrospinning of Alcell lignin without binder polymers. Adv. Mater. 19, 42924296.
de Langre, E., Païdoussis, M. P., Doaré, Olivier & Modarres-Sadeghi, Y. 2007 Flutter of long flexible cylinders in axial flow. J. Fluid Mech. 571, 371389.
Larsen, G., Velarde-Ortiz, R., Minchow, K., Barrero, A. & Loscertales, I. G. 2003 A method for making inorganic and hybrid (organic/inorganic) fibers and vesicles with diameters in the submicrometer and micrometer range via sol-gel chemistry and electrically forced liquid jets. J. Am. Chem. Soc. 125, 11541155.
Lemaitre, C., Hémon, P. & de Langre, E. 2005 Instability of a long ribbon hanging in axial air flow. J. Fluid Struct. 20, 913925.
Li, D. & Xia, Y. 2004 Direct fabrication of composite and ceramic hollow nanofibers by electrospinning. Nano Lett. 4 (5), 933938.
Li, F., Yin, X.-Y. & Yin, X.-Z. 2008 Instability of a viscous coflowing jet in a radial electric field. J. Fluid Mech. 596, 285311.
Li, F., Yin, X.-Y. & Yin, X.-Z. 2009 Axisymmetric and non-axisymmetric instability of an electrified viscous coaxial jet. J. Fluid Mech. 632, 199225.
Lister, J. R. & Stone, H. A. 1998 Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10 (11), 27582765.
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 (5), 535552.
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 295, 16951698.
Loscertales, I. G., Barrero, A., Márquez, M., Spretz, R., Velarde-Ortiz, R. & Larsen, G. 2004 Electrically forced coaxial nanojets for one-step hollow nanofiber design. J. Am. Chem. Soc. 126, 53765377.
Marín, A. G., Loscertales, I. G., Márquez, M. & Barrero, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.
Mestel, A. J. 1994 Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. Digit. Arch. 274 (1), 93113.
Mestel, A. J. 1996 Electrohydrodynamic stability of a highly viscous jet. J. Fluid Mech. Digit. Arch. 312 (1), 311326.
Païdoussis, M. P. 1998 Fluid–Structure Interactions: Slender Structures and Axial Flow, vol. 1. Academic.
Reneker, D. H. & Yarin, A. L. 2008 Electrospinning jets and polymer nanofibers. Polymer 49, 23872425.
Reneker, D. H., Yarin, A. L., Fong, H. & Koombhongse, S. 2000 Bending instability of electrically charged liquid jets of polymer solutions in electrospinning. J. Appl. Phys. 87 (9), 45314547.
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502/14.
Ruo, A.-C., Chen, F. & Chang, M.-H. 2009 Linear instability of compound jets with nonaxisymmetric disturbances. Phys. Fluids 21 (1), 012101.
Shin, Y. M., Hohman, M. M., Brenner, M. P. & Rutledge, G. C. 2001 Experimental characterization of electrospinning: the electrically forced jet and instabilities. Polymer 42, 99559967.
Sun, Z., Zussman, E., Yarin, A. L., Wendorff, J. H. & Greiner, A. 2003 Compound core–shell polymer nanofibers. Adv. Mat. 15, 19291936.
Taylor, G. 1969 Electrically driven jets. Proc. R. Soc. A 313, 453475.
Theron, S. A., Zussman, E. & Yarin, A. L. 2004 Experimental investigation of the governing parameters in the electrospinning of polymer solutions. Polymer 45, 20172030.
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413455.
Yarin, A. L., Koombhongse, S. & Reneker, D. H. 2001 Bending instability in electrospinning of nanofibers. J. Appl. Phys. 89, 30183026.
Zeleny, J. 1917 Instability of electrified liquid surfaces. Phys. Rev. 10 (1), 16.
Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two dimensional wind. Nature 408, 835839.
Zhang, X. & Basaran, O. A. 1996 Dynamics of drop formation from a capillary in the presence of an electric field. J. Fluid Mech. 326, 239263.
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Whipping instability characterization of an electrified visco-capillary jet



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