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Whipping instability characterization of an electrified visco-capillary jet

Published online by Cambridge University Press:  07 February 2011

GUILLAUME RIBOUX*
Affiliation:
Escuela Técnica Superior de Ingenieros, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Av. de los Descubrimientos s/n, 41092, Sevilla, Spain
ÁLVARO G. MARÍN
Affiliation:
Escuela Técnica Superior de Ingenieros, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Av. de los Descubrimientos s/n, 41092, Sevilla, Spain
IGNACIO G. LOSCERTALES
Affiliation:
Escuela Técnica Superior de Ingenieros Industriales, Universidad de Málaga, C/Pedro Ortiz Ramos, s/n 29071, Málaga, Spain
ANTONIO BARRERO
Affiliation:
Escuela Técnica Superior de Ingenieros, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Av. de los Descubrimientos s/n, 41092, Sevilla, Spain
*
Email address for correspondence: griboux@us.es.

Abstract

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.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

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.CrossRefGoogle ScholarPubMed
Barrero, A. & Loscertales, I. G. 2007 Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89106.CrossRefGoogle Scholar
Bassett, E. B. 1894 Waves and jets in a viscous liquid. Am. J. Math. 16, 93110.CrossRefGoogle Scholar
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-VillarsGoogle Scholar
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquids in cone-jet mode. J. Electrost. 22, 135159.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Doaré, O. & de Langre, E. 2002 The flow-induced instability of long hanging pipes. Eur. J. Mech. A 21, 857867.CrossRefGoogle Scholar
Doshi, J. & Reneker, D. H. 1995 Electrospinning process and applications of electrospun fibers. J. Electrost. 35 (2–3), 151160.CrossRefGoogle Scholar
Fernández De La Mora, J. & Loscertales, I. G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260, 155184.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Higuera, F. J. 2006 Stationary viscosity-dominated electrified capillary jets. J. Fluid Mech. 558, 143152.CrossRefGoogle Scholar
Higuera, F. J. 2010 Numerical computation of the domain of operation of an electrospray of a very viscous liquid. J. Fluid Mech. 648, 3552.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Jaeger, R., Bergshoef, M. M., Battle, C. M., Schönher, H. & Vansco, G. J. 1998 Electrospinning of ultrathin polymer fibers. Macromol. Symp. 127, 141150.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Lemaitre, C., Hémon, P. & de Langre, E. 2005 Instability of a long ribbon hanging in axial air flow. J. Fluid Struct. 20, 913925.CrossRefGoogle Scholar
Li, D. & Xia, Y. 2004 Direct fabrication of composite and ceramic hollow nanofibers by electrospinning. Nano Lett. 4 (5), 933938.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Lister, J. R. & Stone, H. A. 1998 Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10 (11), 27582765.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 (5), 535552.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 295, 16951698.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Marín, A. G., Loscertales, I. G., Márquez, M. & Barrero, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.CrossRefGoogle ScholarPubMed
Mestel, A. J. 1994 Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. Digit. Arch. 274 (1), 93113.CrossRefGoogle Scholar
Mestel, A. J. 1996 Electrohydrodynamic stability of a highly viscous jet. J. Fluid Mech. Digit. Arch. 312 (1), 311326.CrossRefGoogle Scholar
Païdoussis, M. P. 1998 Fluid–Structure Interactions: Slender Structures and Axial Flow, vol. 1. Academic.Google Scholar
Reneker, D. H. & Yarin, A. L. 2008 Electrospinning jets and polymer nanofibers. Polymer 49, 23872425.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502/14.CrossRefGoogle ScholarPubMed
Ruo, A.-C., Chen, F. & Chang, M.-H. 2009 Linear instability of compound jets with nonaxisymmetric disturbances. Phys. Fluids 21 (1), 012101.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Sun, Z., Zussman, E., Yarin, A. L., Wendorff, J. H. & Greiner, A. 2003 Compound core–shell polymer nanofibers. Adv. Mat. 15, 19291936.CrossRefGoogle Scholar
Taylor, G. 1969 Electrically driven jets. Proc. R. Soc. A 313, 453475.Google Scholar
Theron, S. A., Zussman, E. & Yarin, A. L. 2004 Experimental investigation of the governing parameters in the electrospinning of polymer solutions. Polymer 45, 20172030.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413455.CrossRefGoogle Scholar
Yarin, A. L., Koombhongse, S. & Reneker, D. H. 2001 Bending instability in electrospinning of nanofibers. J. Appl. Phys. 89, 30183026.CrossRefGoogle Scholar
Zeleny, J. 1917 Instability of electrified liquid surfaces. Phys. Rev. 10 (1), 16.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar