Abstract
Nonlinear instability in electrically charged jets is studied using the governing electro-hydrodynamic equations describing stretching and thinning of a liquid jet. A jet flow system subject to both space and time evolving disturbances is considered. At the linear stage, the Rayleigh and conducting jet flow instability modes are uncovered. Nonlinear instability in the flow is explored via triad resonant waves which uncover fa- vorable operating modes not previously detected in the linear study of the problem. In particular, the jet radius is significantly reduced, and the electric field of the jet is properly oriented under the nonlinear study. It is found that taking into account the resonance triad modes provides a better mathematical description of a jet that stretches and thins due to tangential electric field effects. Both linear and nonlinear instability results in the jet flow system are presented and discussed.
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References
Melcher, J. R. and Taylor, G. I. Electrically driven jets. Proceedings of the Royal Society London A, 313, 453–475 (1969)
Melcher, J. R. and Taylor, G. I. Electro-hydrodynamics: a review of the interfacial shear stresses. Annual Review of Fluid Mechanics, 1, 111–146 (1969)
Hohman, M. M., Shin, M., Rutledge, G., and Brenner, M. P. jets, I, stability theory. Physics of Fluids, 13(8), 2201–2220 (2001)
Hohman, M. M., Shin, M., Rutledge, G., and Brenner, M. P. Electrospinning and electrically forced jets,II, applications. Physics of Fluids, 13(8), 2221–2236 (2001)
Schlichting, H. Boundary Layer Theory, 7th ed., McGraw-Hill, New York, 100–145 (1979)
Shkadov, V. Y. and Shutov, A. A. Disintegration of a charged viscous jet in a high electric field. Fluid Dynamics Research, 28, 23–29 (2001)
Tam, C. K. W. and Thies, A. T. Instability of rectangular jet. Journal of Fluid Mechanics, 248, 425–448 (1993)
Healey, J. J. Inviscid axisymmetric absolute instability of swirling jets. Journal of Fluid Mechanics, 613, 1–33 (2008)
Michalke, A. On spatially growing disturbances in an inviscid shear layer. Journal of Fluid Mechanics, 23, 521–544 (1965)
Feng, J. J. The stretching of an electrified non-Newtonian jet: a model for electrospinning. Physics of Fluids, 14(11), 3912–3926 (2002)
Baily, A. G. Electro-Static Spraying of Liquid, Wiley, New York (1988)
Reneker, D. H. and Yarin, A. L. H. Bending instability of electrically charged liquid jets of polymer solutions in electrospinning. Journal of Applied Physics, 87, 4531–4547 (2000)
Li, D. and Xia, Y. Direct fabrication of composite and ceramic hollow nanofibers by electrospinning. Nano Letters, 4, 933–938 (2004)
Yu, J. H., Fridrikh, S. V., and Rutledge, G. C. Production of sub-micrometer diameter fibers by two-fluid electrospinning. Advanced Materials, 16, 1562–1566 (2004)
Orizaga, S., Riahi, D. N., and Hou, L. S. Nonlinear spatio-temporal instability regime for electrically forced viscous jets. International Journal of Nonlinear Mechanics, 67, 218–230 (2014)
Riahi, D. N. On spatial instability of electrically forced axisymmetric jets with variable applied field. Applied Mathematical Modelling, 33, 3546–3552 (2009)
Orizaga, S. and Riahi, D. N. Resonant instability and nonlinear wave interactions in electrically forced jets. Nonlinear Analysis: Real World Applications, 12, 1300–1313 (2011)
Orizaga, S. and Riahi, D. N. On combined spatial and temporal instabilities of electrically driven jets with constant or variable applied field. Journal of Theoretical and Applied Mechanics, 50(1), 301–319 (2012)
Orizaga, S. and Riahi, D. N. Spatial instability of electrically driven jets with finite conductivity and under constant or variable applied field. Applications and Applied Mathematics an International Journal, 4(2), 249–262 (2009)
Rott, N. A multiple pendulum for the demonstration of non-linear coupling. Zeitschrift für Angewandte Mathematik und Physik, 21, 570–582 (1970)
El-Had, N. M. Evolution of resonant wave triads in three-dimensional boundary layers. Physics of Fluids A, 1, 549–561 (1989)
Drazin, P. G. and Reid, W. H. Hydrodynamic Stability, Cambridge University Press, Cambridge (1981)
Vonderwell, M. P. and Riahi, D. N. Resonant instability mode triads in the compressible boundary layer flow over a swept wing. International Journal of Engineering Science, 36, 599–624 (1998)
Craik, A. D. D. Wave Interactions and Fluid Flows, Cambridge University Press, Cambridge (1985)
Craik, A. D. D. Nonlinear resonant instability in boundary layers. Journal of Fluid Mechanics, 50, 393–413 (1971)
Stakgold, I. Greens Functions and Boundary Value Problems, 2nd ed., Wiley, New York (1998)
Huerre, P. and Monkewitz, P. A. Local and global instabilities in spatially developing flows. Annual Review of Fluid Mechanics, 22, 473–537 (1990)
Soderberg, D. L. Absolute and convective instability of a relaxational plane liquid jet. Journal of Fluid Mechanics, 439, 89–119 (2003)
Orizaga, S. and Riahi, D. N. On nonlinear spatio-temporal instability regime for electrically forced viscous jets [Errata Corrige]. International Journal of Non-Linear Mechanics, 74, 38–39 (2015)
Riahi, D. N. On spatial instability of an electrically forced non-axisymmetric jet with curved centerline. Applied Mathematical Modelling, 35, 1124–1133 (2011)
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Project supported by the National Science Foundation of U. S. A. (No. DMS-0946431)
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Orizaga, S., Riahi, D.N. Triad resonant wave interactions in electrically charged jets. Appl. Math. Mech.-Engl. Ed. 38, 1127–1148 (2017). https://doi.org/10.1007/s10483-017-2229-9
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DOI: https://doi.org/10.1007/s10483-017-2229-9