Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-28T14:10:42.183Z Has data issue: false hasContentIssue false

Effects of charge relaxation on the electrohydrodynamic breakup of leaky-dielectric jets

Published online by Cambridge University Press:  19 August 2021

Qichun Nie
Affiliation:
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Fang Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Qianli Ma
Affiliation:
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Haisheng Fang*
Affiliation:
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Zhouping Yin*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
*
Email addresses for correspondence: hafang@hust.edu.cn, yinzhp@hust.edu.cn
Email addresses for correspondence: hafang@hust.edu.cn, yinzhp@hust.edu.cn

Abstract

The breakup process of a charged, leaky-dielectric jet subjected to an axial perturbation is computationally analysed from the perspectives of linear and nonlinear dynamics using the arbitrary Lagrangian–Eulerian technique. The linear dynamics of the leaky-dielectric jet is quantitatively predicted by the dispersion relation from the linear stability analysis. Regarding the nonlinear dynamics, it is found that the charge relaxation is responsible for the radial compression of satellite droplets, which is validated by experiments. Two types of charge relaxations, namely, ohmic conduction and surface charge convection, define the pinching process into three breakup modes, i.e. ligament pinching, end pinching and transition pinching. In the ligament-pinching mode, the ohmic conduction dominates the jet breakup since the charge relaxes to the jet ligament instantaneously. In contrast, the surface charge convection takes effect in the end-pinching mode since the surface charge is convected to the jet end via fluid flow. When the ohmic conduction is comparable to the surface charge convection, the breakup occurs simultaneously at the end and the ligament. Finally, the influences of the perturbed wavenumber, the electric field intensity and the viscosity on the breakup mode and the local dynamics at pinch-off are comprehensively discussed.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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

Ambravaneswaran, B., Phillips, S.D. & Basaran, O.A. 2000 Theoretical analysis of a dripping faucet. Phys. Rev. Lett. 85, 53325335.CrossRefGoogle ScholarPubMed
Ambravaneswaran, B., Subramani, H.J., Phillips, S.D. & Basaran, O.A. 2004 Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.CrossRefGoogle Scholar
Artana, G., Romat, H. & Touchard, G. 1998 Theoretical analysis of linear stability of electrified jets flowing at high velocity inside a coaxial electrode. J. Electrostat. 43, 83100.CrossRefGoogle Scholar
Ashgriz, N. & Mashayek, F. 1995 Temporal analysis of capillary jet breakup. J. Fluid Mech. 291, 163190.CrossRefGoogle Scholar
Basset, A.B. 1894 Waves and jets in a viscous liquid. Am. J. Maths 16, 93.CrossRefGoogle Scholar
Bhardwaj, N. & Kundu, S.C. 2010 Electrospinning: a fascinating fiber fabrication technique. Biotechnol. Adv. 28, 325347.CrossRefGoogle ScholarPubMed
Brown, P.N., Hindmarsh, A.C. & Petzold, L.R. 1994 Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 14671488.CrossRefGoogle Scholar
Burton, J.C. & Taborek, P. 2011 Simulations of coulombic fission of charged inviscid drops. Phys. Rev. Lett. 106, 14.CrossRefGoogle ScholarPubMed
Collins, R.T., Harris, M.T. & Basaran, O.A. 2007 Breakup of electrified jets. J. Fluid Mech. 588, 75129.CrossRefGoogle Scholar
Collins, R.T., Jones, J.J., Harris, M.T. & Basaran, O.A. 2008 Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4, 149154.CrossRefGoogle Scholar
COMSOL Inc 2019 COMSOL multiphysics reference manual. COMSOL.Google Scholar
Conroy, D.T., Matar, O.K., Craster, R.V. & Papageorgiou, D.T. 2011 Breakup of an electrified viscous thread with charged surfactants. Phys. Fluids 23, 022103.CrossRefGoogle Scholar
Donea, J., Giuliani, S. & Halleux, J.P. 1982 An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput. Methods Appl. Mech. Engng 33, 689723.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865930.CrossRefGoogle Scholar
Eggers, J. & Dupont, T.F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205221.CrossRefGoogle Scholar
Eggers, J. & Fontelos, M.A. 2015 Singularities: Formation, Structure, and Propagation. Cambridge University Press.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Fernández de la Mora, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39, 217243.CrossRefGoogle Scholar
Gañán-Calvo, A.M., López-Herrera, J.M., Herrada, M.A., Ramos, A. & Montanero, J.M. 2018 Review on the physics of electrospray: from electrokinetics to the operating conditions of single and coaxial Taylor cone-jets, and AC electrospray. J. Aerosol Sci. 125, 3256.CrossRefGoogle Scholar
Giglio, E., Rangama, J., Guillous, S. & Le Cornu, T. 2020 Influence of the viscosity and charge mobility on the shape deformation of critically charged droplets. Phys. Rev. E 101, 013105.CrossRefGoogle ScholarPubMed
Ha, J.-W. & Yang, S.-M. 2000 Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field. J. Fluid Mech. 405, 131156.CrossRefGoogle Scholar
Huebner, A.L. & Chu, H.N. 1971 Instability and breakup of charged liquid jets. J. Fluid Mech. 49, 361372.CrossRefGoogle Scholar
Jaworek, A., Sobczyk, A.T. & Krupa, A. 2018 Electrospray application to powder production and surface coating. J. Aerosol Sci. 125, 5792.CrossRefGoogle Scholar
Lanauze, J.A., Walker, L.M. & Khair, A.S. 2015 Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774, 245266.CrossRefGoogle Scholar
Li, F., Ke, S., Xu, S., Yin, X.X. & Yin, X.X. 2020 Radial deformation and disintegration of an electrified liquid jet. Phys. Fluids 32, 021701.Google Scholar
Li, F., Ke, S.Y., Yin, X.Y. & Yin, X.Z. 2019 Effect of finite conductivity on the nonlinear behaviour of an electrically charged viscoelastic liquid jet. J. Fluid Mech. 874, 537.CrossRefGoogle Scholar
Li, Y. & Sprittles, J.E. 2016 Capillary breakup of a liquid bridge: identifying regimes and transitions. J. Fluid Mech. 797, 2959.CrossRefGoogle Scholar
López-Herrera, J.M. & Ganan-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, 303326.CrossRefGoogle Scholar
López-Herrera, J.M., Gañán-Calvo, A.M. & Perez-Saborid, M. 1999 One-dimensional simulation of the breakup of capillary jet of conducting liquids: application to E.H.D. spraying. J. Aerosol Sci. 30, 895912.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
Martínez-Calvo, A., Rivero-Rodríguez, J., Scheid, B. & Sevilla, A. 2020 Natural break-up and satellite formation regimes of surfactant-laden liquid threads. J. Fluid Mech. 883, A35.CrossRefGoogle Scholar
Melcher, J.R. & Taylor, G.I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111146.CrossRefGoogle Scholar
Mestel, A.J. 1994 Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. 274, 93113.CrossRefGoogle Scholar
Mestel, A.J. 1996 Electrohydrodynamic stability of a highly viscous jet. J. Fluid Mech. 312, 311326.CrossRefGoogle Scholar
Montanero, J.M. & Gañán-Calvo, A.M. 2020 Dripping, jetting and tip streaming. Rep. Prog. Phys. 83, 097001.CrossRefGoogle ScholarPubMed
Onses, M.S., Sutanto, E., Ferreira, P.M., Alleyne, A.G. & Rogers, J.A. 2015 Mechanisms, capabilities, and applications of high-resolution electrohydrodynamic jet printing. Small 11, 42374266.CrossRefGoogle Scholar
Papageorgiou, D.T. 1995 On the breakup of viscous liquid threads. Phys. Fluids 7, 15291544.CrossRefGoogle Scholar
Plateau, J. 1857 I. Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity. Third series. Lond. Edinb. Dublin Philos. Mag. J. Sci. 14, 122.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 14, 413.CrossRefGoogle Scholar
Rayleigh, Lord 1882 On the equilibrium of liquid conducting masses charged with electricity. Lond. Edinb. Dublin Philos. Mag. J. Sci. 14, 184186.CrossRefGoogle Scholar
Rivero-Rodriguez, J. & Scheid, B. 2018 Bubble dynamics in microchannels: inertial and capillary migration forces. J. Fluid Mech. 842, 215247.CrossRefGoogle Scholar
Rosell-Llompart, J., Grifoll, J. & Loscertales, I.G. 2018 Electrosprays in the cone-jet mode: from Taylor cone formation to spray development. J. Aerosol Sci. 125, 231.CrossRefGoogle Scholar
Sahay, R., Teo, C.J. & Chew, Y.T. 2013 New correlation formulae for the straight section of the electrospun jet from a polymer drop. J. Fluid Mech. 735, 150175.CrossRefGoogle Scholar
Saville, D.A. 1971 a Stability of electrically charged viscous cylinders. Phys. Fluids 14, 10951099.CrossRefGoogle Scholar
Saville, D.A. 1971 b Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet. J. Fluid Mech. 48, 815827.CrossRefGoogle Scholar
Saville, D.A. 1997 Electrohydrodynamics:the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 2764.CrossRefGoogle Scholar
Sengupta, R., Walker, L.M. & Khair, A.S. 2017 The role of surface charge convection in the electrohydrodynamics and breakup of prolate drops. J. Fluid Mech. 833, 2953.CrossRefGoogle Scholar
Setiawan, E.R. & Heister, S.D. 1997 Nonlinear modeling of an infinite electrified jet. J. Electrostat. 42, 243257.CrossRefGoogle Scholar
Wang, Q. 2012 Breakup of a poorly conducting liquid thread subject to a radial electric field at zero Reynolds number. Phys. Fluids 24, 102102.CrossRefGoogle Scholar
Wang, Q. & Papageorgiou, D.T. 2011 Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities. J. Fluid Mech. 683, 2756.CrossRefGoogle Scholar
Yang, W., Duan, H., Li, C. & Deng, W. 2014 a Crossover of varicose and whipping instabilities in electrified microjets. Phys. Rev. Lett. 112, 054501.CrossRefGoogle ScholarPubMed
Yang, K., Hong, F. & Cheng, P. 2014 b A fully coupled numerical simulation of sessile droplet evaporation using arbitrary Lagrangian-Eulerian formulation. Intl J. Heat Mass Transfer 70, 409420.CrossRefGoogle Scholar
Yin, Z.P., Huang, Y.A., Bu, N.B., Wang, X.M. & Xiong, Y.L. 2010 Inkjet printing for flexible electronics: materials, processes and equipments. Chinese Sci. Bull. 55, 33833407.CrossRefGoogle Scholar
Yuen, M.C. 1968 Non-linear capillary instability of a liquid jet. J. Fluid Mech. 33, 151163.CrossRefGoogle Scholar
Zienkiewicz, O.C., Taylor, R.L., & Zhu, J.Z. 2013 Shape functions, derivatives, and integration. In The Finite Element Method: Its Basis and Fundamentals, pp. 151–209. Elsevier.CrossRefGoogle Scholar