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Effect of finite conductivity on the nonlinear behaviour of an electrically charged viscoelastic liquid jet

Published online by Cambridge University Press:  03 July 2019

Fang Li Open the ORCID record for Fang Li [Opens in a new window] ,
Shi-You Ke ,
Xie-Yuan Yin  and
Xie-Zhen Yin
Fang Li*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Shi-You Ke
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Xie-Yuan Yin
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Xie-Zhen Yin
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
*
†Email address for correspondence: [email protected]
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Abstract

In this paper a one-dimensional numerical study on the nonlinear behaviour of an electrically charged jet of Oldroyd-B viscoelastic, Taylor–Melcher leaky dielectric liquid is carried out. The effect of surface charge level, axial wavenumber and finite conductivity on the nonlinear evolution of the jet is investigated. Different structures including beads-on-a-string with/without satellite droplets, quasi-spikes and spikes are detected, and their domains in the plane of the non-dimensional axial wavenumber and the electrical Bond number are illustrated. The underlying mechanisms in the formation of the structures are examined. It is found that tangential electrostatic force plays a key role in the formation of a quasi-spike structure. Decreasing liquid conductivity may lead to a decrease in the size of satellite droplets or even the complete removal of them from a beads-on-a-string structure, induce the transition from a beads-on-a-string to a quasi-spike structure or postpone the appearance of a spike. On the other hand, finite conductivity has little influence on filament thinning in a beads-on-a-string structure, owing to the fact that the electrostatic forces are of secondary importance compared with the capillary force. The difference between the finite conductivity, large conductivity and other cases is elucidated. An experiment is carried out to observe spike structures.

JFM classification

Wakes/Jets: Jets Instability: Nonlinear instability Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 5 - 37
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Copyright
© 2019 Cambridge University Press 

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References

Alsharif, A. M., Uddin, J. & Afzaal, M. F. 2015 Instability of viscoelastic curved liquid jets. Appl. Math. Model. 39, 3924–3938.Google Scholar
Ambravaneswaran, B., Wilkes, E. D. & Basaran, O. A. 2002 Drop formation from a capillary cube: comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops. Phys. Fluids 14, 2606–2621.Google Scholar
Anna, S. L. & McKinley, G. H. 2001 Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol. 45, 115–138.Google Scholar
Ardekani, A. M., Sharma, V. & McKinley, G. H. 2010 Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J. Fluid Mech. 665, 46–56.Google Scholar
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.Google Scholar
Bazilevskii, A. V. & Rozhkov, A. N. 2014 Dynamics of capillary breakup of elastic jets. Fluid Dyn. 49, 827–843.Google Scholar
Bhat, P. P., Appathurai, S., Harris, M. T. & Basaran, O. A. 2012 On self-similarity in the drop-filament corner region formed during pinch-off of viscoelastic fluid threads. Phys. Fluids 24, 083101.Google Scholar
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6, 625–631.Google Scholar
Bousfield, D. W., Keunings, R., Marrucci, G. & Denn, M. M. 1986 Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. J. Non-Newtonian Fluid Mech. 1986, 79–97.Google Scholar
Brenn, G. & Teichtmeister, S. 2013 Linear shape oscillations and polymeric time scales of viscoelastic drops. J. Fluid Mech. 733, 504–527.Google Scholar
Chang, H.-C., Demekhin, E. A. & Kalaidin, E. 1999 Iterated stretching of viscoelastic jets. Phys. Fluids 11, 1717–1737.Google Scholar
Christanti, Y. & Walker, L. M. 2001 Surface tension driven jet break up of strain-hardening polymer solutions. J. Non-Newtonian Fluid Mech. 100, 9–26.Google Scholar
Christanti, Y. & Walker, L. M. 2002 Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J. Rheol. 46, 733–748.Google Scholar
Clasen, C., Bico, J., Entov, V. M. & McKinley, G. H. 2009 ‘Gobbling drops’: the jetting-dripping transition in flows of polymer solutions. J. Fluid Mech. 636, 5–40.Google Scholar
Clasen, C., Eggers, J., Fontelos, M. A., Li, J. & McKinley, G. H. 2006 The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283–308.Google Scholar
Collins, R. T., Harris, M. T. & Basaran, O. A. 2007 Breakup of electrified jets. J. Fluid Mech. 588, 75–129.Google Scholar
Deblais, A., Velikov, K. P. & Bonn, D. 2018 Pearling instabilities of a viscoelastic thread. Phys. Rev. Lett. 120, 194501.Google Scholar
Eda, G. & Shivkumar, S. 2007 Bead-to-fiber transition in electrospun polystyrene. J. Appl. Polym. Sci. 106, 475–487.Google Scholar
Eggers, J. 2014 Instability of a polymeric thread. Phys. Fluids 26, 033106.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Elcoot, A. E. K. 2007 Nonlinear instability of charged liquid jets: effect of interfacial charge relaxation. Phys. A 375, 411–428.Google Scholar
Entov, V. M. & Hinch, E. J. 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newtonian Fluid Mech. 72, 31–53.Google Scholar
Feng, J. J. 2003 Streching of a straight electrically charged viscoelastic jet. J. Non-Newtonian Fluid Mech. 116, 55–70.Google Scholar
Fontelos, M. A. & Li, J. 2004 On the evolution and rupture of filaments in Giesekus and FENE models. J. Non-Newtonian Fluid Mech. 118, 1–16.Google Scholar
Gañán-Calvo, A. M., López-Herrere, 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. Aero. Sci. 125, 32–56.Google Scholar
Greiciunas, E., Wong, J., Gorbatenko, I., Hall, J., Wilson, M. C. T., Kapur, N., Harlen, O. G., Vadillo, D. & Threlfall-Holmes, P. 2017 Design and operation of a Rayleigh Ohnesorge jetting extensinoal rheometer (ROJER) to study extensional properties of low viscosity polymer solutions. J. Rheol. 61, 467–476.Google Scholar
Gupta, K. & Chokshi, P. 2015 Weakly nonlinear stability analysis of polymer fibre spinning. J. Fluid Mech. 776, 268–289.Google Scholar
Higuera, F. J. 2003 Flow rate and electric current emitted by a Taylor cone. J. Fluid Mech. 484, 303–327.Google Scholar
Higuera, F. J. 2006 Stationary viscosity-dominated electrified capillary jets. J. Fluid Mech. 558, 143–152.Google Scholar
Ismail, N., Maksoud, F. J., Ghaddar, N., Ghali, K. & Tehrani-Bagha, A. 2016 Simplified modeling of the electrospinning process from the stable jet region to the unstable region for predicting the final nanofiber diameter. J. Appl. Polym. Sci. 133, 44112.Google Scholar
James, D. F. 2009 Boger fluids. Annu. Rev. Fluid Mech. 41, 129–142.Google Scholar
Jimenez, L. N., Dinic, J., Parsi, N. & Sharma, V. 2018 Extensional relaxation time, pinch-off dynamics, and printability of semidilute polyelectrolyte solutions. Macromolecules 51, 5191–5208.Google Scholar
Khismatullin, D. B. & Nadim, A. 2001 Shape oscillations of a viscoelastic drop. Phys. Rev. E 63, 061508.Google Scholar
Kulichikhin, V. G., Malkin, A. Y., Semakov, A. V., Skvortsov, I. Y. & Arinstein, A. 2014 Liquid filament instability due to stretch-induced phase separation in polymer solutions. Eur. Phys. J. E. 37, 10.Google Scholar
Lakdawala, A. M., Sharma, A. & Thaokar, R. 2016 A dual grid level set method based study on similarity and difference bewteen interface dynamics for surface tension and radial electric field induced jet breakup. Chem. Engng Sci. 148, 238–255.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2011 Axisymmetric and non-axisymmetric instability of an electrically charged viscoelastic liquid jet. J. Non-Newtonian Fluid Mech. 166, 1024–1032.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2016 One-dimensional nonlinear instability study of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. Phys. Fluids 28, 053103.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2017a Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet. Phys. Rev. Fluids 2, 013602.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2017b Transition from a beads-on-string to a spilke structure in an electrified viscoelastic jet. Phys. Fluids 29, 023106.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2019 Small-amplitude shape oscillation and linear instability of an electrically charged viscoelastic liquid droplet. J. Non-Newtonian Fluid Mech. 264, 85–97.Google Scholar
Li, J. & Fontelos, M. A. 2003 Drop dynamics on the beads-on-string structure for viscoelastic jets: a numerical study. Phys. Fluids 15, 922–937.Google Scholar
López-Herrera, J. M. & Gañán-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, 303–326.Google Scholar
López-Herrera, J. M., Gañán-Calvo, A. M. & Perez-Saborid, M. 1999 One-dimensional simulation of the breakup of capillary jets of conducting liquids. Application to E.H.D. spraying. J. Aero. Sci. 30, 895–912.Google Scholar
López-Herrera, J. M., Gañán-Calvo, A. M., Popinet, S. & Herrada, M. A. 2015 Electrokinetic effects in the breakup of electrified jets: a volume-of-fluid numerical study. Intl J. Multiphase Flow 71, 14–22.Google 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.Google Scholar
Malkin, A. Y., Arinstein, A. & Kulichikhin, V. G. 2014 Polymer extension flows and instabilities. Prog. Polym. Sci. 39, 959–978.Google Scholar
Mathues, W., Formenti, S., McIlroy, C., Harlen, O. G. & Clasen, C. 2018 CaBER vs ROJER – different time scales for the thinning of a weakly elastic jet. J. Rheol. 62, 1135–1153.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111–146.Google Scholar
Mohamed, A. S., Herrada, M. A., Gañán-Calvo, A. M. & Montanero, J. M. 2015 Convective-to-absolute instability transition in a viscoelastic capillary jet subject to unrelaxed axial elastic tension. Phys. Rev. E 92, 023006.Google Scholar
Morrison, N. F. & Harlen, O. G. 2010 Viscoelasticity in inkjet printing. Rheol. Acta 49, 619–632.Google Scholar
Oliveira, M. S. N., Yeh, R. & McKinley, G. H. 2006 Iterated stretching, extensional rheology and formation of beads-on-a-string structures in polymer solutions. J. Non-Newtonian Fluid Mech. 137, 137–148.Google Scholar
Onses, M. S., Sutanto, E., Ferreira, P. M. & Alleyne, A. G. 2015 Mechanisms, capabilities, and applications of high-resolutions electrohydrodynamic jet printing. Small 11, 4237–4266.Google Scholar
Prilutski, G., Gupta, R. K., Sridhar, T. & Ryan, M. E. 1983 Model viscoelastic liquids. J. Non-Newtonian Fluid Mech. 12, 233–241.Google Scholar
Rayleigh, L. 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Rosell-Llompart, J., Grifoll, J. & Loscertales, I. G. 2018 Electrosprays in the cone-jet mode: from Taylor cone formation to spray development. J. Aero. Sci. 125, 2–31.Google Scholar
Ruo, A.-C., Chen, K.-H., Chang, M.-H. & Chen, F. 2012 Instability of a charged non-Newtonian liquid jet. Phys. Rev. E 85, 016306.Google Scholar
Sattler, R., Gier, S., Eggers, J. & Wagner, C. 2012 The final stages of capillary break-up of polymer solutions. Phys. Fluids 24, 023101.Google Scholar
Sattler, R., Wagner, C. & Eggers, J. 2008 Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions. Phys. Rev. Lett. 100, 164502.Google Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.Google Scholar
Schümmer, P. & Thelen, H.-G. 1988 Break-up of a viscoelastic liquid jet. Rheol. Acta 27, 39–43.Google Scholar
Setiawan, E. R. & Heister, S. D. 1997 Nonlinear modeling of an infinite electrified jet. J. Electrostat. 42, 243–257.Google Scholar
Tembely, M., Vadillo, D., Mackley, M. R. & Soucemarianadin, A. 2012 The matching of a one-dimensional numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up. J. Rheol. 56, 159–183.Google Scholar
Tirtaatmadja, V., McKinley, G. H. & Cooper-White, J. J. 2006 Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys. Fluids 18, 043101.Google Scholar
Turkoz, E., Lopez-Herrera, J. M., Eggers, J., Arnold, C. B. & Deike, L. 2018 Axisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model. J. Fluid Mech. 851, R2.Google Scholar
Varchanis, S., Dimakopoulos, Y., Wagner, C. & Tsamopoulos, J. 2018 How viscoelastic is human blood plasma? Soft Matt. 14, 4238–4251.Google Scholar
Wagner, C., Amarouchene, Y., Bonn, D. & Eggers, J. 2005 Droplet detachment and satellite bead formation in viscoelastic fluids. Phys. Rev. Lett. 95, 164504.Google Scholar
Wagner, C., Bourouiba, L. & McKinley, G. H. 2015 An analytic solution for capillary thinning and breakup of FENE-P fluids. J. Non-Newtonian Fluid Mech. 218, 53–61.Google Scholar
Wang, C., Wang, Y. & Hashimoto, T. 2016 Impact of entanglement density on solution electrospinning: a phenomenological model for fiber diameter. Macromolecules 49, 7985–7996.Google 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.Google Scholar
Wang, Q., Mählmann, S. & Papageorgiou, D. T. 2009 Dynamics of liquid jets and threads under the action of radial electric fields: microthread formation and touchdown singularities. Phys. Fluids 21, 032109.Google 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 radial electric fields: breakup and touchdown singularities. J. Fluid Mech. 683, 27–56.Google Scholar
Wang, Y., Hashimoto, T., Li, C.-C., Li, Y.-C. & Wang, C. 2018 Extension rate of the straight jet in electrospinning of poly(N-isopropylacrylamide) solutions in dimethylformamide: influences of flow rate and applied voltage. J. Polym. Sci. B 56, 319–329.Google Scholar
Yang, L. J., Liu, Y. X. & Fu, Q. F. 2012 Linear stability analysis of an electrified viscoelastic liquid jet. J. Fluids Engng 134, 071303.Google Scholar
Yoon, J., Yang, H.-S., adn, B.-S. L. & Yu, W.-R. 2018 Recent progress in coaxial electrospinning: new parameters, various structures, and wide applications. Adv. Mater. 30, 1704765.Google Scholar
Yu, J. H., Fridrikh, S. V. & Rutledge, G. C. 2006 The role of elasticity in the formation of electrospun fibers. Polymer 47, 4789–4797.Google Scholar
Zell, A., Gier, S., Rafaï, S. & Wagner, C. 2010 Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient? J. Non-Newtonian Fluid Mech. 165, 1265–1274.Google Scholar