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Electric-field-induced transitions from spherical to discocyte and lens-shaped drops

Published online by Cambridge University Press:  12 October 2020

Brayden W. Wagoner ,
Petia M. Vlahovska Open the ORCID record for Petia M. Vlahovska [Opens in a new window] ,
Michael T. Harris  and
Osman A. Basaran Open the ORCID record for Osman A. Basaran [Opens in a new window]
Brayden W. Wagoner
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Petia M. Vlahovska
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL60208, USA
Michael T. Harris
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Osman A. Basaran*
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
*
†Email address for correspondence: [email protected]
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Abstract

When a poorly conducting drop that is surrounded by a more conducting exterior fluid is subjected to an electric field, the drop can deform into an oblate shape at low field strengths. Such drops become unstable at high field strengths and display two types of dynamics, dimpling and equatorial streaming, the physics of which is currently not understood. If the drop is more viscous, dimples form and grow at the poles of the drop and eventually the discocyte-shaped drop breaks up to form a torus. If the exterior fluid is more viscous, the drop deforms into a lens and sheds rings from the equator that subsequently break into a number of smaller droplets. A theoretical explanation as to why dimple- and lens-shaped drops occur, and the mechanisms for the onset of these instabilities, are provided by determining steady-state solutions by simulation and inferring their stability from bifurcation analysis. For large drop viscosities, electric shear stress is shown to play a dominant role and to result in dimpling. For small drop viscosities, equatorial normal stresses (electric, hydrodynamic and capillary) become unbounded and lead to the lens shape.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Electrohydrodynamic effects
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , R4
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abbott, J. P. 1978 An efficient algorithm for the determination of certain bifurcation points. J. Comput. Appl. Maths 4 (1), 19–27.CrossRefGoogle Scholar
Barrero, A. & Loscertales, I. G. 2007 Micro-and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89–106.CrossRefGoogle Scholar
Basaran, O. A. & Scriven, L. E. 1988 The Taylor pump: viscous-free surface flow driven by electric shear stress. Chem. Engng Commun. 67 (1), 259–273.CrossRefGoogle Scholar
Basaran, O. A. & Scriven, L. E. 1990 Axisymmetric shapes and stability of pendant and sessile drops in an electric field. J. Colloid Interface Sci. 140 (1), 10–30.CrossRefGoogle Scholar
Basaran, O. A. & Wohlhuter, F. K. 1992 Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field. J. Fluid Mech. 244, 1–16.CrossRefGoogle Scholar
Baygents, J. C., Rivette, N. J. & Stone, H. A. 1998 Electrohydrodynamic deformation and interaction of drop pairs. J. Fluid Mech. 368, 359–375.CrossRefGoogle Scholar
Bentenitis, N. & Krause, S. 2005 Droplet deformation in DC electric fields: the extended leaky dielectric model. Langmuir 21 (14), 6194–6209.CrossRefGoogle Scholar
Bird, J. C., Ristenpart, W. D., Belmonte, A. & Stone, H. A. 2009 Critical angle for electrically driven coalescence of two conical droplets. Phys. Rev. Lett. 103 (16), 164502.CrossRefGoogle ScholarPubMed
Brosseau, Q. & Vlahovska, P. M. 2017 Streaming from the equator of a drop in an external electric field. Phys. Rev. Lett. 119 (3), 034501.CrossRefGoogle Scholar
Brown, R. A. & Scriven, L. E. 1980 The shapes and stability of captive rotating drops. Phil. Trans. R. Soc. Lond. A 297 (1429), 51–79.Google Scholar
Burton, J. C. & Taborek, P. 2011 Simulations of coulombic fission of charged inviscid drops. Phys. Rev. Lett. 106 (14), 144501.CrossRefGoogle ScholarPubMed
Christodoulou, K. N. & Scriven, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99 (1), 39–55.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 (2), 149.CrossRefGoogle Scholar
Collins, R. T., Sambath, K., Harris, M. T. & Basaran, O. A. 2013 Universal scaling laws for the disintegration of electrified drops. Proc. Natl Acad. Sci. 110 (13), 4905–4910.CrossRefGoogle ScholarPubMed
Das, D. & Saintillan, D. 2017 a Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations. J. Fluid Mech. 829, 127–152.CrossRefGoogle Scholar
Das, D. & Saintillan, D. 2017 b A nonlinear small-deformation theory for transient droplet electrohydrodynamics. J. Fluid Mech. 810, 225–253.CrossRefGoogle Scholar
Deen, W. M. 1998 Analysis of transport phenomena. Oxford University Press.Google Scholar
DePaoli, D. W., Feng, J. Q., Basaran, O. A. & Scott, T. C. 1995 Hysteresis in forced oscillations of pendant drops. Phys. Fluids 7 (6), 1181–1183.CrossRefGoogle Scholar
Eow, J. S., Ghadiri, M., Sharif, A. O. & Williams, T. J. 2001 Electrostatic enhancement of coalescence of water droplets in oil: a review of the current understanding. Chem. Engng J. 84 (3), 173–192.CrossRefGoogle Scholar
Feng, J. Q. 1999 Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number. Proc. R. Soc. Lond. A 455 (1986), 2245–2269.CrossRefGoogle Scholar
Feng, J. J. 2002 The stretching of an electrified non-Newtonian jet: a model for electrospinning. Phys. Fluids 14 (11), 3912–3926.CrossRefGoogle Scholar
Feng, J. Q. & Basaran, O. A. 1994 Shear flow over a translationally symmetric cylindrical bubble pinned on a slot in a plane wall. J. Fluid Mech. 275, 351–378.CrossRefGoogle Scholar
Feng, J. Q. & Scott, T. C. 1996 A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field. J. Fluid Mech. 311, 289–326.CrossRefGoogle Scholar
Fenn, J. B., Mann, M., Meng, C. K., Wong, S. F. & Whitehouse, C. M. 1989 Electrospray ionization for mass spectrometry of large biomolecules. Science 246 (4926), 64–71.CrossRefGoogle ScholarPubMed
Fernández de La Mora, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39, 217–243.CrossRefGoogle Scholar
Ganán-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. Aero. Sci. 125, 32–56.CrossRefGoogle Scholar
Gilbert, W. 1958 De Magnete. Courier Corporation.Google Scholar
Glendinning, P. 1994 Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations, vol. 11. Cambridge University Press.CrossRefGoogle Scholar
Harris, M. T., Sisson, W. G. & Basaran, O. A. 1992 Computation, visualization, and chemistry of electric field-enhanced production of ceramic precursor powders. MRS Online Proc. Library Arch. 271, 945–950.CrossRefGoogle Scholar
Iooss, G. & Joseph, D. D. 2012 Elementary Stability and Bifurcation Theory. Springer Science & Business Media.Google Scholar
Jayasinghe, S. N., Qureshi, A. N. & Eagles, P. A. M. 2006 Electrohydrodynamic jet processing: an advanced electric-field-driven jetting phenomenon for processing living cells. Small 2 (2), 216–219.CrossRefGoogle ScholarPubMed
Kamat, P. M., Wagoner, B. W., Thete, S. S. & Basaran, O. A. 2018 Role of Marangoni stress during breakup of surfactant-covered liquid threads: reduced rates of thinning and microthread cascades. Phys. Rev. Fluids 3 (4), 043602.CrossRefGoogle Scholar
Kistler, S. F. & Scriven, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (ed. Pearson, J. R. A. & Richardson, S. M.), pp. 243–299. Springer.CrossRefGoogle Scholar
Lac, E. & Homsy, G. M. 2007 Axisymmetric deformation and stability of a viscous drop in a steady electric field. J. Fluid Mech. 590, 239–264.CrossRefGoogle Scholar
Lanauze, J. A., Walker, L. M. & Khair, A. S. 2015 Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774, 245–266.CrossRefGoogle Scholar
Marín, A. G., Loscertales, I. G., Marquez, M. & Barrero, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98 (1), 014502.CrossRefGoogle ScholarPubMed
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1 (1), 111–146.CrossRefGoogle Scholar
Miksis, M. J. 1981 Shape of a drop in an electric field. Phys. Fluids 24 (11), 1967–1972.CrossRefGoogle Scholar
Oddershede, L. & Nagel, S. R. 2000 Singularity during the onset of an electrohydrodynamic spout. Phys. Rev. Lett. 85 (6), 1234.CrossRefGoogle ScholarPubMed
Rayleigh, Lord 1882 On the equilibrium of liquid conducting masses charged with electricity. Phil. Mag. 14 (87), 184–186.CrossRefGoogle Scholar
Reneker, D. H. & Yarin, A. L. 2008 Electrospinning jets and polymer nanofibers. Polymer 49 (10), 2387–2425.CrossRefGoogle Scholar
Ristenpart, W. D., Bird, J. C., Belmonte, A., Dollar, F. & Stone, H. A. 2009 Non-coalescence of oppositely charged drops. Nature 461 (7262), 377–380.CrossRefGoogle ScholarPubMed
Sambath, K. & Basaran, O. A. 2014 Electrohydrostatics of capillary switches. AIChE J. 60 (4), 1451–1459.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 27–64.CrossRefGoogle Scholar
Seydel, R. 2009 Practical Bifurcation and Stability Analysis, vol. 5. Springer Science & Business Media.Google Scholar
Smith, C. V. & Melcher, J. R. 1967 Electrohydrodynamically induced spatially periodic cellular Stokes-flow. Phys. Fluids 10 (11), 2315–2322.CrossRefGoogle Scholar
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280 (1382), 383–397.Google Scholar
Taylor, G. I. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field. Proc. R. Soc. Lond. A 291 (1425), 159–166.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1971 Electrohydrodynamic deformation and bursts of liquid drops. Phil. Trans. R. Soc. Lond. A 269 (1198), 295–319.Google Scholar
Tsamopoulos, J. A., Akylas, T. R. & Brown, R. A. 1985 Dynamics of charged drop break-up. Proc. R. Soc. Lond. A 401 (1820), 67–88.Google Scholar
Ungar, L. H. & Brown, R. A. 1982 The dependence of the shape and stability of captive rotating drops on multiple parameters. Phil. Trans. R. Soc. Lond. A 306 (1493), 347–370.Google Scholar
Vlahovska, P. M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51, 305–330.CrossRefGoogle Scholar
Wagoner, B. W., Anthony, C. R., Vlahovska, P. M., Harris, M. T. & Basaran, O. A. 2019 Electrohydrodynamic equatorial streaming. Bull. Am. Phys. Soc. 64, B23.001.Google Scholar
Yamaguchi, Y., Chang, C. J. & Brown, R. A. 1984 Multiple buoyancy-driven flows in a vertical cylinder heated from below. Phil. Trans. R. Soc. Lond. A 312 (1523), 519–552.Google Scholar
Yariv, E. & Rhodes, D. 2013 Electrohydrodynamic drop deformation by strong electric fields: slender-body analysis. SIAM J. Appl. Maths 73 (6), 2143–2161.CrossRefGoogle Scholar
Zabarankin, M. 2013 A liquid spheroidal drop in a viscous incompressible fluid under a steady electric field. SIAM J. Appl. Maths 73 (2), 677–699.CrossRefGoogle Scholar
Zeleny, J. 1917 Instability of electrified liquid surfaces. Phys. Rev. 10 (1), 1.CrossRefGoogle Scholar
Zhang, X., Basaran, O. A. & Wham, R. M. 1995 Theoretical prediction of electric field-enhanced coalescence of spherical drops. AIChE J. 41 (7), 1629–1639.CrossRefGoogle Scholar
Zubarev, N. M. 2001 Formation of conic cusps at the surface of liquid metal in electric field. J. Expl Theor. Phys. Lett. 73 (10), 544–548.CrossRefGoogle Scholar