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Electrohydrodynamic tuning of the migration characteristics of a sedimenting compound drop

Published online by Cambridge University Press:  06 December 2022

Manash Protim Boruah ,
Pitambar R. Randive Open the ORCID record for Pitambar R. Randive [Opens in a new window]  and
Sukumar Pati
Manash Protim Boruah
Affiliation:
Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar-788010, India
Pitambar R. Randive*
Affiliation:
Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar-788010, India
Sukumar Pati
Affiliation:
Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar-788010, India
*
†Email address for correspondence: pitambar@mech.nits.ac.in
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Abstract

Electrohydrodynamic sedimentation of simple drops has been a topic well-studied by researchers. However, electrohydrodynamic sedimentation of a compound drop would be critically influenced by the density of the involved phases and this has hitherto remained unaddressed. Herein, we develop a semi-analytical model for an eccentric compound drop settling under the action of gravity and an electric field using bispherical coordinates. The sedimentation velocity of the two drops (shell and core) is determined, and the same is applied to capture the influence of concomitant physical, hydrodynamic and electric properties on compound droplet sedimentation. The findings indicate that the compound drop may either sediment or de-sediment depending on the amount of eccentricity and its interplay with electrohydrodynamic parameters. Thereafter, the critical limit of eccentricity and time within which similar results are furnished by concentric and eccentric configurations is determined. It is found that, based on the property ratios, the eccentricity remains lower than 0.1 up to a non-dimensional time range of the order of 102–103, within which both the configurations can furnish a similar solution.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Electrohydrodynamic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 953 , 25 December 2022 , A13
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Bandopadhyay, A., Mandal, S., Kishore, N.K. & Chakraborty, S. 2016 Uniform electricfield- induced lateral migration of a sedimenting drop. J. Fluid Mech. 792, 553–589.CrossRefGoogle Scholar
Basaran, O.A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48 (9), 1842–1848.CrossRefGoogle Scholar
Behjatian, A. & Esmaeeli, A. 2013 Electrohydrodynamics of a liquid column under a transverse electric field in confined domains. Intl J. Multiphase Flow 48, 71–81.CrossRefGoogle Scholar
Boruah, M.P., Randive, P.R., Pati, S. & Sahu, K.C. 2022 Charge convection and interfacial deformation of a compound drop in plane Poiseuille flow under an electric field. Phys. Rev. Fluid 7, 013703.CrossRefGoogle Scholar
Brunn, P.O. & Roden, T. 1985 On the deformation and drag of a type-A multiple drop at low Reynolds number. J. Fluid Mech. 160, 211–234.CrossRefGoogle Scholar
Castellanos, A. 2014 Electrohydrodynamics. Springer.Google Scholar
Choi, S. & Saveliev, A.V. 2017 Oscillatory coalescence of droplets in an alternating electric field. Phys. Rev. Fluids 2 (6), 063603.CrossRefGoogle Scholar
Das, D. & Saintillan, D. 2016 A nonlinear small-deformation theory for transient droplet electrohydrodynamics. J. Fluid Mech. 810, 225–253.CrossRefGoogle Scholar
Dey, R., Ghosh, U.U., Chakraborty, S. & Dasgupta, S. 2015 Dynamics of electrically modulated colloidal droplet transport. Langmuir 31 (41), 11 269–11 278.CrossRefGoogle ScholarPubMed
Draxler, J. & Marr, R. 1986 Emulsion liquid membranes part I: phenomenon and industrial application. Chem. Engng Process. 20 (6), 319–329.CrossRefGoogle Scholar
Eow, J.S., Ghadiri, M. & Sharif, A.O. 2007 Electro-hydrodynamic separation of aqueous drops from flowing viscous oil. J. Petrol. Sci. Engng 55 (1–2), 146–155.CrossRefGoogle Scholar
Esmaeeli, A. & Sharifi, P. 2011 Transient electrohydrodynamics of a liquid drop. Phys. Rev. E 84, 036308.CrossRefGoogle ScholarPubMed
Fabiilli, M.L., Lee, J.A., Kripfgans, O.D., Carson, P.L. & Fowlkes, J.B. 2010 Delivery of water-soluble drugs using acoustically triggered perfluorocarbon double emulsions. Pharmaceut. Res. 27 (12), 2753–2765.CrossRefGoogle ScholarPubMed
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, 32–56.Google Scholar
Gouz, H.N. & Sadhal, S.S. 1989 Fluid dynamics and stability analysis of a compound droplet in an electric field. Q. J. Mech. Appl. Maths 42 (1), 65–83.CrossRefGoogle Scholar
Ha, J.-W. & Yang, S.-M. 2000 Rheological responses of oil-in-oil emulsions in an electric field. J. Rheol. 44 (2), 235–256.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 2012 Low Reynolds number hydrodynamics: with special applications to particulate media. Springer.Google Scholar
Jadhav, S.N. & Ghosh, U. 2021 a Thermocapillary effects on eccentric compound drops in Poiseuille flows. Phys. Rev. Fluid 6, 073602.CrossRefGoogle Scholar
Jadhav, S.N. & Ghosh, U. 2021 b Effect of surfactant on the settling of a drop towards a wall. J. Fluid Mech. 912, A4.CrossRefGoogle Scholar
Jaworek, A. & Krupa, A. 1999 Jet and drops formation in electrohydrodynamic spraying of liquids: a systematic approach. Exp. Fluids 27 (1), 43–52.CrossRefGoogle Scholar
Johnson, R.E. & Sadhal, S.S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Annu. Rev. Fluid Mech. 17 (1), 289–320.CrossRefGoogle Scholar
Karyappa, R.B., Deshmukh, S.D. & Thaokar, R.M. 2014 Breakup of a conducting drop in a uniform electric field. J. Fluid Mech. 754, 550–589.CrossRefGoogle Scholar
Karyappa, R.B., Naik, A.V. & Thaokar, R.M. 2016 Electroemulsification in a uniform electric field. Langmuir 32 (1), 46–54.CrossRefGoogle Scholar
Kim, S.-H., Kim, J.W., Cho, J.-C. & Weitz, D.A. 2011 Double-emulsion drops with ultra-thin shells for capsule templates. Lab Chip 11, 3162.Google ScholarPubMed
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
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016 a The effect of uniform electric field on the cross-stream migration of a drop in plane Poiseuille flow. J. Fluid Mech. 809, 726–774.CrossRefGoogle Scholar
Mandal, S., Ghosh, U. & Chakraborty, S. 2016 b Effect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows. J. Fluid Mech. 803, 200–249.CrossRefGoogle Scholar
Mandal, S., Sinha, S., Bandopadhyay, A. & Chakraborty, S. 2018 Drop deformation and emulsion rheology under the combined influence of uniform electric field and linear flow. J. Fluid Mech. 841, 408–433.CrossRefGoogle Scholar
Morton, D.S., Subramanian, R.S. & Balasubramaniam, R. 1990 The migration of a compound drop due to thermocapillarity. Phys. Fluids A 2 (12), 2119.CrossRefGoogle Scholar
Nakano, M. 2000 Places of emulsions in drug delivery. Adv. Drug Deliv. Rev. 45 (1), 1–4.CrossRefGoogle ScholarPubMed
Pak, O.S., Feng, J. & Stone, H.A. 2014 Viscous Marangoni migration of a drop in a Poiseuille flow at low surface Péclet numbers. J. Fluid Mech. 753, 535–552.Google Scholar
Palaniappan, D. & Daripa, P. 2000 Compound droplet in extensional and paraboloidal flows. Phys. Fluids 12 (10), 2377.CrossRefGoogle Scholar
Pethig, R. 2013 Dielectrophoresis: an assessment of its potential to aid the research and practice of drug discovery and delivery. Adv. Drug Deliv. Rev. 65 (11–12), 1589–1599.Google ScholarPubMed
Poddar, A., Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2018 Sedimentation of a surfactant-laden drop under the influence of an electric field. J. Fluid Mech. 849, 277–311.CrossRefGoogle Scholar
Poddar, A., Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2019 Electrical switching of a surfactant coated drop in Poiseuille flow. J. Fluid Mech. 870, 27–66.CrossRefGoogle Scholar
Rushton, E. & Davies, G.A. 1983 Settling of encapsulated droplets at low Reynolds numbers. Intl J. Multiphase Flow 9 (3), 337–342.CrossRefGoogle Scholar
Sadhal, S.S. 1983 A note on the thermocapillary migration of a bubble normal to a plane surface. J. Colloid Interface Sci. 95, 283–285.CrossRefGoogle Scholar
Sadhal, S.S. & Oguz, H.N. 1985 Stokes flow past compound multiphase drops: the case of completely engulfed drops/bubbles. J. Fluid Mech. 160, 511–529.CrossRefGoogle Scholar
Santra, S., Das, S. & Chakraborty, S. 2020 Electrically modulated dynamics of a compound droplet in a confined microfluidic environment. J. Fluid Mech. 882.CrossRefGoogle Scholar
Santra, S., Mandal, S. & Chakraborty, S. 2019 Confinement effect on electrically induced dynamics of a droplet in shear flow. Phys. Rev. E 100 (3), 33101.CrossRefGoogle ScholarPubMed
Soni, P., Dixit, D. & Juvekar, V.A. 2017 Effect of conducting core on the dynamics of a compound drop in an AC electric field. Phys. Fluids 29 (11), 112108.CrossRefGoogle Scholar
Soni, P., Juvekar, V.A. & Naik, V.M. 2013 Investigation on dynamics of double emulsion droplet in a uniform electric field. J. Electrostat. 71 (3), 471–477.CrossRefGoogle Scholar
Soni, P., Thaokar, R.M. & Juvekar, V.A. 2018 Electrohydrodynamics of a concentric compound drop in an AC electric field. Phys. Fluids 30 (3), 032102.CrossRefGoogle Scholar
Stimson, M. & Jeffery, G.B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A 111 (757), 110–116.Google Scholar
Stone, H.A. & Leal, L.G. 1990 Breakup of concentric double emulsion droplets in linear flows. J. Fluid Mech. 211, 123–156.CrossRefGoogle Scholar
Taylor, G. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. R. Soc. Lond. A 291 (1425), 159–166.Google Scholar
Tsukada, T., Mayama, J., Sato, M. & Hozawa, M. 1997 Theoretical and experimental studies on the behavior of a compound drop under a uniform DC electric field. J. Chem. Engng Japan 30 (2), 215–222.CrossRefGoogle Scholar
Utada, A.S., Lorenceau, E., Link, D.R., Kaplan, P.D., Stone, H.A. & Weitz, D.A. 2005 Monodisperse double emulsions generated from a microcapillary device. Science 308 (5721), 537–541.CrossRefGoogle ScholarPubMed
Vlahovska, P.M. 2011 On the rheology of a dilute emulsion in a uniform electric field. J. Fluid Mech. 670, 481–503.CrossRefGoogle Scholar
Wacholder, E. & Weihs, D. 1972 Slow motion of a fluid sphere in the vicinity of another sphere or a plane boundary. Chem. Engng Sci. 27 (10), 1817–1828.CrossRefGoogle Scholar
Ward, T. & Homsy, G.M. 2006 Chaotic streamlines in a translating drop with a uniform electric field. J. Fluid Mech. 547, 215–230.CrossRefGoogle Scholar
Xu, X. & Homsy, G.M. 2006 The settling velocity and shape distortion of drops in a uniform electric field. J. Fluid Mech. 564, 395–414.CrossRefGoogle Scholar
Yariv, E. & Almog, Y. 2016 The effect of surface-charge convection on the settling velocity of spherical drops in a uniform electric field. J. Fluid Mech. 797, 536–548.CrossRefGoogle Scholar
Zhang, J., Zahn, J. & Lin, H. 2013 Transient solution for droplet deformation under electric fields. Phys. Rev. E 87 (4), 043008.CrossRefGoogle ScholarPubMed
Zheng, B., Tice, J.D. & Ismagilov, R.F. 2004 Formation of droplets of alternating composition in microfluidic channels and applications to indexing of concentrations in droplet-based assays. Anal. Chem. 76 (17), 4977–4982.CrossRefGoogle Scholar