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Electrical switching of a surfactant coated drop in Poiseuille flow

Published online by Cambridge University Press:  07 May 2019

Antarip Poddar ,
Shubhadeep Mandal ,
Aditya Bandopadhyay  and
Suman Chakraborty Open the ORCID record for Suman Chakraborty [Opens in a new window]
Antarip Poddar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal – 721302, India
Shubhadeep Mandal
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal – 721302, India Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany
Aditya Bandopadhyay*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal – 721302, India
Suman Chakraborty*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal – 721302, India
*
†Email addresses for correspondence: aditya@mech.iitkgp.ernet.in, suman@mech.iitkgp.ernet.in
†Email addresses for correspondence: aditya@mech.iitkgp.ernet.in, suman@mech.iitkgp.ernet.in
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Abstract

Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 27 - 66
Copyright
© 2019 Cambridge University Press 

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References

Anna, S. L. 2016 Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48 (1), 285–309.Google Scholar
Bandopadhyay, A., Mandal, S., Kishore, N. K. & Chakraborty, S. 2016 Uniform electric-field-induced lateral migration of a sedimenting drop. J. Fluid Mech. 792 (2016), 553–589.Google Scholar
Baret, J. C. 2012 Surfactants in droplet-based microfluidics. Lab on a Chip 12, 422–433.Google Scholar
Baroud, C. N., Gallaire, F. & Dangla, R. 2010 Dynamics of microfluidic droplets. Lab on a Chip 10 (16), 2032–2045.Google Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48 (9), 1842–1848.Google Scholar
Bhaumik, S. K., Das, S., Chakraborty, S. & Dasgupta, S. 2014 Droplet transport through dielectrophoretic actuation using line electrode. Microfluid. Nanofluid. 16 (3), 597–603.Google Scholar
Chakraborty, S. & Mittal, R. 2007 Droplet dynamics in a microchannel subjected to electrocapillary actuation. J. Appl. Phys. 101 (10), 104901.Google Scholar
Chan, P. C.-H. & Leal, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92 (01), 131–170.Google Scholar
Das, S., Mandal, S. & Chakraborty, S. 2017a Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow. Phys. Fluids 29 (8), 082004.Google Scholar
Das, S., Mandal, S., Som, S. K. & Chakraborty, S. 2017b Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow. Phys. Fluids 29 (1), 012002.Google Scholar
Dey, R., Ghosh, U. U., Chakraborty, S. & Dasgupta, S. 2015 Dynamics of electrically modulated colloidal droplet transport. Langmuir 31 (41), 11269–11278.Google Scholar
Eggleton, C. D., Pawar, Y. P. & Stebe, K. J. 1999 Insoluble surfactants on a drop in an extensional flow: a generalization of the stagnated surface limit to deforming interfaces. J. Fluid Mech. 385, 79–99.Google Scholar
Ervik, Å., Penne, T. E., Hellesø, S. M., Munkejord, S. T. & Müller, B. 2018 Influence of surfactants on the electrohydrodynamic stretching of water drops in oil. Intl J. Multiphase Flow 98, 96–109.Google 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.Google Scholar
Fischer, P. & Erni, P. 2007 Emulsion drops in external flow fields–the role of liquid interfaces. Curr. Opin. Colloid Interface Sci. 12 (4–5), 196–205.Google Scholar
Ha, J.-W. & Yang, S.-M. 1995 Effects of surfactant on the deformation and stability of a drop in a viscous fluid in an electric field. J. Colloid Interface Sci. 175 (2), 369–385.Google Scholar
Ha, J.-W. & Yang, S.-M. 1998 Effect of nonionic surfactant on the deformation and breakup of a drop in an electric field. J. Colloid Interface Sci. 206 (1), 195–204.Google 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.Google Scholar
Haber, S. & Hetsroni, G. 1971 The dynamics of a deformable drop suspended in an unbounded Stokes flow. J. Fluid Mech. 49 (02), 257–277.Google Scholar
Hanna, J. A. & Vlahovska, P. M. 2010 Surfactant-induced migration of a spherical drop in Stokes flow. Phys. Fluids 22 (1), 1–7.Google Scholar
Happel, J. & Brenner, H. 1981 Low Reynolds Number Hydrodynamics. Springer.Google Scholar
Hetsroni, G. & Haber, S. 1970 The flow in and around a droplet or bubble submerged in an unbound arbitrary velocity field. Rheol. Acta 9 (4), 488–496.Google Scholar
Hoburg, J. F. & Melcher, J. R. 1977 Electrohydrodynamic mixing and instability induced by co-linear fields and conductivity gradients. Phys. Fluids 20 (6), 903–911.Google Scholar
Lamb, H. 1975 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Lanauze, J. A., Walker, L. M. & Khair, A. S 2015 Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774, 245–266.Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.Google Scholar
Li, X. & Pozrikidis, C. 1997 The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow. J. Fluid Mech. 341 (1997), 165–194.Google Scholar
Link, D. R., Grasland-Mongrain, E., Duri, A., Sarrazin, F., Cheng, Z., Cristobal, G., Marquez, M. & Weitz, D. A. 2006 Electric control of droplets in microfluidic devices. Angew. Chem. Intl Ed. Engl. 45 (16), 2556–2560.Google Scholar
Magnaudet, J. 2003 Small inertial effects on a spherical bubble, drop or particle moving near a wall in a time-dependent linear flow. J. Fluid Mech. 485, 115–142.Google Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016a Dielectrophoresis of a surfactant-laden viscous drop. Phys. Fluids 28 (6), 062006.Google Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016b Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop. Phys. Rev. E 93 (4), 043127.Google Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016c The effect of uniform electric field on the cross-stream migration of a drop in plane Poiseuille flow. J. Fluid Mech. 809 (2016), 726–774.Google Scholar
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.Google Scholar
Mhatre, S. & Thaokar, R. M. 2013 Drop motion, deformation, and cyclic motion in a non-uniform electric field in the viscous limit. Phys. Fluids 25 (7).Google Scholar
Mortazavi, S. & Tryggvason, G. 2000 A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid Mech. 411, 325–350.Google Scholar
Mukherjee, S. & Sarkar, K. 2013 Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wall-bounded shear. J. Fluid Mech. 727, 318–345.Google Scholar
Nganguia, H., Young, Y. N., Vlahovska, P. M., Bławzdziewcz, J., Zhang, J. & Lin, H. 2013 Equilibrium electro-deformation of a surfactant-laden viscous drop. Phys. Fluids 25 (9).Google Scholar
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
Panigrahi, D. P., Das, S. & Chakraborty, S. 2018 Deformation of a surfactant-laden viscoelastic droplet in a uniaxial extensional flow. Phys. Fluids 30 (12), 122108.Google Scholar
Pawar, Y. & Stebe, K. J. 1996 Marangoni effects on drop deformation in an extensional flow: the role of surfactant physical chemistry. I. Insoluble surfactants. Phys. Fluids 8, 1738–1751.Google Scholar
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.Google Scholar
Ptasinski, K. J. & Kerkhof, P. J. A. M. 1992 Electric field driven separations: phenomena and applications. Sep. Sci. Technol. 27 (8–9), 995–1021.Google Scholar
Santra, S., Das, S., Das, S. S. & Chakraborty, S. 2018 Surfactant-induced retardation in lateral migration of droplets in a microfluidic confinement. Microfluid. Nanofluid. 22 (8), 88.Google Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 27–64.Google Scholar
Schwalbe, J. T., Phelan, F. R. Jr, Vlahovska, P. M. & Hudson, S. D. 2011 Interfacial effects on droplet dynamics in Poiseuille flow. Soft Matt. 7 (17), 7797–7804.Google 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, 29–53.Google Scholar
Stan, C. A., Guglielmini, L., Ellerbee, A. K., Caviezel, D., Stone, H. A. & Whitesides, G. M. 2011 Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels. Phys. Rev. E 84 (3), 036302.Google Scholar
Stone, H. A. & Leal, L. G. 1990 The effects of surfactants on drop deformation and breakup. J. Fluid Mech. 220, 161.Google Scholar
Subramanian, R. S. & Balasubramaniam, R. 2005 The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.Google Scholar
Taylor, G. 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
Teigen, K. & Munkejord, S. T. 2010 Influence of surfactant on drop deformation in an electric field. Phys. Fluids 22 (11).Google Scholar
Tsouris, C., Culbertson, C. T., DePaoli, D. W., Jacobson, S. C., De Almeida, V. F. & Ramsey, J. M. 2003 Electrohydrodynamic mixing in microchannels. AIChE J. 49 (8), 2181–2186.Google Scholar
Valkovska, D. S. & Danov, K. D. 2000 Determination of bulk and surface diffusion coefficients from experimental data for thin liquid film drainage. J. Colloid Interface Sci. 223 (2), 314–316.Google Scholar
Vlahovska, P., Blawzdziewicz, J. & Loewenberg, M. 2005 Deformation of a surfactant-covered drop in a linear flow. Phys. Fluids 17 (10), 103103.Google Scholar
Wu, Y. & Clark, R. L. 2008 Electrohydrodynamic atomization: a versatile process for preparing materials for biomedical applications. J. Biomater. Sci. Polym. Ed. 19 (5), 573–601.Google Scholar
Xu, J. J., Li, Z., Lowengrub, J. & Zhao, H. 2006 A level-set method for interfacial flows with surfactant. J. Comput. Phys. 212 (2), 590–616.Google 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.Google 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.Google Scholar
Zhang, L., He, L., Ghadiri, M. & Hassanpour, A. 2015 Effect of surfactants on the deformation and break-up of an aqueous drop in oils under high electric field strengths. J. Petrol. Sci. Engng 125, 38–47.Google Scholar
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