Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T15:47:38.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrorheology of a dilute emulsion of surfactant-covered drops

Published online by Cambridge University Press:  24 October 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: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the effects of surfactant coating on a deformable viscous drop under the combined action of shear flow and a uniform electric field. Employing a comprehensive three-dimensional approach, we analyse the non-Newtonian shearing response of the bulk emulsion in the dilute suspension regime. Our results reveal that the location of the peak surfactant accumulation on the drop surface may get shifted from the plane of shear to a plane orthogonal to it, depending on the tilt angle of the applied electric field and strength of the electrical stresses relative to their hydrodynamic counterparts. The surfactant non-uniformity creates significant alterations in the flow perturbation around the drop, triggering modulations in the bulk shear viscosity. Overall, the shear-thinning or shear-thickening behaviour of the emulsion appears to be greatly influenced by the interplay of surface charge convection and Marangoni stresses. We show that the balance between electrical and hydrodynamic stresses renders a vanishing surface tension gradient on the drop surface for some specific shear rates, rendering negligible alterations in the bulk viscosity. This critical condition largely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also, the physical mechanisms of charge convection and surface deformation play their roles in determining this critical shear rate. As a consequence, we obtain new discriminating factors, involving electrical property ratios and the electric field configuration, which govern the same. Consequently, the surfactant-induced enhancement or attenuation of the bulk emulsion viscosity depends on the electrical conductivity and permittivity ratios. The concerned description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion may provide a fundamental understanding of a more complex emulsion system encountered in industrial practice.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 524 - 550
Check for updates
Copyright
© 2019 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

Allan, R. S. & Mason, S. G. 1962 Particle behaviour in shear and electric fields. I. Deformation and burst of fluid drops. Proc. R. Soc. Lond. A 267, 45–61.Google Scholar
Anna, S. L., Bontoux, N. & Stone, H. A. 2003 Formation of dispersions using ‘flow focusing’ in microchannels. Appl. Phys. Lett. 82 (3), 364–366.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
Barnes, H. A. 1994 Rheology of emulsions – a review. Colloids Surf. A 91, 89–95; a selection of papers presented at the First World Congress on Emulsions.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1–21.Google Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41 (3), 545–570.Google Scholar
Bentley, B. J. & Leal, L. G. 1986 An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J. Fluid Mech. 167, 241–283.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics. John Wiley and Sons.Google Scholar
Bousmina, M. 1999 Rheology of polymer blends: linear model for viscoelastic emulsions. Rheol. Acta 38 (1), 73–83.Google Scholar
Das, D. & Saintillan, D. 2016 A nonlinear small-deformation theory for transient droplet electrohydrodynamics. J. Fluid Mech. 810, 225–253.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
Eow, J. S. & Ghadiri, M. 2002 Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology. Chem. Engng J. 85 (2), 357–368.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
Esmaeeli, A. & Sharifi, P. 2011 Transient electrohydrodynamics of a liquid drop. Phys. Rev. E 84 (3), 036308.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
Fernàndez, A. 2008 Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: drops less conductive than the suspending fluid. Phys. Fluids 20, 043304.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
Guazzelli, E. & Morris, J. F. 2011 A Physical Introduction to Suspension Dynamics, vol. 45. Cambridge University Press.Google Scholar
Ha, J.-W., Moon, J.-H. & Yang, S.-M. 1999 Effect of nonionic surfactants on the electrorheology of emulsions. Korea-Aust Rheol. J. 11 (3), 241–246.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. 2000 Rheological responses of oil-in-oil emulsions in an electric field. J. Rheol. 44 (2), 235–256.Google Scholar
Haliburton, J. R., Kim, S. C., Clark, I. C., Sperling, R. A., Weitz, D. A. & Abate, A. R. 2017 Efficient extraction of oil from droplet microfluidic emulsions. Biomicrofluidics 11 (3), 034111.Google Scholar
Happel, J. & Brenner, H. 1981 Low Reynolds Number Hydrodynamics. Springer.Google Scholar
Hu, Y. & Lips, A. 2003 Estimating surfactant surface coverage and decomposing its effect on drop deformation. Phys. Rev. Lett. 91, 044501.Google Scholar
Jeon, H. K. & Macosko, C. W. 2003 Visualization of block copolymer distribution on a sheared drop. Polymer 44, 5381–5386.Google Scholar
Lanauze, J. A., Walker, L. M. & Khair, A. S. 2013 The influence of inertia and charge relaxation on electrohydrodynamic drop deformation. Phys. Fluids 25, 112101.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
Li, X. & Sarkar, K. 2005 Effects of inertia on the rheology of a dilute emulsion of drops in shear. J. Rheol. 49 (6), 1377–1394.Google Scholar
Lin, C.-J., Peery, J. H. & Schowalter, W. R. 1970 Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech. 44 (1), 1–17.Google Scholar
Maehlmann, S. & Papageorgiou, D. T. 2009 Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number. J. Fluid Mech. 626, 367–393.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 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
Mandal, S., Chakrabarti, S. & Chakraborty, S. 2017a Effect of nonuniform electric field on the electrohydrodynamic motion of a drop in Poiseuille flow. Phys. Fluids 29 (5), 052006.Google Scholar
Mandal, S. & Chakraborty, S. 2017a Effect of uniform electric field on the drop deformation in simple shear flow and emulsion shear rheology. Phys. Fluids 29 (7), 072109.Google Scholar
Mandal, S. & Chakraborty, S. 2017b Uniform electric-field-induced non-Newtonian rheology of a dilute suspension of deformable Newtonian drops. Phys. Rev. Fluids 2, 093602.Google Scholar
Mandal, S., Das, S. & Chakraborty, S. 2017b Effect of Marangoni stress on the bulk rheology of a dilute emulsion of surfactant-laden deformable droplets in linear flows. Phys. Rev. Fluids 2, 113604.Google 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.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
Milliken, W. J., Stone, H. A. & Leal, L. G. 1993 The effect of surfactant on transient motion of Newtonian drops. Phys. Fluids A 5, 69–79.Google Scholar
Na, Y. H., Aida, K., Sakai, R., Kakuchi, T. & Orihara, H. 2009 Response of shear stress to ac electric fields under steady shear flow in a droplet-dispersed phase. Phys. Rev. E 80 (6), 061803.Google Scholar
Nganguia, H., Young, Y.-N., Layton, A. T., Lai, M.-C. & Hu, W.-F. 2016 Electrohydrodynamics of a viscous drop with inertia. Phys. Rev. E 93 (5), 053114.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), 092106.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
Palierne, J. F. 1990 Linear rheology of viscoelastic emulsions with interfacial tension. Rheol. Acta 29 (3), 204–214.Google Scholar
Pan, X. D. & McKinley, G. H. 1997 Characteristics of electrorheological responses in an emulsion system. J. Colloid Interface Sci. 195, 101–113.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 (7), 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
Poddar, A., Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2019 Electrical switching of a surfactant coated drop in Poiseuille flow. J. Fluid Mech. 870, 27–66.10.1017/jfm.2019.236Google Scholar
Puyvelde, P. V., Velankar, S. & Moldenaers, P. 2001 Rheology and morphology of compatibilized polymer blends. Curr. Opin. Colloid Interface Sci. 6 (5), 457–463.Google Scholar
Salipante, P. F. & Vlahovska, P. M. 2010 Electrohydrodynamics of drops in strong uniform dc electric fields. Phys. Fluids 22 (11), 112110.Google Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 27–64.Google Scholar
Schowalter, W. R., Chaffey, C. E. & Brenner, H. 1968 Rheological behavior of a dilute emulsion. J. Colloid Interface Sci. 26 (2), 152–160.Google Scholar
Stone, H. A. 1990 A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys. Fluids A 2, 111–112.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
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
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138 (834), 41–48.Google Scholar
Teigen, K. & Munkejord, S. T. 2010 Influence of surfactant on drop deformation in an electric field. Phys. Fluids 22 (11), 112104.Google Scholar
Thaokar, R. M. 2012 Dielectrophoresis and deformation of a liquid drop in a non-uniform, axisymmetric ac electric field. Eur. Phys. J. E 35 (8), 76.Google Scholar
Tsukada, T., Katayama, T., Ito, Y. & Hozawa, M. 1993 Theoretical and experimental studies of circulations inside and outside a deformed drop under a uniform electric field. J. Chem. Eng. Jpn. 26 (6), 698–703.Google Scholar
Tucker, C. & Moldenaers, P. 2002 Microstructural evolution in polymer blends. Annu. Rev. Fluid Mech. 34, 177–210.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
Velankar, S., Van Pyuvede, P., Mewis, J. & Moldenaers, P. 2001 Effect of compatibilization on the breakup of polymeric drops in shear flow. J. Rheol. 45, 1007–1019.Google Scholar
Velankar, S., Van Puyvelde, P., Mewis, J. & Moldenaers, P. 2004 Steady shear rheological properties of model compatibilized blends. J. Rheol. 48, 725–744.Google Scholar
Vlahovska, P. M. 2011 On the rheology of a dilute emulsion in a uniform electric field. J. Fluid Mech. 670, 481–503.Google Scholar
Vlahovska, P. M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51 (1), 305–330.Google Scholar
Vlahovska, P. M., Bławzdziewicz, J. & Loewenberg, M. 2009 Small-deformation theory for a surfactant-covered drop in linear flows. J. Fluid Mech. 624, 293–337.Google Scholar
Vlahovska, P. M., Loewenberg, M. & Blawzdziewicz, J. 2005 Deformation of a surfactant-covered drop in a linear flow. Phys. Fluids 17 (10), 103103.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, 395–414.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
Supplementary material: File

Poddar et al. supplementary material

Poddar et al. supplementary material

Download Poddar et al. supplementary material(File)
File 944.2 KB