Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T08:14:33.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Drop deformation and emulsion rheology under the combined influence of uniform electric field and linear flow

Published online by Cambridge University Press:  23 February 2018

Shubhadeep Mandal ,
Sudipta Sinha ,
Aditya Bandopadhyay  and
Suman Chakraborty Open the ORCID record for Suman Chakraborty [Opens in a new window]
Shubhadeep Mandal
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal-721302, India
Sudipta Sinha
Affiliation:
Department of Chemistry, Indian Institute of Technology Ropar, Punjab-140001, India
Aditya Bandopadhyay
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal-721302, India
Suman Chakraborty*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal-721302, India
*
†Email address for correspondence: suman@mech.iitkgp.ernet.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Electrohydrodynamics of a leaky dielectric suspended drop subjected to the combined influence of a uniform electric field and linear velocity field is analysed analytically and numerically. In the limit of small charge convection and small shape deformation, an analytical solution is obtained for the deformed drop shape when the imposed linear flow is of uniaxial extensional type with the extensional component aligned in the direction of the electric field. This perturbation approach is then applied towards obtaining the effect of a uniform electric field on the effective extensional rheology of a dilute emulsion. Key results indicate that the magnitude and sense of drop deformation not only depends on the material properties of the drop and medium but is also governed by the strength of the applied electric field relative to the applied flow field. The interfacial charge convection is found to increase or decrease the drop deformation depending on the direction of electrohydrodynamic flow and relative strength of electric field. The electrohydrodynamic flow and drop deformation modulates the effective extensional viscosity of the emulsion. Importantly, the presence of the electric field leads to strain-rate-dependent effective extensional viscosity of the emulsion. The emulsion is found to exhibit strain-rate thinning/thickening behaviour depending on the drop to medium charge relaxation time scale. The analytically obtained drop shape and deformation are in excellent agreement with numerical simulations for the small deformation ranges.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 408 - 433
Check for updates
Copyright
© 2018 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

Ahn, K., Kerbage, C., Hunt, T. P., Westervelt, R. M., Link, D. R. & Weitz, D. A. 2006 Dielectrophoretic manipulation of drops for high-speed microfluidic sorting devices. Appl. Phys. Lett. 88 (2), 24104.CrossRefGoogle Scholar
Ajayi, O. O. 1978 A note on Taylor’s electrohydrodynamic theory. Proc. R. Soc. Lond. A 364 (1719), 499–507.Google Scholar
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 (1328), 45–61.Google Scholar
Bandopadhyay, A., Mandal, S., Kishore, N. K. K. & Chakraborty, S. 2016 Uniform electric-field-induced lateral migration of a sedimenting drop. J. Fluid Mech. 792, 553–589.CrossRefGoogle Scholar
Barthès-Biesel, D. 2012 Microhydrodynamics and Complex Fluids. CRC Press.Google Scholar
Barthés-Biesel, D. & Acrivos, A. 1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61 (1), 1–22.CrossRefGoogle Scholar
Cogswell, F. N. 1972 Measuring the extensional rheology of polymer melts. Trans. Soc. Rheol. 16 (3), 383–403.Google Scholar
Das, D. & Saintillan, D. 2017 A nonlinear small-deformation theory for transient droplet electrohydrodynamics. J. Fluid Mech. 810, 225–253.Google 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, 173–192.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
Fernández, A. 2008a Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: drops more conductive than the suspending fluid. Phys. Fluids 20, 43303.Google Scholar
Fernández, A. 2008b Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: drops less conductive than the suspending fluid. Phys. Fluids 20 (4), 43304.Google Scholar
Fernández, A. 2009 Shear flow of an emulsion of drops less conductive than the suspending fluid immersed in an electric field by numerical simulation. Colloids Surf. A 338, 68–79.Google Scholar
Ha, J.-W. & Yang, S.-M. 2000a Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field. J. Fluid Mech. 405, 131–156.CrossRefGoogle Scholar
Ha, J.-W. & Yang, S.-M. 2000b Rheological responses of oil-in-oil emulsions in an electric field. J. Rheol. 44 (2), 235.Google 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.Google 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
Leal, L. G. 2007 Advanced Transport Phenomena. Cambridge University Press.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. 45 (16), 2556–2560.CrossRefGoogle ScholarPubMed
López-Herrera, J. M., Popinet, S. & Herrada, M. A. 2011 A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid. J. Comput. Phys. 230 (5), 1939–1955.Google Scholar
Mählmann, 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.Google Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016a Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop. Phys. Rev. E 93 (4), 1–21.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, 726–774.CrossRefGoogle Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2017a The effect of surface charge convection and shape deformation on the settling velocity of drops in nonuniform electric field. Phys. Fluids 29 (1), 12101.Google Scholar
Mandal, S., Chakrabarti, S. & Chakraborty, S. 2017b Effect of nonuniform electric field on the electrohydrodynamic motion of a drop in Poiseuille flow. Phys. Fluids 29 (5), 52006.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), 72109.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 (9), 93602.CrossRefGoogle 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., Vivacqua, V., Ghadiri, M., Abdullah, A. M., Hassanpour, A., Hewakandamby, B., Azzopardi, B. & Kermani, B. 2015 Electrostatic phase separation: a review. Chem. Engng Res. Des. 96, 177–195.CrossRefGoogle Scholar
Minale, M. 2010 Models for the deformation of a single ellipsoidal drop: a review. Rheol. Acta 49 (8), 789–806.Google Scholar
O’Konski, C. T. & Thacher, H. C. 1953 The distortion of aerosol droplets by an electric field. J. Phys. Chem. 57 (9), 955–958.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
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 (2), 572–600.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.Google Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16 (1), 45–66.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.CrossRefGoogle Scholar
Schramm, L. L. 1992 Emulsions: Fundamentals and Applications in the Petroleum Industry. Americal Chemical Society.Google Scholar
Sherwood, J. D. 1988 Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188 (1), 133.CrossRefGoogle Scholar
Shroff, R. N., Cancio, L. V. & Shida, M. 1977 Extensional flow of polymer melts. Trans. Soc. Rheol. 21 (3), 429–446.Google Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26 (1), 65–102.Google Scholar
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.Google 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
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
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146 (858), 501–523.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1971 Electrohydrodynamic deformation and burst of liquid drops. Phil. Trans. R. Soc. Lond. A 269 (1198), 295–319.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
Wehking, J. D., Chew, L. & Kumar, R. 2013 Droplet deformation and manipulation in an electrified microfluidic channel. Appl. Phys. Lett. 103, 54101.Google Scholar
Wehking, J. D. & Kumar, R. 2015 Lab on a chip droplet actuation in an electrified microfluidic. Lab Chip 15, 793–801.CrossRefGoogle 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
Xie, J., Jiang, J., Davoodi, P., Srinivasan, M. P. & Wang, C. 2015 Electrohydrodynamic atomization: a two-decade effort to produce and process micro-/nanoparticulate materials. Chem. Engng Sci. 125, 32–57.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
Supplementary material: File

Mandal et al. supplementary material

Mandal et al. supplementary material 1

Download Mandal et al. supplementary material(File)
File 111.5 KB