The dynamics of a droplet in shear flow under the influence of an external electric field are investigated by performing extensive numerical simulations. The study is carried out by solving two-dimensional electrohydrodynamic equations, and the interface is captured using a volume-of-fluid approach. It is observed that with an increase in the drop size, a confined drop exhibits enhanced deformation and preferred orientation with the flow direction. For the case of dielectric fluids, the deformation of the drops can be either enhanced or reduced by varying the permittivity ratio and electric field strength. The nature of the polarisation forces acting at the interface can be either compressive or tensile depending on the magnitude of the permittivity ratio. The local electric field intensity inside the drop is significantly altered due to the permittivity contrast between the fluids. The computations for leaky dielectric fluids reveal that the deformation of the drop can be effectively tuned by altering the permittivity as well as the conductivity ratios. The nature of charge accumulation and the electric forces acting at the interface are critically dependent on the relative contrast between the electric properties of both the phases. The conductivity ratio decides the magnitude and nature of charge at the upper and lower portions of the droplet interface, thereby fundamentally maneuvering the droplet dynamics under the applied electric field.
REFERENCES
1.
M.
Shapira
and S.
Haber
, “Low Reynolds number motion of a droplet in shear flow including wall effects
,” Int. J. Multiphase Flow
16
, 305
–321
(1990
).2.
V.
Sibillo
, G.
Pasquariello
, M.
Simeone
, V.
Cristini
, and S.
Guido
, “Drop deformation in microconfined shear flow
,” Phys. Rev. Lett.
97
, 054502
(2006
).3.
G. I.
Taylor
, “The viscosity of a fluid containing small drops of another fluid
,” Proc. R. Soc. London, Ser. A
138
, 41
–48
(1932
).4.
G. I.
Taylor
, “The formation of emulsions in definable fields of flow
,” Proc. R. Soc. London, Ser. A
146
, 501
–523
(1934
).5.
S.
Torza
, R.
Cox
, and S.
Mason
, “Particle motions in sheared suspensions XXVII. Transient and steady deformation and burst of liquid drops
,” J. Colloid Interface Sci.
38
, 395
–411
(1972
).6.
J.
Elmendorp
, “Dispersive mixing in liquid systems
,” in Mixing in Polymer Processing
(John Wiley & Sons
, 1991
), Chap. 2, pp. 17
–100
.7.
K. S.
Sheth
and C.
Pozrikidis
, “Effects of inertia on the deformation of liquid drops in simple shear flow
,” Comput. Fluids
24
, 101
–119
(1995
).8.
J.
Li
, Y. Y.
Renardy
, and M.
Renardy
, “Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method
,” Phys. Fluids
12
, 269
–282
(2000
).9.
Y.
Renardy
, “The effects of confinement and inertia on the production of droplets
,” Rheol. Acta
46
, 521
–529
(2007
).10.
Y. Y.
Renardy
and V.
Cristini
, “Scalings for fragments produced from drop breakup in shear flow with inertia
,” Phys. Fluids
13
, 2161
–2164
(2001
).11.
J.
Lee
and C.
Pozrikidis
, “Effect of surfactants on the deformation of drops and bubbles in Navier-Stokes flow
,” Comput. Fluids
35
, 43
–60
(2006
).12.
A.
Wagner
, L.
Wilson
, and M.
Cates
, “Role of inertia in two-dimensional deformation and breakdown of a droplet
,” Phys. Rev. E
68
, 045301
(2003
).13.
F.-D.
Rumscheidt
and S.
Mason
, “Particle motions in sheared suspensions XII. Deformation and burst of fluid drops in shear and hyperbolic flow
,” J. Colloid Interface Sci.
16
, 238
–261
(1961
).14.
M.
Kennedy
, C.
Pozrikidis
, and R.
Skalak
, “Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow
,” Comput. Fluids
23
, 251
–278
(1994
).15.
H. A.
Stone
, “Dynamics of drop deformation and breakup in viscous fluids
,” Annu. Rev. Fluid Mech.
26
, 65
–102
(1994
).16.
X.
Li
, R.
Charles
, and C.
Pozrikidis
, “Simple shear flow of suspensions of liquid drops
,” J. Fluid Mech.
320
, 395
–416
(1996
).17.
X.
Li
, H.
Zhou
, and C.
Pozrikidis
, “A numerical study of the shearing motion of emulsions and foams
,” J. Fluid Mech.
286
, 379
–404
(1995
).18.
L.
Liu
, J.
Chen
, and L.
An
, “Individual circular polyelectrolytes under shear flow
,” J. Chem. Phys.
149
, 163316
(2018
).19.
B.
Nath
, G.
Biswas
, A.
Dalal
, and K. C.
Sahu
, “Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field
,” Phys. Rev. E
97
, 063106
(2018
).20.
G. I.
Taylor
, “Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field
,” Proc. R. Soc. London, Ser. A
291
, 159
–166
(1966
).21.
E.
Lac
and G.
Homsy
, “Axisymmetric deformation and stability of a viscous drop in a steady electric field
,” J. Fluid Mech.
590
, 239
–264
(2007
).22.
J. Q.
Feng
, “Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number
,” Proc. R. Soc. London, Ser. A
455
, 2245
–2269
(1999
).23.
J. Q.
Feng
, “A 2D electrohydrodynamic model for electrorotation of fluid drops
,” J. Colloid Interface Sci.
246
, 112
–121
(2002
).24.
J. Q.
Feng
and T. C.
Scott
, “A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field
,” J. Fluid Mech.
311
, 289
–326
(1996
).25.
R. T.
Collins
, J. J.
Jones
, M. T.
Harris
, and O. A.
Basaran
, “Electrohydrodynamic tip streaming and emission of charged drops from liquid cones
,” Nat. Phys.
4
, 149
(2008
).26.
M. P.
Borthakur
, G.
Biswas
, and D.
Bandyopadhyay
, “Dynamics of drop formation from submerged orifices under the influence of electric field
,” Phys. Fluids
30
, 122104
(2018
).27.
A.
Fernández
, G.
Tryggvason
, J.
Che
, and S. L.
Ceccio
, “The effects of electrostatic forces on the distribution of drops in a channel flow: Two-dimensional oblate drops
,” Phys. Fluids
17
, 093302
(2005
).28.
O.
Ozen
, N.
Aubry
, D.
Papageorgiou
, and P.
Petropoulos
, “Monodisperse drop formation in square microchannels
,” Phys. Rev. Lett.
96
, 144501
(2006
).29.
D.
Saville
, “Electrohydrodynamics: The Taylor-Melcher leaky dielectric model
,” Annu. Rev. Fluid Mech.
29
, 27
–64
(1997
).30.
G.
Tomar
, D.
Gerlach
, G.
Biswas
, N.
Alleborn
, A.
Sharma
, F.
Durst
, S. W.
Welch
, and A.
Delgado
, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach
,” J. Comput. Phys.
227
, 1267
–1285
(2007
).31.
J.
Brackbill
, D.
Kothe
, and C.
Zemach
, “A continuum method for modeling surface tension
,” J. Comput. Phys.
100
, 335
–354
(1992
).32.
S.
Mandal
and S.
Chakraborty
, “Influence of interfacial viscosity on the dielectrophoresis of drops
,” Phys. Fluids
29
, 052002
(2017
).33.
M. R.
Hassan
, J.
Zhang
, and C.
Wang
, “Deformation of a ferrofluid droplet in simple shear flows under uniform magnetic fields
,” Phys. Fluids
30
, 092002
(2018
).34.
M. P.
Borthakur
, G.
Biswas
, and D.
Bandyopadhyay
, “Dynamics of deformation and pinch-off of a migrating compound droplet in a tube
,” Phys. Rev. E
97
, 043112
(2018
).35.
B.
Nath
, G.
Biswas
, A.
Dalal
, and K. C.
Sahu
, “Migration of a droplet in a cylindrical tube in the creeping flow regime
,” Phys. Rev. E
95
, 033110
(2017
).36.
M. P.
Borthakur
, G.
Biswas
, and D.
Bandyopadhyay
, “Formation of liquid drops at an orifice and dynamics of pinch-off in liquid jets
,” Phys. Rev. E
96
, 013115
(2017
).37.
S.
Popinet
, “Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries
,” J. Comput. Phys.
190
, 572
–600
(2003
).38.
J.
López-Herrera
, S.
Popinet
, and M.
Herrada
, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid
,” J. Comput. Phys.
230
, 1939
–1955
(2011
).39.
R.
Cimpeanu
, D. T.
Papageorgiou
, and P. G.
Petropoulos
, “On the control and suppression of the Rayleigh-Taylor instability using electric fields
,” Phys. Fluids
26
, 022105
(2014
).40.
C.
Ferrera
, J. M.
López-Herrera
, M. A.
Herrada
, J. M.
Montanero
, and A. J.
Acero
, “Dynamical behavior of electrified pendant drops
.” Phys. Fluids
25
, 012104
(2013
).41.
S.
Popinet
, “An accurate adaptive solver for surface-tension-driven interfacial flows
,” J. Comput. Phys.
228
, 5838
–5866
(2009
).42.
M. P.
Borthakur
, G.
Biswas
, D.
Bandyopadhyay
, and K. C.
Sahu
, “Dynamics of an arched liquid jet under the influence of gravity
,” Eur. J. Mech. B: Fluids
74
, 1
–9
(2019
).43.
H.
Hua
, J.
Shin
, and J.
Kim
, “Dynamics of a compound droplet in shear flow
,” Int. J. Heat Fluid Flow
50
, 63
–71
(2014
).44.
O.
Ajayi
, “A note on Taylor’s electrohydrodynamic theory
,” Proc. R. Soc. London, Ser. A
364
, 499
–507
(1978
).45.
J.-W.
Ha
and S.-M.
Yang
, “Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field
,” J. Fluid Mech.
405
, 131
–156
(2000
).46.
C.
Burcham
and D.
Saville
, “The electrohydrodynamic stability of a liquid bridge: Microgravity experiments on a bridge suspended in a dielectric gas
,” J. Fluid Mech.
405
, 37
–56
(2000
).47.
G. I.
Taylor
, “Disintegration of water drops in an electric field
,” Proc. R. Soc. London, Ser. A
280
, 383
–397
(1964
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
