In this paper, a numerical model is developed that can simulate the unsteady axisymmetric free-surface flow of a perfectly conductive liquid under an electrostatic field. The effect of the electrostatic field is modeled by a force distributed on the liquid free surface. Assuming the liquid as a perfect conductor makes it possible to reduce the general electromagnetic equations to electrostatic equations. The Navier–Stokes equations are solved to find the velocity and pressure fields. The free surface advection and reconstruction are performed based on the volume-of-fluid method using Youngs’ algorithm. To evaluate the effect of the electric field on the free surface, the electrostatic potential is first solved for the entire computational domain. Next, the electric field intensity and the surface density of the electric charge are calculated on the free surface after which the electric force can be determined. The computational method for treating this force is similar to that of the surface tension using the continuum surface force method. The developed model is validated by a comparison between the calculated results with those of the analytics as well as experiments for an electrowetting scenario.

References

References
1.
Tomar
,
G.
,
Gerlach
,
D.
,
Biswas
,
G.
,
Alleborn
,
N.
,
Sharma
,
A.
,
Durst
,
F.
,
Welch
,
S. W. J.
, and
Delgado
,
A.
, 2007, “
Two-Phase Electrohydrodynamic Simulations Using a Volume-of-Fluid Approach
,”
J. Comput. Phys.
,
227
(
2
), pp.
1267
1285
.
2.
López-Herrera
,
J. M.
,
Popinet
,
S.
, and
Herrada
,
M. A.
, 2011, “
A Charge-Conservative Approach for Simulating Electrohydrodynamic Two-Phase Flows Using Volume-of-Fluid
,”
J. Comput. Phys.
,
230
(
5
), pp.
1939
1955
.
3.
Bateni
,
A.
,
Susnar
,
S. S.
,
Amirfazli
,
A.
, and
Neumann
,
A. W.
, 2005, “
A Novel Methodology to Study Shape and Surface Tension of Drops in Electric Fields
,”
Microgravity Sci. Technol.
,
16
, pp.
153
157
.
4.
Bateni
,
A.
,
Susnar
,
S. S.
,
Amirfazli
,
A.
, and
Neumann
,
A. W.
, 2004, “
Development of a New Methodology to Study Drop Shape and Surface Tension in Electric Fields
,”
Langmuir
,
20
, pp.
7589
7597
.
5.
Bateni
,
A.
,
Amirfazli
,
A.
,
Neumann
,
A. W.
, 2006, “
Effects of an Electric Field on the Surface Tension of Conducting Drops
,”
Colloids. Surf., A
,
289
, pp.
25
38
.
6.
Mugele
,
F.
, and
Buehrle
,
J.
, 2007, “
Equilibrium Drop Surface Profiles in Electric Fields
,”
J. Phys: Condens. Matter
,
19
, p.
375112
.
7.
Adamiak
,
K.
, 2006, “
Capillary and Electrostatic Limitations to the Contact Angle in Electrowetting-on-Dielectric
,”
Microfluid. Nanofluid.
,
2
, pp.
471
480
.
8.
Monnier
,
J.
,
Witomski
,
P.
,
Chow-Wing-Bom
,
P.
, and
Scheid
,
C.
, 2009, “
Numerical Modeling of Electrowetting by Shape Inverse Approach
,”
SIAM J. Appl. Math.
,
69
, pp.
1477
1500
.
9.
Song
,
S. P.
, and
Li
,
B. Q.
, 2000, “
Free Surface Profiles and Thermal Convection in Electrostatically Levitated Droplets
,”
Int. J. Heat Mass Transfer
,
43
, pp.
3589
3606
.
10.
Benignos
,
J. A. C.
, 2005, “
Numerical Simulation of a Single Emitter Colloid Thruster in Pure Droplet Cone-Jet Mode
,” Ph.D. thesis, Massachusetts Institute of Technology, MA.
11.
Yan
,
F.
,
Farouk
,
B.
, and
Ko
,
F.
, 2003, “
Numerical Modeling of an Electrostatically Driven Liquid Meniscus in the Cone–Jet Mode
,”
J. Aerosol Sci.
,
34
, pp.
99
116
.
12.
Young
,
P. M.
, and
Mohseni
,
K.
, 2008, “
Calculation of DEP and EWOD Forces for Application in Digital Microfluidics
,”
ASME J. Fluids Eng.
,
130(8)
, p.
081603
.
13.
Baird
,
E.
,
Young
,
P.
, and
Mohseni
,
K.
, 2007, “
Electrostatic Force Calculation for an EWOD-Actuated Droplet
,”
Microfluid. Nanofluid.
,
3
, pp.
635
644
.
14.
Chiarot
,
P. R.
,
Gubarenko
,
S. I.
,
Mrad
,
R. B.
, and
Sullivan
,
P.
, 2008, “
Application of an Equilibrium Model for an Electrified Fluid Interface Electrospray Using a PDMS Microfluidic Device
,”
J. Microelectromech. Syst.
,
17
(
6
), pp.
1362
1375
.
15.
Chiarot
,
P. R.
,
Gubarenko
,
S. I.
,
Mrad
,
R. B.
, and
Sullivan
,
P.
, 2009, “
On the Pulsed and Transitional Behavior of an Electrified Fluid Interface
,”
ASME J. Fluids Eng.
,
131
, p.
091202
.
16.
Gubarenko
,
S. I.
,
Chiarot
,
P. R.
,
Mrad
,
R. B.
, and
Sullivan
,
P.
, 2008, “
Plane Model of Fluid Interface Rupture in an Electric Field
,”
Phys. Fluids
,
20
, p.
043601
.
17.
Collins
,
R. T.
,
Harris
,
M. T.
, and
Basaran
,
O. A.
, 2007, “
Breakup of Electrified Jets
,”
J. Fluid Mech.
,
588
, pp.
75
129
.
18.
Collins
,
R. T.
,
Jones
,
J. J.
,
Harris
,
M. T.
, and
Basaran
,
O. A.
, 2008, “
Electrohydrodynamic Tip Streaming and Emission of Charged Drops From Liquid Cones
,”
Nat. Phys.
,
4
, pp.
149
154
.
19.
Zhang
,
H. B.
,
Yan
,
Y. Y.
, and
Zu
,
Y. Q.
, 2010, “
Numerical Modelling of EHD Effects on Heat Transfer and Bubble Shapes of Nucleate Boiling
,”
Appl. Math. Model.
,
34
, pp.
626
638
.
20.
Lastow
,
O.
, and
Balachandran
,
W.
, 2006, “
Numerical Simulation of Electrohydrodynamic (EHD) Atomization
,”
J. Electrost.
,
64
, pp.
850
859
.
21.
Keshavarz-Motamed
,
Z.
,
Kadem
,
L.
, and
Dolatabadi
,
A.
, 2009, “
Effects of Dynamic Contact Angle on Numerical Modeling of Electrowetting in Parallel Plate Microchannels
,”
Microfluid. Nanofluid.
,
8
, pp.
47
56
.
22.
Arzpeyma
,
A.
,
Bhaseen
,
S.
,
Dolatabadi
,
A.
, and
Wood-Adams
,
P.
, 2008, “
A Coupled Electro-Hydrodynamic Numerical Modeling of Droplet Actuation by Electrowetting
,”
Colloids Surf., A
,
323
, pp.
28
35
.
23.
Mohseni
,
K.
, and
Dolatabadi
,
A.
, 2006, “
An Electrowetting Microvalve: Numerical Simulation
,”
Ann. N.Y. Acad. Sci.
,
1077
(
1
), pp.
415
425
.
24.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
, 1992, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
, pp.
335
354
.
25.
Jackson
,
J. D.
, 1999,
Classical Electrodynamics
,
3rd ed.
,
Wiley
,
New York
.
26.
Melcher
,
R. J.
, 1981,
Continuum Electromechanics
,
MIT Press
,
Cambridge
.
27.
Berry
,
S.
, 2008, “
Electrowetting Phenomenon for Microsized Fluidic Devices
,” Ph.D. thesis, Tufts University, MA.
28.
Passandideh-Fard
,
M.
, and
Roohi
,
E.
, 2008, “
Transient Simulations of Cavitating Flows Using a Modified Volume-of-Fluid (VOF) Technique
,”
Int. J. Comput. Fluid. Dyn.
,
22
, pp.
97
114
.
29.
Bussmann
,
M.
, 2000, “
A Three-Dimensional Model of an Impact Droplet
,” Ph.D. thesis, University of Toronto, Toronto.
30.
Youngs
,
D. L.
, 1982, “
Time-Dependent Multi-Material Flow With Large Fluid Distortion
,”
Numerical Methods for Fluid Dynamics
,
K. W.
Morton
, and
M. J.
Baines
, eds.,
Academic
,
New York
, p.
273
.
31.
Meier
,
M.
,
Yadigaroglu
,
G.
, and
Smith
,
B. L.
, 2002, “
A Novel Technique for Including Surface Tension in PLIC-VOF Methods
,”
Eur. J. Mech. B/Fluids
,
21
, pp.
61
73
.
32.
Aulisa
,
E.
,
Manservisi
,
S.
,
Scardovelli
,
R.
, and
Zaleski
S.
, 2007, “
Interface Reconstruction With Least-Squares Fit and Split Advection in Three-Dimensional Cartesian Geometry
,”
J. Comput. Phys.
,
225
, pp.
2301
2319
.
33.
Jeans
,
J. H.
, 1927,
The Mathematical Theory of Electricity and Magnetism
,
5th ed.
,
Cambridge University Press
,
Cambridge
.
34.
Mugele
,
F.
, and
Baret
,
J. C.
, 2005, “
Electrowetting: From Basics to Applications
,”
J. Phys. Condens. Matter
,
17
, pp.
705
774
.
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