We investigate the behavior of dielectric droplets and films placed onto a solid surface under the action of electric field of different configurations. The mesoscopic thermal multiphase lattice Boltzmann model [A. Kupershtokh, D. Medvedev, and I. Gribanov, “Thermal lattice Boltzmann method for multiphase flows,” Phys. Rev. E 98, 023308 (2018)] is used for simulation. Different configurations of electric field were produced by using dissected flat electrodes of various shapes. On a simple flat electrode, droplets elongate after the application of electric voltage. Quite different behavior was observed when the central round part of the electrode was made non-conductive. In this case, the droplet spreads under the action of a non-uniform electric field, and the breakup and the formation of an annular structure were observed. A film of dielectric liquid flowing along a solid surface made of conductive and non-conductive transversal stripes exhibits a variety of regimes. When the voltage is low, the action of electric field produces waves at the surface of liquid. At a high voltage, the liquid is pinned to the edges of stripes, and the flow may be stopped completely. The purpose of this article is precisely to attract experimenters to the study of this type of phenomena.

1.
A.
Kupershtokh
,
D.
Medvedev
, and
I.
Gribanov
, “
Thermal lattice Boltzmann method for multiphase flows
,”
Phys. Rev. E
98
,
023308
(
2018
).
2.
L.
Tonks
, “
A theory of liquid surface rupture by a uniform electric field
,”
Phys. Rev.
48
,
562
568
(
1935
).
3.
G.
Taylor
, “
Disintegration of water drops in an electric field
,”
Proc. R. Soc. A
280
,
383
397
(
1964
).
4.
N.
Zubarev
, “
Formation of conic cusps at the surface of liquid metal in electric field
,”
JETP Lett.
73
,
544
548
(
2001
).
5.
N.
Zubarev
, “
Self-similar solutions for conic cusps formation at the surface of dielectric liquids in electric field
,”
Phys. Rev. E
65
,
055301(R)
(
2002
).
6.
K.
Bobrov
,
N.
Zubarev
, and
O.
Zubareva
, “
Conditions for explosive growth of free surface perturbations for a dielectric liquid in a normal electric field in confined axisymmetric geometry
,” in
Proceedings of 20th IEEE International Conference on Dielectric Liquids
(
IEEE
, Roma, Italy,
2019
), pp.
1
4
.
7.
C.
Zhou
and
S.
Troian
, “
Multiplicity of inertial self-similar conical shapes in an electrified liquid metal
,”
Phys. Rev. Appl.
15
,
044001
(
2021
).
8.
S.
Reznik
,
A.
Yarin
,
A.
Theron
, and
E.
Zussman
, “
Transient and steady shapes of droplets attached to a surface in a strong electric field
,”
J. Fluid Mech.
516
,
349
377
(
2004
).
9.
L.
Corson
,
C.
Tsakonas
,
B.
Duffy
,
N.
Mottram
,
I.
Sage
,
C. C. V.
Brown
, and
S.
Wilson
, “
Deformation of a nearly hemispherical conducting drop due to an electric field: Theory and experiment
,”
Phys. Fluids
26
,
122106
(
2014
).
10.
D.
Zong
,
Z.
Yang
, and
Y.
Duan
, “
Wettability of a nano-droplet in an electric field: A molecular dynamics study
,”
Appl. Therm. Eng.
122
,
71
79
(
2017
).
11.
Y.
Tian
,
H.
Wang
,
Q.
Deng
,
X.
Zhu
,
R.
Chen
,
Y.
Ding
, and
Q.
Liao
, “
Dynamic behaviors and charge characteristics of droplet in a vertical electric field before bouncing
,”
Exp. Therm. Fluid Sci.
119
,
110213
(
2020
).
12.
M.
Gibbons
,
A.
Garivalis
,
S.
O'Shaughnessy
,
P.
Di Marco
, and
A.
Robinson
, “
Evaporating hydrophilic and superhydrophobic droplets in electric fields
,”
Int. J. Heat Mass Transfer
164
,
120539
(
2021
).
13.
K.
Takeda
,
A.
Nakajima
,
K.
Hashimoto
, and
T.
Watanabe
, “
Jump of water droplet from a super-hydrophobic film by vertical electric field
,”
Surf. Sci.
519
,
L589
L592
(
2002
).
14.
J.
Liu
and
S.
Liu
, “
Dynamics behaviors of droplet on hydrophobic surfaces driven by electric field
,”
Micromachines
10
,
778
(
2019
).
15.
A.
Kupershtokh
, “
Three-dimensional modeling of droplets dynamics of liquid dielectric on wettable surface in electric field
,”
J. Phys. Conf. Ser.
1677
,
012067
(
2020
).
16.
A.
Samanta
, “
Effect of electric field on an oscillatory film flow
,”
Phys. Fluids
31
,
034109
(
2019
).
17.
V.
Pandey
,
G.
Biswas
, and
A.
Dalal
, “
Effect of superheat and electric field on saturated film boiling
,”
Phys. Fluids
28
,
052102
(
2016
).
18.
D.
Medvedev
and
A.
Kupershtokh
, “
Use of the lattice Boltzmann equation method to simulate charge transfer and electrohydrodynamic phenomena in dielectric liquids
,” in
Proceedings of the Second International Workshop on Electrical Conduction, Convection and Breakdown in Fluids
, Grenoble, France, edited by
P.
Atten
and
A.
Denat
(
IEEE
,
2000
), pp.
60
63
.
19.
A.
Kupershtokh
and
D.
Medvedev
, “
Lattice Boltzmann method in electrohydrodynamic problems
,”
J. Electrost.
64
,
581
585
(
2006
).
20.
G.
McNamara
and
G.
Zanetti
, “
Use of the Boltzmann equation to simulate lattice-gas automata
,”
Phys. Rev. Lett.
61
,
2332
2335
(
1988
).
21.
Y.
Qian
,
D.
d'Humières
, and
P.
Lallemand
, “
Lattice BGK models for Navier-Stokes equation
,”
Europhys. Lett.
17
,
479
484
(
1992
).
22.
P.
Lallemand
and
L.-S.
Luo
, “
Theory of the lattice Boltzmann method: Dispersion, dissipation Galilean invariance and stability
,”
Phys. Rev. E
61
,
6546
6562
(
2000
).
23.
D.
D'Humieres
,
I.
Ginzburg
,
M.
Krafczyk
,
P.
Lallemand
, and
L.-S.
Luo
, “
Multiple-relaxation-time lattice Boltzmann models in three dimensions
,”
Philos. Trans. R. Soc. A
360
,
437
451
(
2002
).
24.
J.
Koelman
, “
A simple lattice Boltzmann scheme for Navier–Stokes fluid flow
,”
Europhys. Lett.
15
,
603
607
(
1991
).
25.
A.
Kupershtokh
, “
New method of incorporating a body force term into the lattice Boltzmann equation
,” in
Proceedings of the 5th International EHD Workshop
(
University of Poitiers
,
Poitiers, France
,
2004
), pp.
241
246
.
26.
A.
Kupershtokh
, “
Criterion of numerical instability of liquid state in LBE simulations
,”
Comput. Math. Appl.
59
,
2236
2245
(
2010
).
27.
I.
Ginzburg
and
P.
Adler
, “
Boundary flow condition analysis for the three-dimensional lattice Boltzmann model
,”
J. Phys. II
4
,
191
214
(
1994
).
28.
X.
Shan
and
H.
Chen
, “
Lattice Boltzmann model for simulating flows with multiple phases and components
,”
Phys. Rev. E
47
,
1815
1819
(
1993
).
29.
R.
Zhang
and
H.
Chen
, “
Lattice Boltzmann method for simulations of liquid-vapor thermal flows
,”
Phys. Rev. E
67
,
066711
(
2003
).
30.
A.
Kupershtokh
,
D.
Medvedev
, and
D.
Karpov
, “
On equations of state in a lattice Boltzmann method
,”
Comput. Math. Appl.
58
,
965
974
(
2009
).
31.
M.
Swift
,
W.
Osborn
, and
J.
Yeomans
, “
Lattice Boltzmann simulation of nonideal fluids
,”
Phys. Rev. Lett.
75
,
830
833
(
1995
).
32.
M.
Swift
,
E.
Orlandini
,
W.
Osborn
, and
J. M.
Yeomans
, “
Lattice Botzmann simulations of liquid-gas and binary fluid systems
,”
Phys. Rev. E
54
,
5041
5052
(
1996
).
33.
Y.
Qian
and
S.
Chen
, “
Finite size effects in lattice-BGK models
,”
Int. J. Mod. Phys. C
8
,
763
771
(
1997
).
34.
X.
He
and
G.
Doolen
, “
Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows
,”
J. Stat. Phys.
107
,
309
328
(
2002
).
35.
R.
Nourgaliev
,
T.
Dinh
,
T.
Theofanous
, and
D.
Joseph
, “
The lattice Boltzmann equation method: Theoretical interpretation, numerics and implications
,”
Int J. Multiphase Flow
29
,
117
169
(
2003
).
36.
A.
Kupershtokh
and
D.
Medvedev
, “
Dielectric droplet on a superhydrophobic substrate in an electric field
,” in
Proceedings of 20th IEEE International Conference on Dielectric Liquids
(
IEEE
,
Roma, Italy
,
2019
), pp.
1
4
.
37.
A.
Nemykina
and
D.
Medvedev
, “
Behavior of a bubble in dielectric liquid in uniform and non-uniform electric fields
,”
Interfacial Phenom. Heat Transfer
7
,
323
330
(
2019
).
You do not currently have access to this content.