3rd International Conference on Materials Engineering, Manufacturing Technology and Control (ICMEMTC 2016)
Investigation of the Flow Characteristics of Droplets in Non-uniform
Electric field
Zhonghua Gao
School of Electric Power Engineering, North China Electric Power University, Baoding
071000, China.
1194892568@qq.com
Key Words: Non-uniform electric field, droplets, deformation, Numerical simulation.
Abstract. The motion behavior of droplets under non-uniform electric field is an important branch
the study of electro-hydrodynamic. In this paper, the theoretical analysis of the force of droplets in
non-uniform electric field are carried out, and the study found that the deformation, surface charge
density, velocity and other flow characteristics of droplets will change in the effect of non-uniform
electric field.
In order to study those flow characteristics and the influence of electric field intensity on the
deformation and displacement degree of droplets, we will establish the simulation model of droplets
and the non-uniform electric field.The results show that the polarization charge distribution on the
surface of droplets is not uniform, and the charge density at the center of the electric field is
increased gradually; the increase of the electric field intensity in a certain range can increase the
droplet shape variable and the moving velocity of the droplet to the concentrated area of the electric
field.
Introduction
The electric field is the fundamental driving force for the liquid drop deformation. Under the
non-uniform electric field, the droplets is deformed along the direction of the electric field line and
the displacement occurs at the same time to the field intensity concentration.The relevant scholars
have carried out the research on the movement behavior of the droplets under the uniform electric
field .For example,the dynamics of deformation and rupture of a droplet in uniform electric field is
studied by Kazimierz[1]etc. However, previous studies did not involve the movement behavior of
liquid droplet deformation and displacement under the action of non-uniform electric field.
Therefore, in this paper, based on the level set method of two-phase flow field in Multiphysics
COMSOL 4.4, simulation model is established to study the distribution of the potential, electric
field, droplets and the velocity vectors around the fluid and the deformation and displacement
behaviors of droplets.
Model Assumptions
To simplify the problem, we make the following assumptions :

The molecular shape of droplet is spherica.

Fluid is an incompressible ideal fluid.

Assuming that there are other fluids around the droplet, the droplet is subjected to the
viscous effect of the surrounding fluid.
Theoretical analysis in non-uniform electric field
Force of droplets in a non-uniform electric field
The droplet molecule can be regarded as an electric dipole, the electric dipole moment: pe  ql
(1)
Where l represents the distance between the point charge. As is shown in Figure 1 below, the
electric field force is less than 0 in the non-uniform electric field:
© 2016. The authors - Published by Atlantis Press
996
F  qqE ( r  l )  qE
q ( r )  q (l x
E
E
E
)  ( p e   ) E  q (l   ) E
 ly
 lz
y
z
x
(2)
Fig.1 Forrce of an electtric droplet in a non-uniform
m electric field
ld
Force of per unit voolume of liq
quid in a noon-uniform field:
f
1
f  nF  (npe  ) E  ( P  )E  [ 0 ( r  1) E  ]E   0 ( r  1)E 2
2
(3)
Where n representts liquid mo
olecular dennsity,  0 represents perm
mittivity off vacuum,  r representss
relative perrmittivity.
By the formula abbove, the fo
orce size off the unit vo
olume is prroportional to the grad
dient of thee
square of thhe electric field
f
intensiity.
3.2 Analyssis of the motion
m
beha
avior of drooplets in a non-unifor
n
m electric ffield
e
fieldd, the shapee of the drop
plet is transsformed from
m sphericall
Unnder the noon-uniform electric

to ellipsoiddal and the droplets is deformed aalong the diirection of electric
e
fieldd line and displaced
d
too
the field inntensity concentration.
Inn the process of deforrmation, thee liquid dro
oplets are subjected
s
too the visco
osity of thee

surroundinng fluid.
Droplet Siimulation model
m
Droplet Siimulation model
m
Assuming that the droplet mo
orphology i s spherical,,the simulattion model: liquid drop
p suspendedd
in oil is as follows:
Fig.2 Simulation m
model of water droplets suspended in oil
Initializatiion of the parameters
p
s
Material paarameter
Table 1 Simulatioon of the inpu
ut parameters of droplet
N
Numerical value
Unitt symbol
D
Droplet diameeter（AC）
4.0
mm
electrode voltage
v
400
V
V/mm
Initial velocity off water dropleet
5.0
m
mm/s
Droplet dennsity  A
1000
kgg / m 3
Oil densiity 1
880
kgg / m 3
Waater droplet coonductivity k
5.5
S  m 1
997
Non-unifoorm electricc field Simu
ulation mod
del
In ordeer to study the deform
mation and movement law of thee droplet uunder the non-uniform
n
m
electric fieeld, the simulation analysis
a
waas carried out by thee multi fieeld couplin
ng softwaree
Multiphysiics COMSO
OL 4.4.
Non-unifoorm electricc field mod
del-Coaxial cylinder ellectrode mo
odel
The elecctrode is coonnected to the externall electrode, the inner ellectrode is ggrounded.(R
R1=5mm，
R2=10mm
m)
Fig.3 Siimulation resuults of coaxial cylindrical ellectrodes
As is shhown in fig.3, the distriibution of e lectric potential is conssistent withh electric fieeld intensityy,
and along tthe radius direction
d
aw
way from thee center to the
t far, the electric
e
poteential is low
wer.
Interior an
nd exteriorr electric po
otential disstribution of
o droplets
Fig.4 Interiorr and exterior electric poten
ntial distributio
on of dropletss
From thhe above diiagram, the internal annd external electric pottential distrribution hav
ve a certainn
law：Alonng the radiuus direction away from the center to
t the far, th
he electric ppotential is lower.
Droplet deeformation
n and displa
acement
Deform
mation[2] andd displacem
ment of the droplet in t=0s
t
to t=0
0.1s periodicc are simullated in thee
following ffigure.
t=
=0s
t=0.05s
t==0.1s
Fig.5 Singgle droplet deeformation
As is shhown abovee,the dropleet is graduallly extended
d from spheerica to elliipsoidal. Which
W
showss
that the drooplet is defoormed along
g the directiion of the electric
e
field
d line and thhe displacem
ment occurss
at the samee time to thee field inten
nsity concenntration.
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Deformatiion under different
d
electric field
d intensity
E=400
0V/mm
E=100V
V/mm
Fig.6 Deeformation unnder different electric field
d intensity
F
th
he increasee of electric field inteensity,the m
maximum deformation
d
n
As is sshown in Fig.6,with
degree of droplets inncrease alsso. When tthe field in
ntensity inccreases to a certain degree,
d
thee
deformatioon degree is too large and even ruppture.[3]
Summary
(1)Undeer non-unifo
form electricc field, the polarization
n charge deensity is graadually incrreased from
m
the middlee to both endds of the drroplet, and aat the end of
o the conceentration off electric fieeld intensityy
to reach the maximum
m.
d
along
a
the diirection of the electricc field line and the diisplacementt
(2)The droplet is deformed
me to the field intensityy concentratiion.
occurs at thhe same tim
(3)Withh the increasse of electriic field inteensity, the deformation
d
n degree of droplets inccrease also..
And the drroplet will be
b ruptured under
u
high electric fielld intensity.
Referencees
[1]Kazimieerz Adamiaak, Jerzy M. Floryan, ““Dynamics of water drroplet distor
ortion and breakup in a
uniform eleectric field.” IEEE T. IND.
I
APPL
L, vol. 47, pp
p. 2374-238
82, 2011.
[2] Zhang Jun, He Hongzhou,
H
Huang Guaanxing. Sim
mulation off droplet deeformation in uniform
m
field with dissipativee particle dynamics approach
h[J].CIESC Journal,20
014,65(10)::
electric fi
3872-38777.
[3]Chen Qiingguo, Liaang Wen, So
ong Chunhuui. Effect off electric fielld strength oon crude oil emulsion’ss
demulsification and deehydration[[J]. High Vooltage Engin
neering, 2014, 40 (1):1173-180
999