2003 Annual Repo Con e ence
on
Elec ical Insula ion
and
Dielec ic Phenomena
Dynamics and de o ma ion o
a
d op
in
a
DC
elec ic ield
A. Khaya i', A.
T.
Pe ez',
F.
J.
Ga cia' and A. Cas ellanos'
'
Dp o. de Elec 6nica y Elec mmagne ismo, Facul ad de Fkica
AV& Reina Me cedes s/n,
41012
Se illa, Spain.
Dp o. deFisicaAplicada1, E.U.I.T.A., C a. Uue akm.
1,41013
Se illqSpain.
Abs ac :
We conside
a
single conduc ing d op in
suspension in
a
poo ly conduc ing liquid be ween
wo
ho izon al elec odes. When
a
DC
ield is applied o he
elec odes, he d op cha ges and ises wi hin he'liquid,
hen alls down
as
i s cha ge leaks away, due o he
ini e
elechic elaxa ion ime o he liquid. The d op keeps
bouncing
as
long
as
he high ol age applied
emains
abo e
a
minimum h eshold. We ocus
ou
s udy
on
he
dynamics and he de o ma ion
o
a
wa e d op be o e he
li -o and du ing
i s
mo ion.
Elec odes o di e en
ma-
e ials
a e
used
in
o de
o
illus a e he ole o in e acial
ene gy be ween he elec ode and he wa e .
In oduc ion
When
a
conduc ing pa icle imme sed in
a
poo ly con-
duc ing liquid be ween
wo
elec odes is subjec ed o an
ex e nal elec ic ield,
a
bouncing mo ion o he pa icle
is obse ed. The dynamics
o
he cha ged pa icle de-
pends
on
many pa ame e s, namely he pa icle size and
physical cha ac e is ics o bo h he pa icle and he su -
ounding luid. While solid pa icles
a e
mo e easy o
s udy, luid phase pa icles (d ops o bubbles) p esen
a
mo e complex beha io , due o hei su ace de o ma-
ion and possible b eakup. The de o ma ion
o
liquid
d ops
by an elec ic ield has been ex ensi ely s udied. I
was expe imen ally ound by many au ho s
[I,
21
ha ,
in
su icien ly weak elec ic ields, conduc ing d ops elon-
ga e along he ield di ec ion, p oducing
a
p ola e shaped
Tbe p esen pape ocuses
on
he s udy o dynamics
and de o ma ion o
a
d op ha bounces unde he ac ion
o
an
elec ic ield. This s udy comes
as
con inua ion
o he s udy done by he au ho s
on
a
solid conduc ing
sphe e
131.
Expe imen al se
up
The expe imen al se -up
consis s
o
a
cubic cell
made
o
Plexiglass and
i s
dimensions
a e
70x70~50
mm.
In-
side he cell wo elec odes,
o
ci cula shape and
20
mm
adius, a e ixed hoen ally
2
cm apa . A me allic ing,
1
mm
wid h and adius
20
mm,
es s
on
he lowe elec-
ode in o de o compensa e o he ield di e gence a
he
cen e
o
he
elec odes.
d op.
0-78057910-1/03/$17.00 02003
IEEE
The uppe elec ode is connec ed o
a
high ol age
supply, while he lowe one
is
connec ed
o
a
compu e
h ough
an
ampli ie and
an
acquisi ion boa d. The cell
is illed wi h
a
poo ly conduc ing liquid. A d op o wa-
e is pu ini ially a es upon he lowe elec mde. I s
olume is measu ed wi h an accu a e mic opipe e. The
olume
o
he d ops used was
IO&
which co esponds
o
a
adius
1.337
mm.
The con inuous phase liquid
used was co n oil o densi y
916
kg/m3, pe mi i i y
e
=
26.9~
F/m
and conduc i i y
U
=
19x
S/m.
Conduc i i y and pe mi i i y ha e been measu ed by
a
conduc i ime e
LDTRP-2
supplied by
IRLAB.
Along
wi h he aluminum o iginal elec ode o he
expe imen al cell, we used
h ee
discs which could
be
placed abo e he lowe elec ode. These h ee discs a e
made o s eel, coppe and i anium and
a e
o he same
diame e
as
he aluminum elec ode
ked
in he cell.
Coppe and s eel elec odes
a e
I
mm
hick, while he
i anium one has
a
hickness o
3
mm.
A high speed came a
VDS
model HCCIOOO was
used
o
eco d he mo ion o he d op. A ame g ab-
be pe mi s he eco d o bi map images a
a
esolu ion
o
1024x
1024
pixels. We
used
a
ee
so wa e,
ImageJ,
and p og ams de eloped wi h Ma lab o p ocess images
and mce he d op p o ile.
Time
o
ligh
and
li -o
ol age
When he d op is bouncing elechic pulses
a e
egis e ed
in
he ex e nal ci cui a e e y impac wi h he elec ode.
The ime elapsed be ween cu en pulses co esponds o
he ime o igh o he d op. Fo ol ages abo e, bu
close o, he li -o ol age he pa icle bounces upon he
lowe elec ode. Also, an oscilla o y mo ion be ween he
wo
elec odes was obse ed o some ange
o
ension
wi hou b eakup o he d op.
Le
us
s udy i s bow he ime o igh
o
he d op
depends
on
he applied elec ic ield.
As
long
as
he
d op is no oo de o med and he i s de achmen has oc-
cu ed, we expec he model o
a
solid pa icle
[31
o be
o applica ion, wi h he app op ia e change in he d ag
coe icien .
In
his
model he ine ial e m is neglec ed
and he mo ion o he pa icle
is
de e mined by he equi-
lib ium be ween he elec ic, g a i y and d ag o ces.
The
elec ic o ce is exp essed
as:
Fe
=
QoeC 'E,
.
682
whe e
is he ime elapsed since he las impac and
7
=
€/U
is he elec ic elaxa ion ime o he liquid.
(e
and
U
a e, espec i ely, he pe &li i y and he conduc-
i i y o he liquid).
Qo
is he ini ial cha ge o he pa -
icle acqui ed by con ac wi h he lowe elec ode. I
is
exp essed
as
[41:
In
he case o a solid pa icle, he adhesion o ce be-
ween he pa icle and he elec ode is negligible o
a
millime ic size pa icle. The e o e he minimum h esh-
old
Ec
o he elec ic ield needed
o
li he pa icle
co esponds o he equilib ium be ween he elec ic and
he g a i y o ces. The e o e we can deduce
E,
om:
QoEc
=
(m
-
m )g.
In eg a ing he equa ion o mo ion
[3]
o
a
DC
ield
leads o
a
ela ion be ween he ime o ligh
A
and he
applied ield
Eo:
In
he case o
a
luid phase pa icle,
a
d op, he main
di e ences wi h he solid s a e pa icle
a e
he de o ma-
ion o he d op and he adhesion o he elec ode. The
adhesion o ce ac s jus when he pa icle is in con ac
wi h he elec ode. Howe e du ing
a
ebound he e is
no physical con ac be ween he d op and he elec ode.
T%is
is due o he ac ha elec ic b eakdown akes place
when he d op is e y close o he elec ode.
This
b eak-
down p oduces an elec ical conduc ing pa h ha cha ges
he d op be o e he con ac is p oduced. Expe imen s
show ha he cha ging p ocess, when he d op comes
close
o
he elec ode, is
a
e y quick p ocess. The elec-
ic o ce domina es and he ebound is e y as and
oc-
cu s be o e he con ac is p oduced.
On
he o he hand,
he d op de o ms much a he impac han when in ligh ,
bu du ing he ligh o he d op, which akes ew
sec-
onds, i s shape can be app oxima ed
o
a sphe e.
In
con-
clusion, he model de i ed o he ime o ligh o
a
solid
pa icle is applicable o
a
d op
as
long
as
he i s de ach-
men
has occu ed.
We mus emphasize he e ha he h eshold ield
E,
de e mined om equilib ium be ween elec ic o ce and
g a i y is no he li -o ield in he case o
a
d op.
In-
deed. he elec ic o ce necessa y o i s li he d op has
o o e come bo h g a i y and adhesion o ce. Thus he
li -o ield, ha we will e e o
as
El, -o .
mus
he
highe han
E,.
E,
can be measu ed expe imen ally by
slowly dec easing he ol age o an al eady bouncing
d op un il i e u ns o es . We ha e obse ed ha he
ol age a which he
d op
i s
de aches om he elec-
ode is clea ly highe han ha a which i e u ns
o
es
when dec easing he ol age.
Expe imen al eco ds o ime o ligh o he d op o
a
ange
o
applied elec ic ield
i s
well
he
heo e ical
model
(2).
F om he i we ge
a
alue o he h eshold
ol age
Ec
=
1.1
x
IO5
V/m, and a elaxa ion ime
T
=
2.0
s.
These alues
a e
o be compa ed wi h he alue
di ec ly obse ed o
E,, EYP
=
1.6
x
10'
Vim, and he
alue ob ained om he liquid p ope ies,
e2P
=
./U
=
1.4s.
When he d op is a es
on
he elec ode, and due o
he adhesion
o
he d op
o
he elec ode,
an
inc ease o
he applied ield leads o
a
highe de o ma iono he
d op
be o e
i
li s.
Two
scena ios
a e
possible a li -o . One
is ha he d op li s en i ely conse ing i s ini ial olume
and eco e ing
a
less de o med sphe oidal shape. The
second possibili y is ha he majo olume o he d op
ises wi hin he su ounding liquid, and
a
small d ople
emains s uck a he elec ode.
In
he la e case he d op
engende s egula bounces upon he ip o he d ople a
es
on
he elec ode. I he ol age is kep
a
some alue
sligh ly highe han he
lie-o
h eshold,
an
amoun o
he liquid in he es ing d ople passes o he mo ing d op
a each con ac . A e
a
ew ebounds he d op eco e s
comple ely i s ini ial olume. Then,
as
long
as
he ap-
plied ol age is kep somewha abo e he h eshold, he
d op bounces wi hou any
loss
o
mass.
Wha kind o
beha io we encoun e depends
on
he ma e ial chosen
o he elec ode.
To
e alua e he Li -o ield
Elq-,, .
we ha e o
conside he adhesion
o
he d op
o
he elec ode. The
adhesion o ce, which ends o e ain he d op in con ac
wi h he elec cde can be exp essed as:
F,
=
2 T
sin
0,
whe e
8
is he con ac angle and
T
he adius
o
con ac
a ea.
Fo
a
small
con ac adius
he con ac angle is
a12
<
0
<
a.
The li -o o he d op equi es an elec ic
o ce equal o he adhesion plus he g a i y o ces, ha
is:
QoEli -,,
=
ZXT~
+
(m
-
ml)g,
whe e we ha e
aken
sin8
2
1.
Assuming ha he d op cha ge
Qo
is
ha o he ini ial sphe ical d op
(I),
an es ima ion o he
minimum elec ic ield necessa y o li he d op agains
g a i y and adhesion o ce can be exp essed
as
ollows:
S udying he d op de o ma ion ( ollowing sec ions),
pe mi s an es ima ion o he su ace ension
7
z
1.0
dim.
The e o e an e alua ion
o
he li -o ield o
a adius con ac
T
=
0.44
mm and
R
=
1.34 mm,
gi es
a
alue:
El; -.
=
1.63~
IO5
Vlm.
The expe imen al
alue ound was
E:$-o
=
1.71~10~
V/m,
which is
nea he heo e ical alue.
E*i -.
2
=
w.
683
I
0.18
Figu e
1:
De o ma ion
o
a bouncing wa e d op o adius
I
.34
nun
as
unc ion
o
E;,
De o ma ion
o
he
d op
Fo
an
ellipsoidal d op o
semi
axes
a
>
b,
he deg ee
o
d op de o ma ion can be exp essed con enien ly by
he pa ame e :
D
=
9
wi h
R
he adius
o
he non-
de o med sphe ical d op. Fo a non cha ged conduc -
ing dmp
in
a cons an elec ic ield, he de o ma ion is
de e mined by minimizing he o al ene gy
o
he d op:
elec ic plus su ace ene gy. Acco ding o Taylo
[ll,
o
small de o ma ions is:
D
=
e
=
:+.
In igu e
I
we show how he de o ma ion
D
o he
d op a ies wi h he applied ield. F om he slope
o
he
bes
i
we ob ain
an
es ima ion
o
7
=
1
"/m.
In
his
es ima ion we suppose ha he d op has los enough
cha ge o he heo y o
a
neu al d op o
be
o applica-
ion.
As
we
men ioned a he
beginning,
when he d op
is
s ill a con ac wi h he elecnode, i s de o ma ion un-
de an elec ic ield depends highly on he magni ude o
he adhesion o ce. The go e ning pa ame e s a e he
a ea o con ac and he angle o con ac . Fo li -o
o
he d op o
be
possible, he a ea o con ac has o be
small
o
equi alen ly, he con ac angle
has
o
he
high.
This
is ela ed o he we ing cha ac e is ic o he elec-
ode
ma e ial. Pa ial weking su aces ha e a con ac
angle less han
90"
while no we ing
(o
hyd ophobic)
su aces ha e con ac angles g ea e han
90".
The a ea and angle
o
con ac highly a ec he shape
aken by he d op and he li -o p ocess. We ha e
oh-
se ed
his
p ocess wi h ou di e en ypes o elec ode
ma e ial. Along wi h aluminum elec ode, we used s eel,
i anium and coppe . I was seen ha o
s eel
and cop
Figu e
2
A
wa e d op
o
adius
1.34 nun
es ing
on a s eel
elec cde
and
subjec ed o
an
elecmc ield a)
Eo=
0,
b)
Eo
=
1.316~10~
Vlm,
c)
Eo
=
1.7llxl@
Vlm,
d)
a e
li -o
a
Eo
=
1.716
x105
Vlm.
pe elecuode li -o and bounces o small d ops a e pos-
sible. While o aluminum and i anium elec odes
no
li -o
is possible. In
his
case, inc easing he applied
elec ic ield leads o
a
de o ma ion
o
he d op in o a
bell
shape. Fu he inc ease o he elec ic ield leads
i s o oscilla ions
o
he uppe ip
o
he d op and hen
o an ejec ion o small d ople s om
his
ip owa ds he
uppe elec ode.
Figu e
2
shows
a
wa e d op imme sed
in
co n
oil
on a s eel elec ode o di e en elec ic ield alues.
In
he las ame he d op is mo ing wi hii he liquid jus
a e i s li -o . A
lin ,
he shape o he d op
is
qui e
sphe ical and he con ac adius es ima ed om eco ded
images is abou
0.44
mm.
The con ac angle is
-
160"
wi h no applied ield.
This
angle eaches
a
alue
-
115O
o a alue o he elec ic ield
EO
=
1.71
x
IO5
V/m.
The de o ma ion
D
o he d op o a s eel elec ode
is
plo ed in igu e
3
as
a
unc ion o he elec ic ield.
I is seen ha he deg ee o de o ma ion, o a d op a -
ached o he elec ode, is la gely g ea e han ha o
he bouncing mo ion. Also i s dependence is no linea .
A heo e ical model o he de o ma ion in his case is
much mo e in ol ed han o he d op
in
mo ion. The
cha ge on he d op is no negligible and i s dis ibu ion
o e he su ace depends
on
he shape.
In
um, his shape
will
be
de e mined by he local equilib ium o he elec-
os a ic, g a i y and capilla y p essu es on o he su ace.
The e o e, a comple e heo e ical model mus ake in o
684
Figu e
3
De o ma ion o a wa e d op o
adius
1.34
mm,
a
es
on
a s eel elec mde and subjec ed o an elec ic ield
EO.
accoun he elec ic ield dis ibu ion a ound he cha ge
Fo i anium elec ode, he con ac adius is es i-
ma ed o he
1.1
mm
which is abou wo imes and hal
ha o
a
s eel elec ode. Tha
is
he
a ea
o con ac
is
mo e han six imes g ea e o he i anium elec ode
han he s eel elec ode. The con ac angle wi hou ex-
e nal ield is es ima ed
o
be
-llOO;
and o
&
=
2.71x105V/m (nea b eakup alue) i eaches app oxi-
ma ely
90",
(see igu e
4).
'Ilk
is consis en wi h
a
less
in e acial ene gy o he in e ace i anium-wa e han
o he in e ace s eel-wa e .
d op.
Conclusions
We ha e ca ied ou an expe imen al s udy
o
a bouncing
d op unde e ec o an ex e nal elec ic ield. I has been
shown ha a o me ly es ablished model o a bounc-
ing hall desc ibes well he dynamics
o
he d op in he
limi o small de o ma ion. Unlike he solid pa icle case,
wo
c i ical ol ages a e o impo ance. he h s one is
he h eshold ol age necessa y o he
i s
li -o o he
d op. me second one is ha o which he d op e u ns
o es when dec easing he ol age. The o me is highe
han he la e due
o
he adhesion o ce which ac s he-
o e he
i s
li -o .
The de o ma ion o he d op in mo ion o he ange
o elec ic ield used (be ween
1
and
2.5
x
IO5
V/m) was
ound o be less impo an
in
compa ison o he de o ma-
ion be o e he i s li -o . Indeed, he de o ma ion can
each
a
alue o
0.65
o a wa e d op o adius
-
1.34
mm
be o e i li s, whe eas du ing i s mo ion he de o -
FiguFe
4
Shape aken
by
a
d op o
adius
1.34
m
es ing
on
a
imium
elecmde,
a)
wi hou applied ield,
b)
wi h ield
EO
=1.18x105V/m,c)Eo= 1.77x1O5V/m,d) Eo=2.71x105
V/m.
ma ion do no exceed
0.3.
I has
also
been shown ha
he ma e ial om which he elec ode
is
made in luence
highly he deg ee o he de o ma ion and he c i ical ield
necessa y o li -o .
As
a consequence, o some ma-
e ial he con ac a ea
is
so
high ha he adhesion o ce
p e en s any li -o o he d op. Inc easing he applied
ield only leads
o
he b eakup o he d op.
Acknowledgmen s
This
wo k has been ca ied ou wi h hancial suppo
om he Spanish Minis e io de Ciencia y Tecnologia
(MCYT) unde esea ch p ojec
BFM2000-1056.
Re e ences
[I]
G.
I.
Taylo . Desin eg a ion
o
wa e d ops in an
elec ic ield.
Pmc.
R.
Soc.
Lund.
A
280,
pp
383-
397,1964.
[2]
J.
-W.
Ha and
S.
-M. Yang. De o ma ion and
b eakup
o
new onian and non-New onian conduc -
ing d ops in an elec ic ield.
J.
Fluid
Mech.
ol.
405,
pp
131-156,2000.
[3]
A.
Khaya i and
A.
T. P6 ez. Cha ge acqui ed by
a
sphe ical ball bouncing
on
an elec ode: compa i-
son
be ween heo y and expe imen .
IEEE
T ans.
Dielech:
Elecb
Ins
Vol.
9,
No.
4;
pp
589-595,
2002.
[41
N.
Fklici.
Re .
Gen. kle ec ,
Vol. 75,pp.
1145-1160,
1966.
685