3.

CONDUCTION and BREAKDOWN in LIQUID DIELECTRICS

Liquid dielectrics are used ainl! s"readin# t$r%u#$ in $i#$ &%lta#e ca'les and
ca"acit%rs and (%r (illin# trans(%rers) circuit 'rea*ers) etc. In additi%n t% t$eir (uncti%n
as a dielectric) liquid dielectrics $a&e additi%nal (uncti%ns in certain a""licati%ns. +%r
e,a"le) liquid dielectrics act as $eat trans(er a#ents in trans(%rers and as arc
quenc$in# edia in circuit 'rea*ers. -etr%leu %ils are %st c%%nl! used as liquid
dielectrics. +%r certain a""licati%ns S!nt$etic $!dr%car'%ns and $al%#enated
$!dr%car'%ns and (%r &er! $i#$ te"erature a""licati%ns) silic%ne %ils and (lu%rinated
$!dr%car'%ns are used. In recent ties) certain &e#eta'le %ils and esters are als% 'ein#
used.
Liquid dielectrics n%rall! are i,ture %( $!dr%car'%ns and are .ea*l! "%lari/ed. W$en
used (%r electrical insulati%n "ur"%ses t$e! s$%uld 'e (ree (r% %isture) "r%ducts %(
%,idati%n) and %t$er c%ntainants. T$e %st i"%rtant (act%r t$at a((ects t$e electrical
stren#t$ %( insulatin# %il is t$e "resence %( .ater in t$e (%r %( (ine dr%"lets sus"ended
in t$e %il. T$e "resence %( e&en 0.01 2 .ater in trans(%rer %il reduces t$e electrical
stren#t$ t% 30 2 %( t$e dr! %il &alue. T$e dielectric stren#t$ %( t$e %il reduces %re
s$ar"l!) i( it c%ntains (i'r%us i"urities in additi%n t% .ater. T$e t$ree %st i"%rtant
"r%"erties) %( liquid dielectrics are 4i5 t$e electrical c%nducti&it!) 4ii5 dielectric c%nstant)
and 4iii5 t$e dielectric stren#t$. In additi%n) t$e "$!sical and c$eical "r%"erties suc$ as
&isc%sit!) t$eral sta'ilit!) s"eci(ic #ra&it!) etc. are als% i"%rtant. E,a"les (%r t$e
'rea*d%.n stren#t$ at 30C %n 3.6 standard s"$ere #a" are16 *78 (%r
Trans(%rer Oil) 30 *78 (%r Ca'le Oil) 30 *78 (%r Ca"acit%r Oil) 30936 *78 (%r
As*arels) 309:0 *78 (%r Silic%ne Oils.
In "ractice) t$e c$%ice %( a liquid dielectric (%r a #i&en a""licati%n is ade ainl! %n t$e
'asis %( its c$eical sta'ilit!. In additi%n) %t$er (act%rs li*e sa&in# %( s"ace) c%st)
"re&i%us usa#e) and susce"ti'ilit! t% t$e en&ir%nental in(luences are als% c%nsidered.
In ca"acit%rs) re"laceent %( t$e ca"acit%r %il '! as*arel s"readin# t$r%u#$ in t$e %&erall
si/e %( t$e ca"acit%r '! %re t$an 302. In "ractice) a liquid (%und satis(act%r! %&er a
l%n# "eri%d %( usa#e is "re(erred t% a ne. %ne. -etr%leu liquid are .idel! used
'ecause %( t$eir l%. c%st.
3.1 -URE LIQUIDS AND CO;;ERCIAL LIQUIDS
-ure liquids are t$%se .$ic$ are c$eicall! "ure and d% n%t c%ntain an! %t$er i"urit!
e&en in traces %( 1 in 10
<
) and are structurall! si"le.
E,a"les %( suc$ si"le "ure liquids are n9$e,ane 4C=>1:5. n9$e"tane 4C?>1=5 and %t$er
"ara((in $!dr%car'%ns.
B! usin# si"le and "ure liquids) it is easier t% se"arate %ut t$e &ari%us (act%rs t$at
in(luence c%nditi%n and 'rea*d%.n in t$e.
On t$e %t$er $and) t$e c%ercial liquids .$ic$ are insulatin# liquids li*e %ils) n%t
c$eicall! "ure) n%rall! c%nsist %( i,ture %( c%"le, %r#anic %lecules .$ic$ cann%t
'e easil! s"eci(ied %r re"r%duced in a series %( e,"erients.
-uri(icati%n
T$e ain i"urities in liquid dielectrics are dust) %isture) diss%l&ed) #ases and i%nic
i"urities. 7ari%us et$%ds e"l%!ed (%r "uri(icati%n are (iltrati%n 4t$r%u#$ ec$anical
(ilters) s"ra! (ilters) and electr%static (ilters5) centri(u#in#) de#assin# and distillati%n) and
c$eical treatent 4addin# i%n e,c$an#e aterial suc$ as aluina) (uller@s eart$ etc.
(ilterin#5.
Dust "articles .$en "resent 'ec%e c$ar#ed and reduce t$e 'rea*d%.n stren#t$ %( t$e
liquid dielectrics) and t$e! can 'e re%&ed '! care(ul (iltrati%n.
Liquid .ill n%rall! c%ntain %isture and diss%l&ed #ases in sall quantities. Aases li*e
%,!#en and car'%n di%,ide si#ni(icantl! a((ect t$e 'rea*d%.n stren#t$ %( t$e liquids) and
$ence it is necessar! t% c%ntr%l t$e a%unt %( #as "resent. T$is is d%ne '! distillati%n
and de#assin#.
I%nic i"urit! in liquids) li*e .ater &a"%r .$ic$ easil! diss%ciates) leads t% &er! $i#$
c%nducti&it! and $eatin# %( t$e liquid de"endin# %n t$e a""lied electric (ield. Water is
re%&ed usin# dr!in# a#ents %r '! &acuu dr!in#.
S%eties) liquids are s$a*en .it$ c%ncentrated sul"$uric acid t% re%&e .a, and
residue and .as$ed .it$ caustic s%da and distilled .ater. A c%%nl! used cl%sed9
c!cle liquid "uri(icati%n s!ste t% "re"are liquids as "er t$e a'%&e requireents is
s$%.n in +i#. 3.1.
T$is s!ste "r%&ides (%r c!clin# t$e liquids. T$e liquid (r% t$e reser&%ir (l%.s t$r%u#$
t$e distillati%n c%lun .$ere i%nic i"urities are re%&ed. Water is re%&ed '! dr!in#
a#ents %r (r%/en %ut in t$e l%.9te"erature 'at$. T$e #ases diss%l&e in t$e liquid are
re%&ed '! "assin# t$e t$r%u#$ t$e c%%lin# t%.er and8%r "u"ed %ut '! t$e &acuu
"u"s. T$e liquids t$en "asses t$%u#$t t$e (ilter .$ere dust "articles are re%&ed.
T$e liquid t$us "uri(ied is t$en use in t$e test cell. T$e used liquid t$en (l%.s 'ac* int%
t$e reser&%ir. T$e &acuu s!ste t$us $el"s t% re%&e t$e %isture and %t$er #ase%us
i"urities.
Brea*d%.n Tests
Brea*d%.n tests are n%rall! c%nduced usin# test cell. +%r testin# "ure liquids) t$e test
cells used are sall s% t$at less quantit! %( liquid is used durin# testin#. Als%) test cells
C%%lin#
t%.er
Distillati%n
c%lun
7acuu
Aau#e
7acuu
7al&e
T% 7acuu
-u"
T% 7acuu
-u"
T% 7acuu
-u"
Test cell .it$ electr%des
+ilter
Reser&%ir
+i#. 3.1 Liquid "uri(icati%n s!ste .it$ test cell.
are usuall! an inte#ral "art %( t$e "uri(icati%n s!ste as s$%.n in +i#. 3.1. T$e
electr%des used (%r 'rea*d%.n &%lta#e easureent are usuall! s"$eres %( 0.6 t% 1 c
in diaeter .it$ #a" s"acin# %( a'%ut 1009300 . T$e #as is accuratel! c%ntr%lled '!
usin# a icr%eter. Electr%de se"arati%n is &er! critical in easureent .it$ liquids)
and als% t$e electr%de sur(ace s%%t$ness and t$e "resence %( %,ide (ils $a&e a
ar*ed in(luence %n t$e 'rea*d%.n stren#t$. T$e test &%lta#es required (%r t$ese tests
are usuall! l%.) %( t$e %rder %( 609100 *7) 'ecause %( sall electr%de s"acin#. T$e
'rea*d%.n stren#t$s and d.c c%nducti&ities %'tained in "ure liquids are &er! $i#$) %( t$e
%rder %( 1 ;78c and 10
91B
910
930
$%8c res"ecti&el!) t$e c%nducti&it! 'ein# easured
at electric (ield %( t$e %rder %( 1 *78c. >%.e&er) t$e c%rres"%ndin# &alues in
c%ercial liquids are relati&el! l%..
3.3 CONDUCTION AND BREAKDOWN IN -URE LIQUIDS
W$en l%. electric (ields less t$an 1 *78c are a""lied) c%nducti&ities %(
10
91B
-10
930
$%8c are %'tained. T$ese are "r%'a'l! due t% t$e i"urities reainin#
a(ter "uri(icati%n. >%.e&er) .$en t$e (ields are $i#$ 4C100*78c5 t$e currents n%t %nl!
increase ra"idl!) 'ut als% under#% &i%lent (luctuati%ns .$ic$ .ill die d%.n a(ter s%e
tie. A t!"ical ean &alue %( t$e c%nducti%n current in $e,ane is s$%.n in +i#. 3.3. T$is
is t$e c%nditi%n nearer t% 'rea*d%.n.
>%.e&er) i( t$is (i#ure is redra.n startin# (r% &er! sall currents) a current9electric (ield
c$aracteristics as s$%.n in +i#. 3.3) can 'e %'tained. T$is cur&e .ill $a&e t$ree distinct
re#i%ns as s$%.n. At &er! l%. (ields t$e current is due t% t$e diss%ciati%n %( i%ns. Wit$
interediate (ields t$e current reac$es a saturati%n &alue) and at $i#$ (ields t$e current
#enerated 'ecause %( t$e (ield9aided electr%n eissi%n (r% t$e cat$%de #ets ulti"lied
0.= 0.: 0.B 1.0 1.3
3
0
:
=
B
10
13
1:
C%nducti%n
Current
4A , 10
11
5
Electric (ield 4;78c5
+i#.3.3 C%nducti%n current9electric (ield c$aracteristics in $e,ane
at $i#$ (ields
in t$e liquid ediu '! a T%.nsend t!"e %( ec$anis .T$e current ulti"licati%n als%
%ccurs (r% t$e electr%ns #enerated at t$e inter(aces %( liquid and i"urities. T$e
increase in current '! t$ese "r%cesses c%ntinues till 'rea*d%.n %ccurs.
T$e e,act ec$anis %( current #r%.t$ is n%t *n%.nD $%.e&er) it a""ears t$at t$e
electr%ns are #enerated (r% t$e cat$%de '! (ield eissi%n %( electr%ns.
T$e electr%ns s% li'erated #et ulti"le '! a "r%cess siilar t% T%.nsend@s "riar! and
sec%ndar! i%ni/ati%n in #ases As t$e 'rea*d%.n (ield is a""r%ac$es) t$e current
increases ra"idl! due t% "r%cess siilar t% t$e "riar! i%ni/ati%n "r%cess and als% t$e
"%siti&e i%ns reac$in# t$e cat$%de #enerate sec%ndar! electr%ns) leadin# 'rea*d%.n.
T$e 'rea*d%.n &%lta#e de"ends %n t$e (ield) #a" se"arati%n) cat$%de .%r*9(uncti%n)
and t$e te"erature %( t$e cat$%de. In additi%n) t$e liquid &isc%sit!) t$e liquid
te"erature) t$e
densit!) and t$e %lecular structure %( t$e liquid als% in(luence t$e 'rea*d%.n stren#t$
%( t$e liquid. T!"ical a,iu 'rea*d%.n stren#t$s %( s%e $i#$l! "uri(ied liquids and
lique(ied #ases are #i&en in Ta'le 3.1.
Ta'le 3.1 ;a,iu Brea*d%.n stren#t$ %( s%e liquid
Liquid ;a,iu 'rea*d%.n stren#t$
4;78c5
>e,ane 1.191.3
Ben/ene 1.1
Trans(%rer %il 1.0
Silic%ne 1.091.3
Liquid O,!#en 3.:
Liquid Nitr%#en 1.=91.<
0.= 0.3 0.B 0.: 1.0 0
C%nducti%n
Current
4Ar'itrar!
units5
Electric (ield 4;78c5
+i#.3.3 C%nducti%n current9electric (ield c$aracteristics
in $!dr%car'%n liquid
+ield aided
saturati%n
i%nic
Liquid >!dr%#en 1.0
Liquid >eliu 0.?
Liquid Ar#%n 1.191.:3
It $as %'ser&ed t$at t$e increase in 'rea*d%.n stren#t$ is %re) i( t$e diss%l&ed #ases
are electr%ne#ati&e in c$aracter 4li*e %,!#en5. Siilarl!) t$e increase in t$e liquid
$!dr%static "ressure increases t$e 'rea*d%.n stren#t$.
T% su u") t$is t!"e %( 'rea*d%.n "r%cess in "ure liquids) called t$e electr%nic
'rea*d%.n) in&%l&es eissi%n %( electr%ns at (ields #reater t$an 100 *78c. T$is
eissi%n %ccurs eit$er at t$e electr%de sur(ace irre#ularities %r at t$e inter(aces %(
i"urities and t$e liquid. T$ese electr%ns #et (urt$er ulti"lied '! T%.nsend@s t!"e %(
"riar! and sec%ndar! i%ni/ati%n "r%cesses) leadin# t% 'rea*d%.n.
3.3 CONDUCTION AND BREAKDOWN IN CO;;ERCIAL LIQUIDS
As alread! enti%ned c%ercial insulatin# liquids are n%t c$eicall! "ure and $a&e
i"urities li*e #as 'u''les) sus"ended "articles) etc. T$ese i"urities reduce t$e
'rea*d%.n stren#t$ %( t$ese liquids c%nsidera'l!. T$e 'rea*d%.n ec$aniss are als%
c%nsidera'l! in(luenced '! t$e "resence %( t$ese i"urities. In additi%n) .$en
'rea*d%.n %ccurs in t$ese liquids) additi%nal #ases and #as 'u''les are e&%l&ed and
s%lid dec%"%siti%n "r%ducts are (%red. T$e electr%de sur(aces 'ec%e r%u#$) and at
ties e,"l%si&e s%unds are $eard due t% t$e #enerati%n %( i"ulsi&e "ressure t$r%u#$
t$e liquid.
T$e 'rea*d%.n ec$anis in c%ercial liquids is de"endent %n se&eral (act%rs) suc$
as) t$e nature and c%nditi%n %( t$e electr%des) t$e "$!sical "r%"erties %( t$e liquid) and
t$e i"urities and #ases "resent in t$e liquid. Se&eral t$e%ries $a&e 'een "r%"%sed t%
e,"lain t$e 'rea*d%.n in liquids) and t$e! are classi(ied as (%ll%.sE
a5 Sus"ended -article ;ec$anis
'5 Ca&itati%n and Bu''le ;ec$anis
c5 Stressed Oil 7%lue ;ec$anis
a. Sus"ended -article T$e%r!
In c%ercial liquids) t$e "resence %( s%lid i"urities cann%t 'e a&%ided. T$ese
i"urities .ill 'e "resent as (i'res %r as dis"ersed s%lid "articles. T$e "eritti&it! %(
t$ese "articles ( )
2
.ill 'e di((erent (r% t$e "eritti&it! %( t$e liquid( )
1
. I( .e c%nsider
t$ese i"urities t% 'e s"$erical "articles %( radius r) and i( t$e a""lied (ield is E) t$en t$e
"articles e,"erience %( (%rce +) .$ere
( )
2 1 3
2
1 2
1
F= grad E
2 2
r


+

43.15
T$is (%rce is directed t%.ards areas %( a,iu stress) i(
2 1
) (%r e,a"le) in t$e
case %( t$e "resence %( s%lid "articles li*e "a"er in t$e liquid. On t$e %t$er $and) i( %nl!
#as 'u''les are "resent in t$e liquid) i.e.
2 1
) t$e (%rce .ill 'e in t$e directi%n %( areas
%( l%.er stress. I( t$e &%lta#e is c%ntinu%usl! a""lied 4d.c5 %r t$e durati%n %( t$e &%lta#e
is l%n# 4a.c5) t$en t$is (%rce dri&es t$e "articles t%.ards t$e area %( a,iu stress. I(
t$e nu'er %( "articles is lar#e) t$e! 'ec%e ali#ned due t% t$ese (%rces) and t$us (%r
a sta'le c$ain 'rid#in# t$e electr%de #a" causin# a 'rea*d%.n 'et.een t$e electr%des.
I( t$ere is %nl! a sin#le c%nductin# "article 'et.een t$e electr%des) it .ill #i&e rise t%
l%cal (ield en$anceent de"endin# %n its s$a"e. I( t$is (ield e,ceeds t$e 'rea*d%.n
stren#t$ %( t$e liquid) l%cal 'rea*d%.n .ill %ccur near t$e "article) and t$is .ill result in
t$e (%rati%n %( #as 'u''les .$ic$ a! lead t% 'e 'rea*d%.n %( t$e liquid.
T$e &alue %( t$e 'rea*d%.n stren#t$ %( t$e liquids c%ntainin# s%lid i"urities .as (%und
t% 'e uc$ less t$an t$e &alues (%r "ure liquids. T$e i"urit! "articles reduce t$e
'rea*d%.n stren#t$) and it .as als% %'ser&ed t$at t$e lar#er t$e si/e %( t$e "articles t$e
l%.er .ere t$e 'rea*d%.n stren#t$s.
'. Ca&itati%n and t$e Bu''le T$e%r!
It .as e,"erientall! %'ser&ed t$at in an! liquids) t$e 'rea*d%.n stren#t$ de"ends
str%n#l! %n t$e a""lied $!dr%static "ressure) su##estin# t$at a c$an#e %( "$ase %( t$e
ediu is in&%l&ed in t$e 'rea*d%.n "r%cess) .$ic$ in %t$er .%rds eans t$at a *ind %(
&a"%r 'u''le (%red is res"%nsi'le (%r 'rea*d%.n. T$e (%ll%.in# "r%cesses $a&e 'een
su##ested t% 'e res"%nsi'le (%r t$e (%rati%n %( t$e &a"%r 'u''lesE
a5 Aas "%c*ets at t$e sur(ace %( t$e electr%desD
'5 electr%static re"ulsi&e (%rces 'et.een s"ace c$ar#es .$ic$ a! 'e su((icient t%
%&erc%e t$e sur(ace tensi%nD
c5 #ase%us "r%ducts due t% t$e diss%ciati%n %( liquid %lecules '! electr%n
c%llisi%nsD and
d5 7a"%ri/ati%n %( t$e liquid '! c%r%na t!"e disc$ar#es (r% s$ar" "%ints and
irre#ularities %n t$e electr%de sur(aces.
Once a 'u''le is (%red it .ill el%n#ated 4l%n# and t$in5 in t$e directi%n %( t$e electric
(ield under t$e in(luence %( electr%static (%rces. T$e &%lue %( t$e 'u''le reains
c%nstant durin# el%n#ati%n. Brea*d%.n %ccurs .$en t$e &%lta#e dr%" al%n# t$e len#t$
%( t$e 'u''le 'ec%es equal t% t$e iniu &alue %n t$e -asc$en@s cur&e (%r t$e #as
in t$e 'u''le. T$e 'rea*d%.n (ield is #i&en as
( )
( )
1
2
1 2 h
0
1 2 0
2 2 V 1
E 1
(2rE ) r

+
1

1
' ;

1
]
43.35
.$ere

is t$e sur(ace tensi%n %( t$e liquid)

1
is t$e "eritti&it! %( t$e liquid)
2
is t$e
"eritti&it! %( t$e #as 'u''le) r is t$e initial radius %( t$e 'u''le assued as a s"$ere
and
b
V is t$e &%lta#e dr%" in t$e 'u''le 4c%rres"%ndin# t% iniu %n t$e -asc$en@s
cur&e5. +r% t$is equati%n it can 'e seen t$at t$e 'rea*d%.n stren#t$ de"ends %n t$e
initial si/e %( t$e 'u''le .$ic$ in turn is in(luenced '! t$e $!dr%static "ressure and
te"erature %( t$e liquid. But t$is t$e%r! d%es n%t ta*e int% acc%unt t$e "r%ducti%n %( t$e
initial 'u''le and $ence t$e results #i&en '! t$is t$e%r! d% n%t a#ree .ell .it$ t$e
e,"eriental results.
Later t$is t$e%r! .as %di(ied) and it .as su##ested t$at %nl! inc%"ressi'le 'u''les
li*e .ater #l%'ules can el%n#ate at c%nstant &%lue) acc%rdin# t% t$e si"le #as la.
"& F nRT. Under t$e in(luence %( t$e a""lied electric (ield t$e s$a"e %( t$e #l%'ule is
assued t% 'e a""r%,iatel! a s"$er%id. T$ese inc%"ressi'le 'u''les reac$ t$e
c%nditi%n %( insta'ilit! .$en ) t$e rati% %( t$e l%n#er t% t$e s$%rter diaeter %( t$e
s"$er%id is a'%ut 1.B6) and t$e critical (ield "r%ducin# t$e insta'ilit! .ill 'eE
1
0
1 1 2
600 H E G
R


1

1

]
43.35 .$ere

sur(ace tensi%n) RF initial radius %(
'u''le)
1
"eritti&it! %( t$e liquid dielectric)
1
"eritti&it! %( t$e #l%'ule)
( )
1
1 2
2
2
1 cosh
1
1
1
G

1
1

1

1
]
and
1
2
3
2
1
H 2 2 1

_


,
+%r a .ater #l%'ule $a&in# RF1
m
.it$
1
43dyne/cm and 2.0 4trans(%rer %il5)
t$e a'%&e equati%n #i&es a critical (ield
c
E 226 / Kv cm .$ic$ is a""r%,iatel! t$e
a,iu stren#t$ %'tained (%r c%ercial %ils.
In t$e case %( #as 'u''les t$e equati%n (%r t$e critical (ield is re.ritten as
( )
( )
1
1
1 2 4 1
1 2
2
c
1 2 1 2
8A
E 600 ! cosh
3
R

1 1
1

1 1
]

] ]
.$ere)
( )
2
3 2
1 2
2 1
A= 1
=2 1




A)

and R are as a'%&e (%r liquid #l%'ules) and

( )
1
3
" 2
1 2 #1
3
2$ 1 %&
cosh
3 2B

' ;
1

1
]
.$ere - is t$e $!dr%static "ressure. 4Equati%ns 3.393.: are in c.#.s. units5. T$e
e,"ressi%ns are quite c%"licated) and t$e 'rea*d%.n &%lta#es .ere %'tained usin# a
c%"uter. Results t$us %'tained s$%.ed #%%d a#reeent .it$ t$e e,"eriental results
in n9$e,ane. T$is t$e%r! su##ests t$at su'9icr%sc%"ic "articles 4diaeter 1009360 A5
and 'u''les #reatl! in(luence t$e a,iu electrical stren#t$ attaina'le in c%ercial
liquids. T$e critical c%nditi%n is reac$ed .$en ca&ities are (%red due t% /er% "ressure
c%nditi%ns #i&en '!
c '( es s h
% % % % % ) + +
43.65 .$ere)
c
'(
es
s
h
% co*+omb,c (ress*re)
% 'a(o*r (ress*re ,ns,de -he ca',-y)
% e+ec-ros-a-,c (ress*re)
% (ress*re d*e -o s*r.ace -ens,on) and
% hydros-a-,c (ress*re.

+r% t$is c%nditi%n) an e,"ressi%n $as 'een %'tained (%r t$e a,iu 'rea*d%.n
stren#t$ %( "ure liquids .$ic$ .as (%und t% 'e in #%%d a#reeent .it$ t$e e,"eriental
results.
In #eneral) t$e ca&itati%n and 'u''le t$e%ries tr! t% e,"lain t$e $i#$est 'rea*d%.n
stren#t$s %'taina'le) c%nsiderin# t$e ca&ities %r 'u''les (%red in t$e liquid dielectrics.
T$eral ;ec$anis %( Brea*d%.n
An%t$er ec$anis "r%"%sed t% e,"lain 'rea*d%.n under "ulse c%nditi%ns is t$eral
'rea*d%.n. T$is ec$anis is 'ased %n t$e e,"eriental %'ser&ati%ns %( e,treel!
lar#e currents Gust 'e(%re 'rea*d%.n. T$ese $i#$ current "ulses are 'elie&ed t%
%ri#inate (r% t$e ti"s %( t$e icr%sc%"ic "r%Gecti%ns %n t$e cat$%de sur(ace .it$
densities %( t$e %rder %(
2
1A/cm . T$ese $i#$ densit! current "ulses #i&e rise t% l%cali/ed
$eatin# %( t$e %il .$ic$ a! lead t% t$e (%rati%n %( t$e &a"%r 'u''les. T$e &a"%r
'u''les are (%red .$en t$e ener#! e,ceeds
$ 3
10 //cm . W$en a 'u''le is (%red)
'rea*d%.n (%ll%.s) eit$er 'ecause %( its el%n#ati%n t% a critical si/e %r .$en it
c%"letel! 'rid#es t$e #a" 'et.een t$e electr%des. In eit$er case) it .ill result in t$e
(%rati%n %( a s"ar*. Acc%rdin# t% t$is ec$anis) t$e 'rea*d%.n stren#t$ de"ends %n
t$e "ressure and t$e %lecular structure %( t$e liquid. +%r e,a"le) in n9al*anes t$e
'rea*d%.n stren#t$ .as %'ser&ed t% de"end %n t$e c$ain len#t$ %( t$e %lecule. T$is
t$e%r! is %nl! a""lica'le at &er! sall len#t$s ( )
100 m and d%es n%t e,"lain t$e
reducti%n in 'rea*d%.n stren#t$ .it$ increase #a" len#t$s.
c. Stressed Oil 7%lue T$e%r!
In c%ercial liquids .$ere inute traces %( i"urities are "resent) t$e 'rea*d%.n
stren#t$ is deterined '! t$e Hlar#est "%ssi'le i"urit!I %r H.ea* lin*I. On a statistical
'asis it .as "r%"%sed t$at t$e electrical 'rea*d%.n stren#t$ %( t$e %il is de(ined '! t$e
.ea*est re#i%n in t$e %il) nael!) t$e re#i%n .$ic$ is stressed t% t$e a,iu and '!
t$e &%lue %( %il included in t$at re#i%n. In n%n9uni(%r (ields) t$e stressed %il &%lue is
ta*en as t$e &%lue .$ic$ is c%ntained 'et.een t$e a,iu stress ( )
ma0
E c%nt%ur
and 0.< ( )
ma0
E c%nt%ur. Acc%rdin# t% t$is t$e%r! t$e 'rea*d%.n stren#t$ is in&ersel!
"r%"%rti%nal t% t$e stressed %il &%lue.
T$e 'rea*d%.n &%lta#e is $i#$l! in(luenced '! t$e #as c%ntent in t$e %il) t$e
&isc%sit! %( t$e %il) and t$e "resence %( %t$er i"urities. T$ese 'ein# uni(%rl!
distri'uted) increase in t$e stressed %il &%lue c%nsequentl! results in a reducti%n in t$e
'rea*d%.n &%lta#e. T$e &ariati%n %( t$e 'rea*d%.n &%lta#e stress .it$ t$e stressed %il
&%lue is s$%.n in +i#. 3.:.
3.: CONCLUSIONS
All t$e t$e%ries discussed a'%&e d% n%t c%nsider t$e de"endence %( 'rea*d%.n stren#t$
%n t$e #a" len#t$. T$e! all tr! t% acc%unt (%r t$e a,iu %'taina'le 'rea*d%.n
stren#t$ %nl!. >%.e&er) t$e e,"eriental e&idence s$%.ed t$at t$e 'rea*d%.n stren#t$
%( a liquid de"ends %n t$e #a" len#t$) #i&en '! t$e (%ll%.in# e,"ressi%n)
:00
300
300
100
0
10
93
1.0 10
3
10
:
10
=
Stressed %il &%lue 4cc5
Brea*d%.n
Stress
4*78c5
+i# 3.: -%.er (requenc! 460 >/5 a.c 'rea*d%.n stress as (uncti%n %(
stressed %il &%lue
%ne inute .it$stand &%lta#e
Wit$ stead! &%lta#e rise
n
b
V Ad .$ere)
d=ga( +eng-h)
A=cons-an-)and
n=cons-an-)a+1ays +ess -han 1.
T$e 'rea*d%.n &%lta#e als% de"ends %n t$e nature %( t$e &%lta#e) t$e %de in .$ic$
t$e &%lta#e is a""lied) and t$e tie %( a""licati%n. T$e a'%&e relati%ns$i" is %( "ractical
i"%rtance) and t$e electrical stress %( #i&en %il used in desi#n is %'tained (r% t$is.
Durin# t$e last ten !ears) researc$ .%r* is directed %n t$e easureents %( disc$ar#e
ince"ti%n 4startin#5 le&els in %il and t$e 'rea*d%.n stren#t$s %( lar#e &%lues %( %il
under di((erent c%nditi%ns.
It a! 'e suari/ed t$at t$e actual ec$anis %( 'rea*d%.n in %il is n%t a
si"le "$en%en%n and t$e 'rea*d%.n &%lta#es are deterined '! e,"eriental
in&esti#ati%ns %nl!. Electrical stresses %'tained (%r sall &%lues s$%uld n%t 'e used in
t$e case %( lar#e &%lues.
QUESTIONS
1. E,"lain t$e "$en%ena %( electrical c%nducti%n in liquids. >%. d%es it di((ers (r%
t$%se in #asesJ
3. W$at are t$e c%ercial liquids dielectrics) and $%. are t$e! di((erent (r% "ure
liquids dielectricsJ
3. W$at are t$e (act%rs t$at in(luence c%nducti%n in "ure liquid dielectrics and in
c%ercial liquid dielectricsJ
:. E,"lain t$e &ari%us t$e%ries t$at e,"lain 'rea*d%.n in c%ercial liquids
dielectrics.
6. W$at is Hstressed %il &%lue t$e%r!I) and $%. d%es it e,"lain 'rea*d%.n in lar#e
&%lues %( c%ercial liquid dielectricsJ