APPARATUS AND METHOD FOR PRODUCING ELECTRICAL ENERGY FROM FLUID ENERGY

APPAREIL ET METHODE DE PRODUCTION D'ENERGIE ELECTRIQUE A PARTIR D'ENERGIE LIQUIDE

English Abstract

An apparatus and a method for producing electrical energy from fluid energy
using electrokinetic and hydrodynamic principles. In an apparatus from the
invention is an
energy conversion apparatus including a channel assembly, where the channel
assembly
includes a channel, a first terminal located at a first axial position and in
communication with
the channel, and a second terminal located at a second axial position and in
communication
with the channel. In a method form, the invention involves the steps of
providing the energy
conversion apparatus and passing a fluid through the channel in order to
produce the electrical
energy. In a preferred embodiment the energy conversion apparatus includes a
plurality of
channel assemblies which are electrically connected together in a parallel
configuration in order
to increase the amount of electrical energy which can be produced by the
apparatus.

Claims

The embodiments of the invention in which an exclusive property or privilege
is
claimed are defined as follows:

1. ~An energy conversion apparatus for producing electrical energy from fluid
energy, the energy conversion apparatus comprising a channel assembly, the
channel assembly
comprising:
(a) a channel;

(b) a first terminal located at a first axial position and in communication
whit the channel; and

(c) a second terminal located at a second axial position and in
communication with the channel.

2. ~The apparatus as claimed in claim 1 wherein the apparatus is comprised of
a
plurality of electrically connected channel assemblies.


3. ~The apparatus as claimed in claim 2 wherein the apparatus is comprised of
at
least about 1 × 10 5 electrically connected channel assemblies.

4. ~The apparatus as claimed in claim 2 wherein each of the channels has an
interior
surface, wherein the interior surface of the channels is constructed of a
channel material, and
wherein the channel material is relatively an electrically non-conductive
material.

5. ~The apparatus as claimed in claim 2 wherein the apparatus is comprised of
a
porous bulk material, wherein the channels are defined by pores in the bulk
material, wherein
the pores have an interior surface, wherein the interior surface of the pores
is constructed of a
channel material, and wherein the channel material is relatively an
electrically non-conductive
material.


-1-


6. ~The apparatus as claimed in claim 5 wherein the bulk material is glass.

7. ~The apparatus as claimed in claim 4 wherein each of the channels has a
finite
cross-sectional area which is less than about 300 square millimeters.

8. ~The apparatus as claimed in claim 4 wherein each of the channels has a
finite
cross-sectional area which is less than about 3 square millimeters.

9. ~The apparatus as claimed in claim 4 wherein each of the channels has a
finite
cross-sectional area which is less than about 0.03 square millimeters.

10. ~The apparatus as claimed in claim 4 wherein each of the channels has a
cross-
sectional area of between about 3 × 10 -4 square microns and about 0.03
square millimeters.

11. ~The apparatus as claimed in claim 4 wherein each of the channels has a
cross-
sectional area of between about 0.03 square microns and about 300 square
microns.

12. ~The apparatus as claimed in claim 4 wherein each of the channels has a
length
and wherein the length of each of the channels is a finite distance which is
less than about 10
centimeters.

13. ~The apparatus as claimed in claim 4 wherein each of the channels has a
length
and wherein the length of each of the channels is a finite distance which is
less than about 1
centimeters.

14. ~The apparatus as claimed in claim 4, further comprising a fluid energy
source for
providing the fluid energy to pass an electrolytic fluid through the channels.

15. ~The apparatus as claimed in claim 14, wherein the fluid energy source is
comprised of a fluid reservoir, wherein the fluid reservoir is configured to
provide a hydrostatic
pressure so that the fluid energy is comprised of the hydrostatic pressure.



-2-



16. ~The apparatus as claimed in claim 4, further comprising an electrolytic
fluid for
passing through the channels.

17. ~The apparatus as claimed in claim 16 wherein the fluid and the channel
material
are selected to provide a value for a reciprocal of the electrical double
layer thickness of greater
than about 1 × 10 5/m.

18.~The apparatus as claimed in claim 16 wherein the fluid is selected to
provide a
value for a reciprocal of the electrical double layer thickness of less about
1 × 10 9/m.

19. ~The apparatus as claimed in claim 16 wherein the fluid is selected to
provide a
value for a reciprocal of the electrical double layer thickness of between
about 1 × 10 6/m and
about 1 × 10 9/m.

20. ~The apparatus as claimed in claim 14 wherein the plurality of
electrically
connected channel assemblies is configured in parallel so that the first
terminals of each of the
channel assemblies are electrically connected and so that the second terminals
of each of the
channel assemblies are electrically connected.

21. ~The apparatus as claimed in claim 14 wherein the plurality of
electrically
connected channel assemblies is configured in series so that a pair of channel
assemblies is
electrically connected between the first terminal on one of the pair of
channel assemblies and
the second terminal on the other of the pair of channel assemblies.

22. ~The apparatus as claimed in claim 20 wherein the first terminal of the
plurality
of electrically connected channel assemblies are comprised of a first
electrode and wherein the
second terminals of the plurality of electrically connected channel assemblies
are comprised of
a second electrode.


-3-




23. ~The apparatus as claimed in claim 22 wherein the first electrode is
comprised of
a first connection point, wherein the second electrode is comprised of a
second connection
point, and wherein the first connection point and the second connection point
are adapted to
provide connections for an electrically conducting path between the first
electrode and the
second electrode for carrying an external load current between the first
electrode and the second
electrode.

24. ~The apparatus as claimed in claim 23, further comprising the electrically
conducting path, wherein the electrically conducting path is comprised of an
electrical load.

25. ~The apparatus as claimed in claim 24 wherein the electrical load is
selected such
that a conduction current which is induced in the fluid between the first
axial position and the
second axial position in the channels is minimized.

26. ~The apparatus as claimed in claim 25 wherein the electrical load is
selected to
maximize an amount of electrical work which is produced by the apparatus.

27. ~The apparatus as claimed in claim 26 wherein the fluid is water and
wherein the
electrical load is a resistive load of between about 1 ohm and about 1 ×
10 8 ohms or is a load
which is equivalent to a resistive load of between about 1 ohm and about 1
× 10 8 ohms.

28. ~The apparatus as claimed in claim 26 wherein the fluid is water and
wherein the
electrical load is a resistive load of between about 100 ohms and about 1
× 10 6 ohms or is a load
which is equivalent to a resistive load of between about 100 ohms and about 1
× 10 6 ohms.

29. ~The apparatus as claimed in claim 14, further comprising an alternating
mechanism for causing the fluid alternately to pass through the channels in a
direction toward
the second axial position and in a direction toward the first axial position.

-4-





30. ~The apparatus as claimed in claim 29 wherein the alternating mechanism
causes
a potential difference between the first terminal and the second terminal of
each of the channel
assemblies to alternate sinusoidally.

31. ~A method for producing electrical energy from fluid energy comprising the
following steps:
(a) providing an energy conversion apparatus, wherein the energy conversion
apparatus is comprised of a channel assembly, wherein the channel assembly is
comprised of:

(i) a channel;

(ii) a first terminal located at a first axial position and in communication
with the channel;

(iii) a second terminal located at a second axial position and in
communication with the channel; and

(b) passing an electrolytic fluid through the channel.


32. ~The method as claimed in claim 31 wherein the energy conversion apparatus
is
comprised of a plurality of electrically connected channel assemblies and
wherein the fluid
passing step is comprised of passing the fluid through each of the channels.

33. ~The method as claimed in claim 32 wherein the energy conversion apparatus
is
comprised of at least about 1 × 10 5 electrically connected channel
assemblies.

34. ~The method as claimed in claim 32 wherein the fluid passing step is
performed
by passing the fluid through each of the channels under substantially laminar
flow conditions.

-5-




35. ~The method as claimed in claim 34, further comprising the step of
providing the
fluid with the fluid energy in order to cause the fluid to pass through the
channels.

36. ~The method as claimed in claim 35 wherein the step of providing the fluid
with
the fluid energy is comprised of withdrawing the fluid from a fluid reservoir,
wherein the fluid
reservoir is configured to provide a hydrostatic pressure so that the fluid
energy is comprised of
the hydrostatic pressure.

37. ~The method as claimed in claim 34 wherein the plurality of electrically
connected channel assemblies is configured in parallel so that the first
terminals of each of the
channel assemblies as electrically connected and so that the second terminals
of each of the
channel assemblies as electrically connected.

38. ~The method as claimed in claim 34 wherein the plurality of electrically
connected channel assemblies is configured in series so that a pair of channel
assemblies is
electrically connected between the first terminal on one of the pair of
channel assemblies and
the second terminal on the other of the pair of channel assemblies.

39. ~The method as claimed in claim 37, further comprising the step of
providing an
electrically conducting path between the first terminals and the second
terminals for carrying an
external load current between the first terminals and the second terminals.

40 ~The method as claimed in claim 39, further comprising the step of
providing an
electrical load in the electrically conducting path.

41. ~The method as claimed in claim 37 wherein the fluid passing step is
comprised
of alternately passing the fluid through the channels in a direction toward
the second axial
position and in a direction toward the first axial position.


-6-





42. ~The method as claimed in claim 41 wherein the step of alternately passing
the
fluid causes a potential difference between the first terminal and the second
terminal of each of
the channel assemblies to alternate sinusoidally.

43. ~The method as claimed in claim 39, further comprising the step of
withdrawing a
reduced product from one of the first terminal of the second terminal of at
least of the
channel assemblies.

44. ~The method as claimed in claim 43 wherein the fluid is comprised of water
and
wherein the reduced product is comprised of hydrogen gas.

45. ~The method as claimed in claim 39, further comprising the step of
withdrawing
an oxidized product from one of the first terminal or the second terminal of
at least one of the
channel assemblies.

46. ~The method as claimed in claim 45 wherein the fluid is comprised of water
and
wherein the oxidized product is comprised of oxygen gas.


-7-

Description

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~.J~de~° static c~~d~ti~~~s, ~~:.~es~c ta:.e v'~~~~~ is ga~~
r~a~~~~si~g bct~ti~e z~ rhc solid
s~zri~ce, the redistri~~zti~~~ ~fi~r~s .r~v~tes ~ ~~r~~c~:i~t dig ~rence ~~,
~. :r~~~s~crsc direc~i~r~ ret~ti~m
s~ tote 5~~~d Si~l~~~,e. ~'ii~S IJ~tel'ltAas ~l~~er~~i° iS
~~..f°rY°~lCtrl~y rage::°C~,~d t;: ~~S ~ ''~et'~
~~tE;IB~'.~l".

Image


CA 02437304 2003-08-14
W~Yd"~r~ ~3'1~ i~~t1'!I'~i.Str~al$'S ~r'tC~ ~f 's~'i~: ~~'~'~Y'3.'~l~I''~
cE.~:e'x"_ ~~5~.'~.1~J Y_'Y G'.~3 vtfii~°,3.1'~'~Iii3~°v~~#S
6i~IvC;,7 X13 ',$IY'AP~:z1 t3dra
ges~~sat,~ ~f tIYP r'l~ii~i a~~ar~Y~tl~ iY~~.~~as~s ~i~ed t~ t~~iY~~;r~as~.~
7~~sisrar~~~ 'rc~ fi~~v ~I°tx~~ fl~a~ ire
~i2~ 't~C7%~;~lSti~;ail~ ~IY'~CtY~rY. Ii"Y a~~s ~:'E,~~ra., ~~~~~~raYt'Yg
E.zA~O.~'a t~".'Y-~~ ~~911ee8:~~tY'c7~ti~'~9.'~''~:;~G' t'.~9fed~YYt SLI~'-
~"~.~~y
S?~rfc~c°, ~L"sir~rlt rr!.aJ 't7~ il~~$~'°.,~.' i~ ti!rv
~;i~~°~~i. ~'": st7r~sY~o, ~,e71 t~Ea, ~~.Y°~~.°ti~r.~
C3i~'.3~°~9st~~ tCn t~i~
Stl."~.,~iYYYr°g C'~I~°~Ylt aS a r~SY~~t r;~ ~,i ~
SYrE:~iIYIYY'lg z'SCa.eId~la,~~ '~%Vfi.tf~f~ SY~ria~~ ~zdr"t~Y7f YS tF~ai~~
~~Y~S~C~s~r~CaY aS a ~,'~Y~'~~JCiYI~I~t ~f ~~'k~ ~yua~i~Y~~tI6 fY
>';~Lir_"~Y~~.
~~ill~; ~..f t~lE; C.'f ~;a.tS ~f tt~!t;; F~~~:~ti'°L:LS-tY~~'t:t~
~~Y~'YY::3Zi~i,~~Y4ii'2 "~'Ya tSkY Ifiis'.9'~~! ~7~ a'~~.1~
c~a:r~~gi~ a ~s~Y~~~.~st a~~ b~~~ st~~~~~= ar~~~~;~si~~r~,~.
~.~. ~at~Y~t ~~. ~~~%~.,93'.~ (~tirLc~i ~~~ a~~ ~i~s~iig.~~s a s~rYS~r a~~..~Y-
ar~~s aY~Yd a
~','lPt~~'~T' _'s'a'Jr rr2daSLlrirlg C,'~~~t3°~~~li?~ti~. ~'.ff~a,tu
a~~i.~iSS a C~~'s~~5~'v. ~~.a~L~r ~~iFY~.f;s'~' at a ~C~YrIIYmiatr'~I
~~t'~i~~~;Y'Y
a s~ii~ ~,~~all aY~~ axY i~~i~ fluid fic~~t,~iY~g t~~rc~ø~ga ~ :YaY-~~ci
i:~rr~s~~~~ t~~; ~.~a~i. ;:a~~ i~artic~kar9
.~ i~~tli ~~: ars ~:~re~tesi at ~r~~as~~iag ~ "~~-~~t~;~;t I9~t~Y~tiay9y~
~,~ebx~a~~ ii~~ I~~:°fI'~~t i~~~rv~~Ytial is
1 ~ ~e:,ffsE~C aS t~3e C~aY~gG YP? ''.,°~'t~t ~Jb7ts~,Y~3~~ai
~71~3~~:,a a'1~~°~ri~ ~5~t~rl~~Y3 SIC~itY w (~,;~f'~ ffe:~~~
~~;~'..~3tY~Y2S c°~a~Y~
~t~~~ ~oY-~iti~Y~s. ~t is ~~scri'c~~~I ~ 3 ~~ir~~l ~t ~i what .IY~
Y~~.as~r~~;~~~d~t '~f t~~ I~-~~°~~:~t ~~te~Ytia~.
~~ay be Las;~fi~i fir seYYsiYZg sY.Yafa~~ xj.~~rg~ ~,~'4~~~s ~Y~ Y~~i~Y~rai
~aYw~~;ica ~:uiciY aie sus~~rci~d i~ are
~~~~is~ :f~~i~.
~t3 ~~Y~gsIiY~g ~,9 "~~ '~,~ ~~~- ~i;~c~~t~s 'r f f~,,ts ~;~~ ~r~ ~.svr w-
~ri~~a~Y ~i~ Yni~ ~1 t~m i~
I~I~~Y:~~ar~YZeis'', ~oii~ids anti ~vrfa~.:~,s ~: a°'h~y~si~~~~,~Yi~;ai
a~~ ~i~g~.rz~~;riY~g.~_slaeets i~~ (~~Oi~
~.'~7-~~ Y~I'a~StYg~t~S t~l~ ~%t~rSt t(~ 1~~~~',x? ~~~~;'Nr~-'~i_S~~uS ~?f~CtS
~sl~,S~~ ~~ table ~~I~, SyiY~i"~e L~,~Y1~Y~
rr
a?~~C;t ~'r~.SSY~is~ ~iIV~Y2 ~~~U Y~Y rT'~Y~,Y"a~:~:~~a2nrY~l~i;~y.=~Y3~b
~:;:oYR~~~G~,S t~:~~a.=~ t~~~ ~~:~°C;SSI:Yr~ ~r53~r ~'~fGGts 'c&~C'.
s~gY~Y~~YCa~-~t a,~Ye~ ~Ot~~tiati~ '~Y~p~Y-~a3t t~ :~h~:; c~,sY~;YY ar~~
~r~~~~~ss ~.°~'r~t~°c~i ~_~ r~'~Y~;r~-~I~~tr~-
~ ~~~~i~arYi~;al s~st~,rr~s (t~~,T~JI~~ aY~~ ~t~~> ~~~i~,i~t~~i~~~~hgrr car
x~~~~'~ee,d~Yr~~i~g~ ~.~arat~YS aid
s~;st~r~s.
~'i,.9 ~.~. ~Ir'a ~Y~tr'u a~.,~. "~~i~~" ~s~:.aYai S1S ~9f
~'a~:utY'C~65S~I3~Ftl~. ' ~ ' d
.'9~ 3 ~'°v ~', '~Yu. ~Y ~. t~:~'~?
f ~ ~i
~.i~=Y~g~, i~°~ ~,Pta P~t~r~tiai", .Is~~zs4_a~ ~. ~~. ~Y~ ~r~.~
I~~~:rfa~e ~~~~~~:;~ ~.5~ (~~Q~'-~ ~~~-'~7~
3~ i~ ae:~tigas:~:5 tia~ ~ffv~-ts c~~r a ~l~aY~g~ ~~x :v~~a ;~t~rgtiwi ~a~~~~Y
t~.~; ~,~~;;.~~;ty r~rfii~ a~~ t~r~ssa~re
_~_


CA 02437304 2003-08-14
~iscri~~~~icra cf an cacctr~l,rcic so;= ~i~Y~ L~rxY~E~: ci~;cti~~a~sr~c~~ic
r'~c>~v ~~,~~~'~ a~~d cc~z~ci~:a.~cs ~y~a
YE~Y~~YIif~Y°trY ~~~a p~~cn~iai Ynay ScY;~,~si~r rc,~i~~a;~ ~~.,c
ff~~;iw=~c~ ~:f' ~°i:vctr~p~~~rcsis.
~'~3~~ ~f l~i~ r~f~r~:~c~;S r~f~i_~', ?4a a~,V~ :Ls''e~S~rY~~; ~~r Sl~s~~,Si
~,~~ ;k$L'i~~na;';~Y~ ~f'~i2~
strca~~siY~g p~~cr~~~iai as a s~~rce ~s~~scf~,~i ~~~;c.i°icai c~~cr~~.
~i.Jhiil~i_~'~' Y~~ ~'I-3~ fl~~~~~1'f~~ i~.t.
m nP ~r~S6nYii ir'Y'~C',I'k fi~;~ YS ~YY i~Y'~J~,%aY°G~3JS ari~
v'leS~~~C~6.1. fi:r ~Y'~d~'~;rYi~ ~ ~~~rl~a ~Yi~r
i~; fr~r~ s~~~i~ cric~:gy. ~'~c iY~~m~~~i~r~ ~s ~asc~ ~~~~Y~ a
c~rn~s~3~~.w~cr~ ~f ~i~c ~i~~;n~;r~e~~a ~f
ci°c~r~i~iriccics anti :z~dr~ciyYtaric~,. 'f.e a~~~r~,r~~~:~.
ir~~~~°~vcs ~r~a use ~f a s~r~ar~.~~~~ fa~~cY~ria~.
'4H~~ic~ ~S ~r~a~~~ ~~~ ~~SSIx'2~, a~'Y ~9~~ -~-'~i~~c '~~~:,ry.~~
~4~3°CS~.~~~ ~r';~ ~TY° iT;~r~. c~;~a3~Y~~~S.
l~.~?~'a'~ ~3a1°Il'.".i:~~aY°~~, '~~~~~: ~~"~'a~~~'~Yi~ah?~
'aa2~I2i~~JL.'S '~''J'rLY'~II~~i;~ a ;',:oaf c°T,YYS C7r
r~ut~$"~'s~~alSr"E1 f~r
°~'~~t~lL3Y~~; ~Sfi~ S'~r~aP'YIIY"tb ~~~~ilZY~s~ SCE ~f9a~; ~i~~~
Sir~,a,~;~2~ bn~~s;~~i$~~e.~ ~da~~ ~e~d t..~S~'~ vC3 ~5r~~,%~Ca~ a ~S~bLl~"~
sc~rcc ~f eiec~ricai cYierg~. ~"~YC ~~:cans ur n~cc.~a3~is~~~ f~-r
c~~ra~:~~~iYi~~~e sErcarr_~i~~~; p~tc~~r~f
?'P~a~~ inc~,~3i~c 1~~°Y'I1111a~S ~'s'~~lcr ark ~~~~~Sc:,~~a C~ e~~~~
S~r~:aYY3ln~ ~~sC t~~Y~'vx ~ig~ 1;~3 ~7~3YC1 an °,iccE~ica~
!'m3's~~ Yna"~ IJ''r L:~~°il'1~L~~6'..~ '~.'1~~°Pc~ ~Yr~~r'~~.a
c': YY'i.'~~.Ir~;c~~~.
a~~ a ~rs~ ~~ar~ic~iar ~S~cct, try i~~~rc~~:~i~~ is an ~:_~c~-~w ;~n~rcrsi~n
~~;~~aratvs fir
~r~~~.~ci~ag cicc~ricax encr~~ fr~r~ ~t,~i~ cYfr~r~;~5 ~iYC ~;l~er~f~ c~E~~~
rsr~Y:. a~~ara~~s c~rl~~risin~ a
ci~annei asseY~bi~, tim c~a~inci asscr~~i~ cs~~~risin~:
~a~ a c~annci;
i~y't~; a f7rS~: ~;f;,'3~aS~ ~d~Cur;~~~' ~~,~ a ~~YrSe; "r.~~~a~ ~7 ~SlLi~3Yi.
~°3r1~ 'In c,~~'~ rY::::i~'Ylc'tttY~
~lY ~~~, ~~=u.~~:;~~~ n ai2Ew
Sic~17~ ~:~,'°~"'i"Y~'13P~! i:ac~,$;L;G e'~~; z S~i:;c.'95~:~ ~~~a~
~;3SY~~~n Srl~ !a
~OrI~Ii~.L)11~a~~~ n °~~llt~a -~~~.~; ~~:at'~a'~el.
.°~-


CA 02437304 2003-08-14
MIA a V~~f~~ld ar'Ci~~~~~a ~;5Y~3Cr~~., ~i~'!~ iil~:'t_'.r~~:l~3fi 3S ~, L~~~z
~Jd ~~~I i'~ui:9~bi2g ~~~a:-3~ra~a~
~,Y~~erg~y i'~~~rrr~ ~~L~id energy ~~~r:~ris~.~g i:liv f~i~~:~~i~g ~,~ ~~5:
~i'~Vi~ii3,'g'- ar3. ~3~~' a~'~ ~ ~I'x'~l~Y~>:143Y~ a~y~5,s~.r~~~:zS,
~~lxls~i~sY1 ~~v 4:,l~~rg~J L:~YI'J~ISg~iYi
~~'9~5~ra~;LiS IS ~(3~1i'35~~~ e~3 ~, ~5'ia'~'~~i~' <ISS~ii"°g~~~,
~i''i~;a~'iY~~YF' ~,~~ ail3~~~ a~'S~:~T3~~J "aS
~'.J3l~rlS~d ~i~:
a ~~1~1~~9
.~~i ~i3~y ~ PrS~ ~:~rY3~ir~~;.a ~.C3~~~~>' dL a. :::'lrS~; ct.~la~
~(~~Si~:;;~3i dYid iY~ Cvi.;ir~~xY11~~3~1~TI
~'Jx~'fl ~~i~ ; ~~,~~M~gn
~iil~ a S~~'~9ri~: A~.',~.°allz~: ~v~,~->~~,~~ a~: ~ SP':%~Y?~ aXi2~
~~S'~EQ» aT'~Ci lfi
~~~.'1~,.L~YliCa~l6~~ ':~IA~!t. L~;~ ~~,~ial'°a3~~~~9 ~i~d
1~
~s~; ~aSSi~lg a~~ ~le~Er~~~-"d~, ~~~~~c? ~t~n°~Lg~ 6~1~ ~a~a~~~ei.
-_.~~ Laid ~r~~,Yg~ ~~<gj~ ~~ v~r~:rid~d ~~ a _~~L~id _r~~,rg~= Sc~F~r~e
w:~i~Y~ ~r~~~ideS
~:~Y~.SSLI$'~, .~~lr~,~,~3~ ~?2~rg~9 ~'tfC~rt~S~a~~, n2~a~3'9 !'~Y "s~l'z~
s;~E't1~7.~"'~a~,i~~ e~ fi =~.i~. ~YkES.'b~l C~3Y~9~.~~~'i~°Yi~5. ~'~C'
2~ ~x~~~~~le, ~N~~ ~iid ~rtzurg~ c~Lild ~ ~,~~~~~.d~u ~y t~ ~L~~~ as ~, dL~a ~
~~~~YgJ 5~L4r~~ ~i~i~~~ d~IE~~rS
~:~~° ~'~L~~d ~~ tl~~ ~a~~el a$ a ~~~ r;;°~ ;Yd:~S~a~~ a~~i :~
c~~a~~a~~. ~Y~r~r~hi~ :~~,~~~~~.,Y ~ ~d
9 ' , ~~1~ :'ILi
~Y~~rgy is ~r~~;d~d ,~rixr~a~Pil~~ ~r ~r~~i~Si~~l~~ ~y a i~~d~~c~st~~i~ r~vaca
~sr ~r.;~ss~~src~. ~~Y ~a~~~~.pi~j ~:~
~~~i~r;~i gay ~~: aSS~~aa~~d ~ri~im a_iL<~d -~~S::x~~r~ir aS ~~ ~~L~id ~r~wYg~
5~vr~~ ~Ji~~Y~a~rid~s a
d~Sired E~ydr~s~a~r~ prvSSLire ~~ ~~; 5~ ,W~z ~r=rig ~~ yaS ~~;~~Lga°~
~:~~, ~;~~aram~i.
~J
'i'i1e ~~~~a.~Y~~ ~~° ~"~~ad ~~~~rg~r cr~~y~ ~e ~~~Y~~ ar~~LZ~~ ~__~~~
is SL~a~~a~~~ t~ ~asS ~iae
~'.L~id tr~~~gF~ ~.'~~ ~i~ar~ra'l. ~i~i~~L~~;~~ s;h~ -~ ~yd ~~~ayr ~~ ~~.SS~d
r ~~r~~~g ~ t$a~ ~,har~r~~l v~d~r a~~
<C9~a~~ ~t~'Y°~d~~1~725 370~~11C~'? ,~rd',~r;d~ ~C~~° 5~:~3~
~~.~C3~%I~ f gr~dl~~l-~ iii ~~(~ sr2,a~iS~~~rS~ L~iY~:.C'~i~~1 %~C":~5;: ~~e,
~;~a:~~<. ~~:~ aY~~~~u~~~: ~f 3~~~id ~~~;~gyr ~r~,icra~i~ ~aaS~s ~i~~ ~iwd '~~
bass ~~~~~gi~~ ~ii~~ E:,~~~i~ei
3~ L~~d~r s~~s~an~iaxl~ iaY~i~.~aar z~~v;r ~~~~di~ic~~s ~~ c~~°~.eY ~c~
~Y~'~id~ ~. ~~~i ci~~~~d ~.l~l~~ity gradi~Y~~~
~~;.° tl~e ~ZLi~.d iYi ~i~e tra~ss~~rs~ dir~~ti~~~ ~~.r~~sS vi2e
~l~<~~~Y~~?.
a ~_

Image


CA 02437304 2003-08-14
>ra ~ peefer~'ød erxab~dirne~t, t~:_~, ci~arr :gel ~~as a fi~:.ite cross-
secti~nal ~r,.a ~,vl~ich is
less tiara a'~o~~~ 300 square rui~:~~~:~eters. ~~l~~~e s~referab'iy, ~:r~. ~,
pref~;rred er~bodie~t the
cl°~«.r~~~el has a ~'inite cross-sectc~~~.l area w3~~cl~ is =ess tha.~
sbo~t ~ square ~illirl~ete~°s. ~~re~~
more preferably, in a preferred eboriient the cl~aur~el has ~, i:irite cress-
sectional area ~~hich
is less than about 0.0~ square xnillirneters. i~lost preferably, in a
preferred ec~bedirne~t the
cr~ss-seetie~«l area ~f tl-re cha~~ el ~-~r~~~;s :ream ~et~mer~ abo;at 3 x 1
~~-4 s~u«~-~~ micr~ns and
~~co~t 0.03 square ~a~illimetexs, ~~' free b~a~eers «bo~t X9.03 s~~xare
rsr_icror~s ~,~d about 300
square microns, depe~~di~~g ~i~c~=~ tl7e prep~drties ~~f tl~e .fuid ~ar~~ tl~e
- h«nne= aid upc~r~~ the
desired electrical energy output «f~c~ efficiency of tl~e app«r~.tus.
'fhe cha~~el has an interier surface ~hicm~ provides are interface t~et~rvee~
the
ch«~r~cl and th.e fluid. the interior surfave ~fti~e ch~ra~e~. is prc~fe~ably
cer~struct~,d of a cl~a~mgel
~s~~ate~°ial ~lus~~E is relatively e~ec~:kecally ;aer~-cer~d~eti~~e so
than: a~~y surface curr~~~~t Eaduc;ed l;y
the streaming potential ire the i~~tericsr surlace ef tire cha~~~ei is
relatively srn.ail and thus does
l~ not dissipate the streaming potential. Tire i~~terier sarfac:e of t=~e
chapel may be corr~prised of
the same ra~~terial as the rernaiz~der o f tile chancel er ~~ay lie comprised
of a diffe,ren~: nzater~~al.
~'he chana~aei rrr.ate~~al ~r.z~d~ lye co~r~prised er'° «~~~~ k~«terial
~v~ichs ~~ila e~hi.bit aa~
e~CesS ~l?«r5° at tl~e 3~~:er~ser sld2'.'r~:.~.e ~f t~'1e ~;i'2i~1 do -
~fe pre~er'x~,e ei the flulG'F, sl~,Y'~,e 3t ~s tl~l~S
~0 excess charge ~vhicl~ is respos~sib~e for the ~~j~. pher~o~nenor~. 'f he
xernaindex of the channel
may be comprised of $-irtually an,y material.
Prefc;rably the ~.~te~~t ol'tG~e, ecess charge ~~t the ira-~erior surface
o'::"th~~ cba~~el is
~~xaxiB.~ized i~:~ order to ~na~in~ize ::lie effects of the ~~~, It is ~efeved
that the ~ieve,lep~r.~e~t of
25 excess charge at the interier s~r~~cv ei the char~r~e1 may be due to senae
disseci~.tien of the
ir~F~erior surfGce in the presence =e~~ the flr~id. prefe~~ential absexptien
of fluid lens ir~~t:o the selid
surface, an io~izaticn process res~_ltir~g f~-er~n i~teractien ef the interior
surface a~~d 'the fluid, or
~dy~'32~~3~3at~~17 e~ these Zdnd pe~'ha~S O~11e'_° el'~~e~'LS.
~0 'f he interior su~'~'~p~ce of the cisa~x~~el sl~o~ld pxef~;ra'~ly be
P~,o~npris~ad ~f a channel
~~ateri«l ~.vl~ich will signi~~ca~~tly exf~lbit the development ~f ~~l~~is
excess charge at the interi~r
y_


CA 02437304 2003-08-14
s~.ar face, regarci.less of ~ahici~ effe:lt or effects is ms~or~sibie for ghe
c?ewei~p~neut o~ ~.i~e excess
ehaxYge.
wr a preferred e~~nisodirr~er~t, ~ ~e ch~:.~~nei i:~ cor~strcted entirely of
grass so that
the chapel ~rgaterial as comprised ~i' glassy $~,rgich has beep obse:eci to
res~.zit ir! tie ~rod~ctio~~
r~i° ar~eas~r~bte electrical energy. a'~!iAny c~~i~~e~.°
ateriais ~r,~.y ho >~%e~er be potentially s~iia'r~le or
~3re.I''B~Ta,t~ Ion ~~e aS the CilaYlllea ii:;~o:er~a~, ~,~:Ci~.3d?:C'.zg
Ce:"~;E'E~les, ~~~stiC~ a~1'~..'~~' ~l~stL'ii~~.~y ~3Ce~irr112g
rzateriais such. ~,s rock and s~il.
lt: ~'he charnel has ~ finite l~;~g~i:. the iengtl-~ f~f the chan~ei is
pref~;rabiy
mzr~ir~ized in order to a~z~imi~e ~~id energy losses ti~~°orxgn tb~~
cban~ei. ~'referabl;~ the length
of t:~e chanr~ei is less tit°~;.r~~ about 3 ~ centi~~ters. more z~~-
eferabgy the Length of ripe cha~raei is
less than about 2 centimeters. ~;~e~. ~~zt~re preferably rtes'ength of the
ch~nr~ei is less fihan about
cer~tx~xaeter. the aea~gtb of trte c~°ar~~~el s:y'ee, greatc;r aY~an,
e~uai to, o~° less t~°~a~~ one di.starlCe
is ~et~:~ICell the i rst ax2al ~C3Slt3~~1 a=:~: the, 5ee~.7r~~i 'Ian posh'
~Cn.
'Errs electrolytic i°'~~id ~~i~icb is passdd ~~~rough tire eharriel
gray b~; con~pr~seci of
arEy ~I~id which ~~itt exhibit so~e dissociation into ions. she electrolytic
fi~.~i~ rr~ay be
cor~prise~ ~a~°a liquid or a gas o~° w~
eo~~°ft~br~a=io.~~ ot'ii~r~ids and gases. ~reFerably the eleetrolytic
2~ r'Iuid is a ii~uid.
~enerairy, strong electrolyvic fluids ~~iii ext~i~sit strong ~~9f, effects
arcl ~r~eak
electrolytic ~~:uids gill exhibit ~je~d~ ~~~, effects. it has 'teen generally
o~served that the
thickness of the ~.i"~I, decreases as the elec;t~c~iyfiic; strength ov°
3a~e fluid increases, ~s a results
2~ die properties of the electrolytic. ~~~zid are preferably considered in the
seieetior ~f the charnel
.ateriaz and the size and sh~.~e of t~xe ~;han~~el. In a ore,ferred
eznbodirr~e~at, ~neas,~a-able
eieetrieal e~aergy has beer proclvc~:ed ~-vitl~ f:lae use of deio~~i~ee~~
y~rxte~~ ~a v~ealZ eie~;,t-rolyte~ as the
e,iect-rol~cic ~~.id, buL more eleet_ical energy :gas ~~eer p:rodt~ced with tt-
~e i~~vent~.cn ?~y using tap
water ~a stronger electrolyte ttaa~~ deioni:~e~i eater; as the fluid,
3
a ~


CA 02437304 2003-08-14
'l:he arr°~ot of ele~;~ricai e~e~-gy ~~rod~aced by tl~e
rr°~~er~tiora a~ad the efficiency ~f
tl~e aplaaratus arid r~.etl~od ~a~ the i~i~~er~tio~~ are de~er~de~~t ~;~~o~
tlae tbicl~:~ess of the ELI: and
upon the zeta potential in the cl~a~~,nel, ~v~i~°~iel~ in turn are
deper~de_~.t upon the ~r~~er~ies oi° the
cbs~zr,e~ ~a~ ~>art~.caal~ar the chaz~ne' =~aaterial) and the properties os
the elecvolytic i~~xid vvhicia is
passed ti~r~~gb the cba~~nel. T'l~e ti~icl~r~ess b'f tle ~~i_, arid a t:a~iity
de~~ned as the reciprocal
of the ~.~L thiekness can both ~oe d~~,~'~ned ~~at~~e_r~at~cally.
tt has been obs~~~Je~~ taut bore t~~e a:~o~nt, of electrical energy prodLCed
by the
invention arid tl~e e~~cier~ey o~t~~e a~~ara~.~s and ~Letb~d c~~'the
~rsaention generally increase up
zt'3 to a lalateau value as the reci~ro~,6~~ ~~'the l;~a., t~~ie~ness
increases ~i.e., as ~e t~~ickuess Fs~ the
E~~ decreasesZ. In a preferred embodiment, ~~~r~ere tl~e e~.ectro~y~fc fluid
is deioraEzed water axed
the theme: material is glass, it has ~aeez~ obsercred 'bat i.t is pre:~erable
tbat the recipaocal o~~the
IJI3L, tbicless be greater than ~:~o,~t i ~ i'/n~ and that ~~rll~er be~ef~cial
effeets s.re rAegligible
after tl~e reciprocal of the ~T~~, vhlekness e~.ceeds ~bo~t :~ ~ 1t;~9/~~. ~~s
a resa~lt, in a preferred
1 ~ emb~dn~ent, the reciproeal o f tl~e ~L~L, thil~~~ess is pref~r~~iy
~etv~reer~ abotat l x l~'/m and
about i x i (19/m arid mc~r:°, pre:Cer~.bly bet5~ree3~ a~~o~t 1 ~ I
~~/m and about 1 ~ 1 ~J9/rn.
'i'he first terminal aid the second termir~a~ are sepa-ated by a mite axial
distance
s~ t~.'~ai tile st~'Car~3r~'1Pj '~~tl~~ltlc~cz ~K.~a by e~~t~:'~~lPSaleCf
betVv'e~'Y1 tl"Le ~~.rsi terCTignal ~.~rld tl~e seC'J%f~d
2~ terrr~inal. ~,s a result, the first t~,r~~ir~al i.s located at the drat
axial p~sition ire tl~e sna~el and
the second ter~iral is located ae tie seeor~~:r ~~cial positio~-~ in t;.ve
el~annel. Since tbv streaming
pote~atral is dependent upon the stream.i~.g carrent, the a~-nount of
electrical er~e~-gy produced by
the in~~ention is believed not tc~ ~~. svro~agly depe~clerat upon rb~; a:~ial
dista~~,ee be~;~een tile first
axial position arid tl~e seeo~d axial position.
.~s a result, the lccatiors ~z the ~-rst termir~ai anti the seeond terminal
are
preferably selected having regard to the :overall ciesigr~ c~ the ~,i~a~xnel
assembly. ~~ a preferred
err~b~dirne~3t, tl~e first axial position is :~ccate.~l ad~~.een t to a .fiist
end of flee cl~a=~:~el arrd the
seco~,d axial p~sition is located ad~acerut to a secdr~d end ~~i° the
eizar~.nel so that the aa~ial
Vita dtstar~ce bet~~we~. thze first ~werminal arcd flee secon~~ terrr8ina:~ is
a~:proxir~ately ecxual t~the length
cf th a eh a~rae-~.
l l ._


CA 02437304 2003-08-14
~pecificall~, in a preferred emhodiment the first axial position and ts~fe
second
axial position are located at sc~~~~e s~~all distance outside 'che ends of
th~~ chanr<el i~ order to
simpli-Ay the const~ction of the ~.,h~~o~gn el ass~;rnhly, '~~~t the first
a~i~:l position ~.~zd t~m~e se~o~r~d
axial position could alteanatively be located at some distance vaith in the
ends of the channel,
~.~hxch config:~ratio~ may ser~~e to rrin~~i:eretry and exit elyects ~~i~~ich
~~a~r s~ifecr the
operation and efficiency of the ~3~~ren's_ion.
he first te~-~ninai and the second tei~nina.l are in corr~munication ~~,~ith
the fluid
i~ as it passes through the channel s~:!ch tE~at ~h~ strea~~~ing potential is
exh~~iced ~cet~weer°j the nest
terminal and the second te~ir~al. I~ other ~~ords, tie fret terminal and the
second te~rnin~l are
comprised of an electrically cond~.ctive material ~3~ici1 is in ele<,~trcai
communication =,~itn the
~uld.
preferably the first terninal and the secor~~ terminal extend outside the
channel
and are electrically ins~zlated frog any elecd~ically c:~nductiwe portions of
the chain~el.
h_lternatively, n~rle first ternir~al ~;K~d the s~;cor~d ~:er~~i~~al rnay ~e
connected to a suitably
insulated electG-ical conductor vahicld exter~.ds wztside of the
chanr°tey.
2~ '"he invention rr~a~ be p.°actsc~d ~~ntl~ a single cha~~r~el
assem~ly if tlae ~n~o~nt of
electrical e~erb~r w'rich is required to be pro~aced by the i~~entio~ is ver~~
small din the order of
a'cout 1 nano-ampere or less per l~ilolsasc,al ~I~a, o~'° fluid
pressnre drop). a,~7here larger amounts
of electrical energy are req~airesi to a prcsd~ced, tl~e in~rention is
preferably practiced using a
pl~.rality of elc,ctrically connected c3~~nrel asser~~:~lies. i~~ a
prefe;rr°~? emhodirnent th a apparatus
of the invention is comprised of at least about 1 x 113 electrically
conr~ecte~ chan,~ael
assPmbiies, and more preferably at least shout ~.d~,~~30 electrically
connected channel
assembi.ies. ~sserkially, th.e i$.aer°~tion r.~a,~ be scaled. to
inclr~~de any :~ur~her o~_ channel
asse~n~'wes.
if the, inve~jvion includes a ~1~~-~~°alitgr <.~f channel
asser~~~hlies, each o:~tl~a., channel
assemblies ma.°~ be identical or n xay be different. for era npie, ~ac~
of the channel ~sserr~hl~ses
... '1 ~s


CA 02437304 2003-08-14
may ir~cla~de ~: separate First terrrsi~al and second terrrainal, or ~~;~o or
tr~ore of tb~; ch~.r~rlel
asse~r~blies may share terrr~ia~als.
'~'he plurality of ch~~-4~~e1 asseanblies nay be elec~~rically
cor~r°3ecte~ in a parallel
con ~~~uration so that the farst terminals of the channel assemblies are
electrically c;oa~nected, a
series confi~uraiion so that the first terminal oi° o~>e of a pair
oi° channel assemblies and the
second ~errninal of the ottzer of t1-~e pair of c,~~arlnel asse-r~~blies are
electrically c,on~~ected, or
some cornbinatiori of parallel aid series configurations. ~on~~~3rin~ the
channel asso,rruiies in
parallel provides additive currents .~hile conii~u~°in~ the,
s.;l~arm~"1 ~5sse~~~~lies irf series provides
l~ additive poter~tiai differences. tr ~ f~rei'erred c~~i~od_~rrie,nt, tlae
plurality ol"cl°~anneF as:~ernblies is
~,oraa~gu~-ed in para11e1 and the v~rsv .erf~~.i~~als arid the sec=ond
tc:~i~~als of each cf tl~e ch~~n~el
~ssea:~bl=es are shared.
1:1' tj~e first te:~arsals and v.~~e se;cor~d terrri~~~a$s a~:e shared :ln ~.
parallel
15 eoniigua-~tioa~ of channel. assemblies, the :l"xrst terminals r~~ay b~~
comprised of a grs~: electrode
and the second terminals may be corr~prised of ~a secc~~~d ~;l~s~t=rode.
~,~There the invention
includes a lust electrode and a second elwfitrode, the first elec~rs;~de
prefera~cly co~z~prises ~. first
connection point and the second electrode preferably comprises a seco=~d con
action poir~C
which are adapted to provide co~x,~ections fo~~ tire electrically cen~ucting
path bet~rveen the ~~rst
~~3 electrode and t~s~e second electr~;dp so p'~afi; an e~ter~aal load
c~ar~ent can be carried be-~vvee~ the
a~rst electrode and the second else erode. '~'1~~:, elects°ode
connection points may he comprised of
the electrodes themselves, or they nay be Llectricall;y converted vaitl-~ the
electrodes.
if the invention includes ~. pa~.~rality e~~ ch~.nnei assemblies, tl~e channel
asse~~blies may be comprised of d iscrete channels or the apparatus o~°
the invention may be
cs~n~priscd of ~ bulk material vvhpcl~ includes a pl~xr~.livy o~~' chan~'els.
'the bulk material rnay be
~~.bricated ox- ~~xay be oaturalty oocivrrin~. ~ 1rt_e ~tar~.liiy ov'
chani~~els snay be defined by pores in
'she b~llc material i f t~~e pores facilitate _~assa~e o~ the l~~.sid froe~n
the first axial 3:osition t~ vie
second a~ia1 position in the pores. ~s a result, the balk ~ate~i~.l should
include pores ~,vhich
~Q provide perrr~eability to the bulk ~~ate~~~~,1. l:f the ch~,r~~els are
de~~ned by pores in a bull
~~aterial, at least the interior surl~c;e ol°t=~e _~yores a preferably
constructed of a r~latlvely nor~-
_t~_


CA 02437304 2003-08-14
~~k'~~~.?~~ale ~'3't~l~'ii'le~ 1'lla~el'ial. ~~ ~ia~..reli'C~=~
~.°.l3_",=°u"'o5°"~~lrl~°.13~, ~.'t~°s~
~~2°cfIe~.,°~s al°e ~eilFYC,'~ '~'~ 5f91°eS 11"~
~.
~c~~~vs Mass vi~e~ ~°~ate~aai.
~~i~e eiee~:~iealiy e~~s~~~ele~ib~~~a~i° ~z~; ~7e ~r~~i~~.ci ~e~~~eell
~;e~r~~~~ais~ be~~,~ee~l
eieeLr~~es, cr be~~aeer eiec~l~~de ~;~i,~~ee~i~~. ~~i~a~s. ~'~e
e.~,e~r~e.~~e~r e~l~~~e~in~ ~~~~~1 ~efe~a'~l~
i~aei~~es an elcc'~ricai i~a~. 'I'iae ei~c.°,~~eai ic~d~i ~~e~'e~abi~
v~~iii~es tie eiec~~eal el~e~ ;;~ ~Y~~acesi
~~ rb a irrver~~:isst~ pe~~~~~~ vse~aF_ wv~3~~. ~'~=u ~,ieetiieai -~~a~ l~~.y
'~~e a~.;~ iy~e ~i' ~~ee~ricai lc~aci
i~e?~~il~~ a ~es~s~i~e9 ea~aea~ive ~r ~r~~zr~~i~re =~~as~h ~ a~bir:a~i~el~
c~i°s~xc~~ i~aa~s.
'~~'x~le e~$ect~-ieai Ie~~~ r~a~ be sewee~e~ s~ ~t~ar Vibe ew.~~~te~:i~bg
e~r~e~:~~ be~~rvee~z rile
~°~l~s"~ ~e~-~~ilZais ~~~. lire see~l~~ ~e~~-u~:~~-~ais is l~
e~i~li~~ci. i~ c~~~er ~~rsg -~:~.e eiee~~Leai i~a~ l~a~r
., .
~e Se~e~~CjC~ GCB ~alt'1~~1C)Il as Ei s~li.=.~i i.~r'1~ Tz ~l~pl° ~L%
lY3i~li~l~~ :~ke~~Y'~3-~ls~~lls ~~~~°,e'',~S i~~ ~:~'le
~~ aT"tile? s.
h S2e ~.,~Se ~9~ file it~FTeI', 1~'9a's La'3 t3:lw'~~loilZ~~..~e~~l°a-
':I1S~°~Eis e~~e~~',S g9. ~-~7e E~~~paa;I~.e~s ll~a''y'
~~~~i~e ~ea~.e~lviai e~i'eets bar ~~i~~.~~r.~~~1~ E.il~; a~~~a:-~1~ ~~
q,ryer~y ~:a~ is ~c,ci~li~e~ ~~ bass f=.t~i~s
~~-~~:~gi~ tie e~a~r~eis aras~ b~ 1~~~~~~izi~~~ e~;:r~~ lasses ~~a'niex2 age
e~~erie~ee~ ~.s fi~lis bass
~~,1~~~,~~~e eba~~l~leis. '~~~ese be~~e~~~eiai e~~e~,ts z~La~~ ~l~
~~:°r~ be ~~i~ieci ~v~~~al-cis ~_~,~jv~il~~ Vibe
~e:_i'~s~r~lal~ce ~~ a~~ara~a~s ~~~lriei~ ~~°'x~~ ~a~~~~~~te ~ass4~~e
~~~ ~i~i~u ~~~~~~~z~~ .~a~.l~e~:,~ ~a~ie~.ia~i~
° ~ y~ °
~'~ '~Je'~7 sl~~.~~~~ Cs~a~l~e~as ~?~' ~1.~~~~~C~e?Eli~"~ea~ . w'~E°
~,j'salY~~ap~~~ a~~ ~~~,1'a~,~~~A~ ~~l'1~ e'~-~l~;Eel'~~.~ va ~~a~~lY~~
a~3~arasi:~s ~l~i~~ xel~1 ~l~~ll ~3assi'~~~ a L~~~el'~~; s'~~~iL~
~::~i3~~.~.~%if a~"%Ii~h~"N°~~ai'll~e~s ~:~ ~~3vT~ ~t~~,~~lani~2~~
~ai~S C3a e~s,C~l'x~~~~ ~,~1~'t~C~~ei~~S Si~~,~° ~~~s ~~~c,;ff-
?°a~eQ ~l<"~'~I~;s ea~i~ ~~;?'~sJ~~~'' e~~~5 l~'I~~7 ,~,~e ~,sl~3a~~e~
'c~~:~ a~~"-'ll~a~le513 ~l'~ i:.~e 11%~~.11~;i~1~ s_~ ~: ~F~al°~>'l~i
~xJ't'ir~"~_ z'Y3.~fl~?i~l~eS v~a,C~l°~-'~J9.S~~~aS e~~ev~5 lea' ~3.1e
Yl~ a~~°~~.~ allile~ls.
~'I°e~eF°a~7~~, _'~~~We'~~~;;s."; ~'~e e~~,~,ba°3~;~~>
~~ia~ ~S se~e~e~ $~ s~~9~xT321Ze 5~ixe s.~TEt9~:~~ s~l~
e;lea,~:l'l~ai -~7J~5i~ '1~Vl;'~~ 1S ~l4~Ct~Ce~. ~~r ~11e
:~~1°~'~~~:lt3~l.. ~ ~~ ~~~al?~~z.e; "s~ ~~e e~3e~:~Y°~C2s
h~~.aa is ~lel°~
s~~ali, ~~e e~~~;A°~3a1 ?~asi ee~~l°ez~~ c~~v3~gia ~I~e '
:eev~ic~~i i~a~ ~~rili ~e veer ia~e9 ~bieil ~~ay ~~a~c
~:~le ~~~' j;~ ~~ ~Cf~~~d~lxl~T Sl~il~~(:.°,aaa'~.y' ~~le
~('.s~:e~~ilax ~zlle:~'e2'aG~ be~.\%~e:,~?'3 ~~e ::IYS'~
~:~~.1°~'l~.ll~l ~irl~i file.
Se~C32~~ ~:a,Y':'~?'h~3~!~ '~i.~e'~ ~Ci ~Ii~~l ~ef'Y'i~'rl~' s t~P1 ~;~~e
~i"kI~3FF".: GPI i.~~'eYl~E; ~~tlkr~~~x lTlLls'~ be ~aiYie~ be~~i'Je~~l.
pile fars~ ~e~nr~a~ aid rile se~,c~~::~,~~~lnaZ. '~x~ rel°wey~5 ~,-
° y~de eae~ihie~~,I ~ca~ is ~~e wy ia~be; ~~e
~, ~.


CA 02437304 2003-08-14
external load current through the e.lcctrical IoErd w~il1 be very srnasl,
~~hich ~~ill ha~~~the effect of
reducing t'_~e electrical power ov~v~.t bet~~~era tl~e f~~°st
t~r~~~inal .~~d the s~;concl terrrninal, ~~ince
electrical power output will vary according to tl~e sq~ pare of the external
load current.
In a prefea~red embodi=rent con~prisin~g an estimated ~.5~,~tI~ charcrFael
assemblies,
it ~~as beer"a obsers~ed that the ele,~;vcaal load is a~~°e~erabl~ a
ress.sr~e load o.f ber~%~een about 1
ohrn and abo~i: I x l~~ ohr_~s (or a load cwhich. is eq~walent to resistive
load of betv~reen about I
ohm and a'eout I x ~z~~ ohms), or ~, .rore ,~refera~ly :z resi srive
h°~~.d -of l~et~~een ab~~~at I~3~ ~ahxns
and about 1 x 1 t~~ ohms for a loan; which is equivaier~t to resistive load of
between about I ~0~
I~ or~~as and about 1 x I~~ ohs~.
~electian of the esec~~ical load to optinii~e the ~:"orlc prod~;_ced by tire
invention
will be dependent aeon the proper~E~s of tire channels, the ~rope~~~~,s of the
electrol~tac fl~id and
the number of channel assemblies v~~hich are utilized in f ie inventio~~.
the invention may be used in a steady state. ~nann er in which the ; ~.~id is
passed
in a single directiozb thro~,~gl~ the 4~°:ivanncls c~thc~~ toward ~,~.e
fr:st axial position ~;~° tovaard the
second axial position.
?A he in=aeration rna~j also be used in an alter~-aating ~-~a~naaer i~~ which
the fla~id is
passed alternately tiirougl~ the ch°w~s~~els ira a dire;cti:>n toveard
tl~.c second a~~ia1 pc~s~tion or in a
direction. tovrard the first axial po>s~tior~ to i~rovide an altc-~atir~g
~Jotential differe~~ce bev~een
the fii°st te~~ninal and the second t~;r~r~inal oi" the ci~ann e1
asserr~bl~es. ~~here the in~rention is
Used in 'the alternating ma~~ner, prc~erabl_~ ts~e f~:~~id is passed tl~ro~gh
the channels so That the
2~ potentiaF difference between tlse ~:rst terminal end tl-~e second terminal
of the channel
assemblies alter$'ates sine.soidally. i~ne fray=enc~ of the airernatin;~
pov;e~~:aal differ~;nce ray«y be
any frequency which can be produc~.d througi:~ the a ~overraent of the fluid
through the channels,
and ~aix1 defsend upon the properti~~~of the, flExid, '~I°~e:
prop4=.::ties r:>f :be chan~~e1 naa~Lrial an~~ the
size of tire chaz~~els.
3~
_y_


CA 02437304 2003-08-14
'~'he apparatus of Y~~l~, ir~~rezrt~~rT ~~ay i~lci~de a~~ aiter~zatir~g
rT~earTs each as an
aite~g~T~taT~Tg F~ae~x~FaF~ism _~or ca~s~~~: tlafi~i~. to pass
~:hT°o~gh vine ~iTar~~~zeis in ara aitematil~g
z~ar~T~ser. The aiterslating mechaT~izsar. ~3ay b~,~ comprised of any
~eei~lanrsT or T~ectT~~Tisrr~s for
causing the flzzid to pass through t~:~e channe=. s iT~ an alternating
~~TaF2l~er, arFd Tray oz- rz~.ay Faot be
associated ~rit~he ~~uid energy so~.~rce.
~~S C~flB llon-iiYllFt=~s~ eisartl~~. ~~'~ an a~tc.!'natFF~g
F~2ef:~l~r~IISFY°~, the alteralatFFTg
z~lechar~isln rrTay bd coz~iprised ~cw: a ~~aive ~Te~haz:zisr~T va~ich
~iteTateiy directs ~i~~e fluid i~~
different directions fsorr~~ the f ~z.zi~ =~w~ergy soz:iz°ce,.
i~
1~s ~, second non-ii~iting ex~h~ pier tire aitez~atin,~:rnecla.arlisrn a~~.y
be c,ognprised
oa' a z~novabie ~no~nt associate. pith the apparat~.as by ~.v3~ich ~3~e
positions of 5the first axial
position and ti°Fe second axial positiorF relative to file r'~zud
energy are altzrnateiy varied ~s the
f~TOVable rrlo~F~z is act~.ated, s~.~ch ~.s for ea~arr~ple by reciprocatioFJz
or roratioF~.
t~
!~s a third zzorz-iin~~vizzg example, tire fiuid energy so~.ree rlFay be
comprised of a
fluid T°esewoir ~aositioneci at each ~;rTd of the chaFZrzc;ls and the
z~elatB ve hydrostatic heads of the
fluid reservoirs bray be alternately varied to create an alterrzatirFg
pressure gradient i:rz the
different direr=ions, either by varo~irTg the ~~uid i~;vels r~ the ~eservoi~-s
or by chgiF~g the
relative a?evatioris ofthe fluid res~.T-~roirs.
r~he second and ti~:~~~~ exarrapa~;s Fa~ay a~so '~~e cor~~bir~ged to provide
an alte~~latiF~g
T~echan.isrT~ wh-~clr corrzprises a rz~ova~-Ae r~~~~x~at vainiciF rzFOVes
°~he ehanreg assen~ii~lres and the
eservoTls LogPther t~' Gre,atPr a~TerSa.~,~FTT.g presSzdre ~ia~TvlFts.
~.s a fourth noT~-ii~-~~tiF~g exana~p.le., the fluid energy source z~nay be
corr=prised of a
r°ciprocatiFag apparatus irTCluding ~> piston ir: a cylinder tniclz
z~~,y be used to alternately apply
pressure az°Fd sz~ctio~F to the fl~id ~o cause tl~le did to pass in
opposite directioFzs thraugl~ the
cl~anrTe:~s. Tine foz~-'ch. T~lorT-iimiti~°~g example ~~,y ~e ~ztili2e~
iFZ coF~~zarlctioF~F ~iitl! a f~~id
F't:Sei'~/~'D.r ~7v"~'BTC;i:r pr~'JVIdeS ~, 5~71!:fCe ~~~~I_GTC~ tp.'°~
'C')C', ~C''iG'd ~~i~.C2:~! ~y t3.:e "s"~ClA~roe.eetln~ c'~Zpy~alatLYS.


CA 02437304 2003-08-14
~n a preferred e~n.~~°c~din2ent where t~~e fluid is deiv~~iz~d water
and the chancel
~~3~teria'is Mass, it has'ceen obsc~er~~d thai: ca~gen ~;as is ~rodus;b,~at
cne of the terminals ~~e to
oxidation of hydroxyl groups and vlaat hy~d~~:~ges~ ga.s is produt;eci at the
other of the terrr~inals
die to reduction of hydrogen ionso The i-~~~ention :nay therefore prc~t~ride
an ancillary function
as an elcctrochernic;~~e cell in ~eic~~~e eie~Jr~vi~r~ic ;~'~.u=d ~a
c,on~~~c~a~into no~~ion~.; constituents,
which ~aanionic constituents ynay be r~ith~aa~~rn from the t~inals either to
increase the
e~=~ciency c~f the apts~ratus of thze ia~~~entio~-s cr ts~ produce ~.he
no.r~ic~~ic consi:i~uenta. ~~.s a Ycsult,
':~.c in~renticrx 3:nay ir~cluc~e one or ~~~.ytrs of °~~~~l~clra~rin; a
~cducc~ ~rc~c~uci; fr~rn ~~~e of the _7rst
terminal or the second terminal or =.~~ithdra.~,Ti=ag an c~xi~ized product
fro~~ the other of the first
1~ germinal csr the seco~~d teraninal oa~c~e or ~~orc cf the chan~~el
a;>se~l~lies.
~~ZIE~' ~~~~~sIPTl~~1 ~F Dl~ ~,~~5
embodiments of tl:e in~er~tion ;gill nox~r be describ~,d with reference to the
I 5 accompanying dra~~~n gs, in wh~cs_a
figure I is a sche~r~atic representation ~f a charge distribution within an
~I'~.
.,~igure 2 is a scher~~~atic representation oa a charge distribution in a
channel
20 containing a li~a~id ~Lnder static coz~~itions.
Figtare 3 is a schematic repres;,ntatioiz of a typical pa~wbolic velocity
f,rofile for
fluid flow through a ch~r~nel ~cn~e: l:~n~inas w.~ co~:~diticns.
2~ figure ~ is a schematic <epresentation of an apparatus according t6 the
invention
i_~cluding a single channel circuit ~~r.~ depicti~:;~ a charge d~stribu'~t:ic~
~.:~3~der fiow~ conditions.
figure. 5 ~.s a sche,~-r~atic zvpYesentaicn cf a s:ia~glM~ channe3 circuit
including
strearnir~ c~,arrent ar~~ conductza~~; ~;~rrent ~~rit~~yut din
electricall°~ ~,cns'auctir~,~ pat:''~~ and about
3~ an electrical load as contemplated b7 the invention.
_l7_


CA 02437304 2003-08-14
~i~gure ~ is a Sc~er~~at~c re;~res~,3~ta'~;o~~ off' ~. c~:rcur~t accordvng to
t.'1e ~~~~c~t~o~
including a plurality cf channel as;se~~'olies conferred i~E parallels ~~
electricall;~ conducting
pith and ~:~ electrical load.
~ige 7 is a schvr~~atic represerrtatlor~ of a cir(~~at as:cording to the
in~rentio~~
ix~cl~ding a plurality of ch~,n~ae1 ~ssc°a~hliE; s c~~~igaa~ed in
serle;t~ a~a electrlc~ll~ conducting patb~
and an electrical load.
~'igz~re ~ is a gr~:p~~ ~,d~hcl~ p~epic~:~ a. tl~eore~tl.c~ n relationship
'~et~,~een seta
t~ potential and external load eurre~~t p~roduced'4Ey the i~~ve~iti~r~.
liigure g is a graph ~ulhicla depicts a theoretical relationship ~ret~~eer the
reciprocal o~ ESL thicl~b~ess and e;xte~~r~x~l toad cv~-re:et produced ~~~
t~~e in~r°r~.tlo~.
l~ ~lgu~e iG is a grapi. vy~hich depicts a theoretical relationship lsei;green
channel
length and external load current pa~o(3uced t~~ ~~e in~,~cntion.
hagure 1 i is a gvaph ~l~ich depicts ~, theoretical ~~el~ tioa~ship l~et~een
the radius
of a circular cha~anel and the ef~ic=er~c~ o~the an~entbon.
2~
1~ig~a~e i~ is a gy°ay.~h ~~rhichg depi~;ts a ~;heo~°e;~.ic~~l
relationship ~er~ee~ the
reciprocal o~~E~L thickness and ~~he ef~cienc~,=ofthc~ iri~ention.
~agure 13 is a gra~ah ~~-hicl~ depicts ~ theoretica2. relationship
'r~et~~aeer~ channel
2~ length axW the ezficienc~ or"the i,~~m~~t:or~.
~ig~are l~. is a graph ~~l~ich depicts a theoretical relationship het~eeri aa~
external
electrical load an~1 the e~ficienc~ o.i'the i~~wer~tl.oa~.
1~igure l~ is a schc~~~:~btlc rer~reser~~~.tror~ oi' a pr~,~er°red
emhodvrnent oC are
e~is~;~-irner~tai apparatus according ~.o tl~~; ila're~t;~o~~..
_. i ~ -


CA 02437304 2003-08-14
~ig~tre lfi is a s~;h~,,ntatic represeration of on~; ernboclirnent of an
~ltert~atirtg
rnFechanism according to the invr~tE.~:io~.
3Higure 1 ~ is a scltetxtatic re~resordation of ,an ~ltErnate embodiment of an
alteatia~g a~echar~ism according to the invention.
C~~~'~~ IL~,I~ ~~S~~l~ ~ I~1T
s~ eferring to ~ig~re l, an electric doable laycw (~~a~ ) (~0) is created at
an
interface between ~ solid surface (~ j) and ~n elwc~~olytic fluid ~>taca~t as
a liquid (~~1). 'fhe ~~~,
(r~) is created as a res~,tlt of a loealized charge (26j at the solid
s~tbfac,e (2~). ~t ~i~9 believed that
the localized charge (26) may i~L cat:~secl lay son:~e dissociati.ort o'=_~
the rnaterias of the solid
s~.trface (22), preferential absor~t=ot-~ of liduid (2~) ions into the solid
;surface (22)., art ionization
1 ~ ~re~cess resulting from interactior'_ ol'the solid s~arfa~~;e (~,2;~ and
ts~e -~idt~id (~~)g or ~~ cotrtbination
o:~these and erlaa~s other effects.
'1"lre l;Iw (~~) includes an i.~nt~t7obile layer (~~) of liqrtita (~~.) ions
a~jayea~t to the
solid surface (2~) and a mobile la~~er (3~ j of liquid (2~) ions ad;ace,:~t to
the is~atnobale layer
2~ (2:~). The creation of the ~~~, (~~~ res~l ~s its a z~,ta po~:erttial. 3 i
) l;et~%vee~1 the solid sty face
(~2) aid the iiq~id (24).
Rhe irnr~tobile layer (2~y~ o~ the ~~1~ (~.Q) consists essentially of
t,o~.tnter-ions
(~~) which have a charge ~p~osite ro the ir~calize~i charge (~sa~ a~~ tr;e
solid stt~'~ace (22) and
2~ ~v~ich are therefore attracted to t=~e'ocaiized charge: (2~). she
t~~o~~ile; layer (30) i~tcudes both
cotulter-ions (33) and co-ions (3~) 1-tavi~;g the same charge as the locaeizea
charge (25), but ~lte
rzaobile layer (3tl) contaitls a relative excess off: co-io:n.s (35 ), due Feo
elec;t~restatic re~u~lsion of the
co-ions (~~) frorc~ the localized char;~e (:~S) .tad die to the relative
sz~c~~'~age of co~ter-ions (3~)
in the mobile layer (~0).
_19_


CA 02437304 2003-08-14
In Ijig:zre i, tl~e ~cc~iize,~cf~arbe '2~) at the selid sc~rl°ace (22)
is negative, the
ce~anter-ioa,s (3.~) in the inarraobil4e layer (2~,) are pcsiti~Jey an ~~ ~e
c~-ions (35) in the a~cbile
layer (3~) are pesitive. ~ hese c~a~~ges are e;xe,rrap>iary cWy, and the
respecti~re charges r;~ay be
re~erse~. ia~ a ~a~ticui~r ~I~I, (2~j system, ~eper3~ing upon t:E.r
~~reaiaerties ef t~~e s~;lid surface
x,22) arzd the Iiqt~id (24).
'fee ;nagnit~de of tine ~I~L (2c~) efi:ect it a, partic~;.lar ~I~I, (20)
s~stc,aa~ ill be
dependent open the properties ef ~~~e sc:~id sa~a°fac~.;° (22)
and zxpen t~~e properties oz' the liquid
(2~.). In general, the greater the localized c;~arge (26) at the scalid
saarface (22), the greater the
J ~I~L ;2C~) effect and the greater wig a elect. oyrtic st~ea~gcf the liquid
(24), the greater the ~l~L
(2~;~ efsect.
Deferring to ~'ig~,~re 2, the EI~L~ (2C;) t~a~r be ~;re~~te~. ire ~ char~r~el.
(32). In a
~reierred embodiment, the c~anr~ei (~2is s~tbsrantia>ly circular in cross-
sectic~a, ba,:t the
I 5 cnaranel (32 j rr_a~ be, any shape.
~'he ~~I, (2~) ~i'F ~ be created in the claararaei (::~2) regardEess of tie
size of the
c~~annel (32). 'fhe size cf the chaa~nei (~2) depic't~,,d in '~ig~aa°e;
2 is such that the rraobile lager
~~0) extends s~bs2ar~tiail~ to the c~~teriine, e-~:a t~3e ci-~~xia~el (~2),
~~riti~ ripe res~ait that the, effects of
2C tl~e ~~L (2~) ire exhibited across ~abstar3tiail~ tire entire cr~s,~-
sectic~~ car the chi"~n~~i (32). In
~~'ig~,~re 2 as ire ~'ig~re I, the iccaiiLed charge (2~; at t-he solid serlace
(22) is cAega~.ive, the
cc~.anter-lens (3~) are positiYve, arid the ce-ions ,~3.~) are negative;.
h'igaare 2 depicts the ~,I~L (2~)
under static (zero flour) conditions.
2~ figure 3 depicts a velocity larolile (~~) v~~hich is j.zca1 for
substantially laminar
aqe~~r. ~'he ~relccity pre~lP (34) is generally parabolic in shape:, ~~=itl_
the ve'1~city varying in a
transverse direction relative to flee sr~lid surface f22) i'r~na cssent.ially
zero velocity (3~) adjacent
to the s~lid surface ;22,~ tc a ar~axr~rrarn erelc~cit~j (.~8~ at the
centerline ~:~f the cham.el (32). 'flee
velocity profile (34.) for trar~sition~l I~o~~ er for s~b,ztant:da~ly
tua:ba~4e~~at ~ovr typica=ly exhibits a
3~ re~ativelv "~iunt" transition betr~ree;n zero velocity (~~) dnd n
~axi~n~:~rn velocity (3~) and is
typically s~ra~ae~.vhat mere ~anpredict~.ble than the ve~ecit;y profile; (3~)
nor la~:rainar I~e~xr. ~~s a
_2~_


CA 02437304 2003-08-14
result, altha~gh '~.he invention rr~~y he ~g~cvice~ nn~er an~r Nor conditians,
preferably the
invention is practiced under s~i~st~antiaily ia3ni ear flog conditions.
~igurd ~ is a gJr~~:ralized sch:.rrtatic representation of ar~ ene~~gy
conversion
~.pparat~.rs (3~according to thw ins%entio~ a=id of a charge
dist~°il=~~atron _~. th~~; c~.annel (~2)
~obtai~8e~ by supep-positioning ljg~~~re 2 abW F'ig~xrL ~ ~:ader steady state
fio~~ conditions. The
energy conversion apparatus (~~) ~;amprises a channel sssernhly (~-~).
The channel assmr=ply (~.~) incl~cl~;s ~:he char~rtel (32) and ova te~»
~~n~,ls a~rhich
~~rs~ ire: camur~icatiagl ~~,ritl~~ the li~l~.id (~~r: a~ it masses
t'~o;.agl~s the, ctmnn~;l (~2). lra Figure ~., the
terminal on the left is a first ters~~inal (42) and tie terYninal ~.~_~ the
right is a second terminal
(4~-), hut the relative positions of tl-~e; ten~in~,ls (4~,~4) is
~rztercl:_anged~,~le.
'The first terminal (~~2) is z~asitzar~ei at ~ first ~:M:~.1 -~:o,~iti~sn (4~)
arid the second
i S terrnir~~.l (44) ~s positioned at a second aria: position (48). The _~rst
axial pasit~o~~ (~; ) and the
second axial position (48) are preferably looted adj~cezgt to th~" en~as of
the chanr~~,l (3~), e.ither
~.t th.e ends of the chaisnel (~~), ~~a some ~listax-~ce ~:~ntside of the
:e~:~ds of the cl3an~~el (~2), or at
some distance vaithin the ends of t.e channel (32). 'l'he fret ~.~i~,l
oaitic~n (4E) ~~~d the second
~xi~,l position (48) are se~aa~ate:l c:y a i~r~ite dista~:r~ce. ~'l~e
vre~in~ls (~-2,44) are electrically
20 cor~da~ctive to facilitate an electrical cannectio~a h~;tiuee~a the
i;~.rt~irzt~ls (42744) ~n.d the li~nid
(24).
In ~'i,~L~re 4, negat-ivy co-io~~.s (:~~) ~.~r; prcfcrentiw3ly tra:r~sparted
da~x~r~strvar~ (to
the right in ~zg~.re 4~) as a result a~'" tire ~;or~~hir~ed effects of the
relative excess of ca-ions (3~) in
tze rna5oile layer (3~) and the velocity ~rofiae (~4) ~l~ich provides tl:~w,
rr~.ax Arna~r~~ vegocit~r (~8) at
the cer_terline of the charbnPl (~~).
The tej~rrainals (427~.E) i°~nc9;ioJ~ ~~s electrodes. ~~r~ the
c:Jnfig~ratior= clepEcted irq
1=~ig~.re ~., the fprst terminal (42) func=:ior~s as a cathode and the
sek,an~. terminal (44j, functio~~s ~s
an anode. In otl~e~-wards, there is a~ excess of negative co-ions (~.~) at the
se~;and terr~i~~~.l (4~.)
relative to tl3e first terminal (~,2). °~~Ihc;re the c~~a:~ges of l;he
canter-inns (~:3) and the co-ions
_ ~t


CA 02437304 2003-08-14
(3~~) are reversed, tire ~irst teri~~~.l (~.~) ~~~~311 ~.inctvon as an ~:rsode
and the second tennir~al will
fa~nctirsrn as a oathode (44). ~~hexw the ir~~zva~tion is practices: in ~~.n
ahcerc~~ting n:~,nne~~, the first
terminal (~2) ~.r~.d the secoT~~d cep inai ;~~) ~nrii sash ~:lter°~~ate
'~etyx~e~~~a functioning ws a ;,ath~de
~r~d ar anode.
The teF°~ninals (~r9~~) rrgay extend outside ofthe channel (~2) or
tern2inate within
the channel (~~). 'here the teri~n3nals (4~,~.~) extend ~t~tside ofthe channel
(32), tre ter_~inals
#;42,4.4) are preferably ins~zlated at :any points of cor~t~.ct Wraith other
co~~ducting materials in order
to avoid electrical energy losses die to sl~.ort-circuiting.
~nlhere the ter~nin~.h9 (4-~,4-~) do not extend out;~~de of the ch~nnei (3
~)., th~,y are
preferably electrically coreneete~ v,~itl~ °~ires or other
cor~~a~uetors in order to -provide an
extension of the ~errninals (~.2, ~-~~.) outside of ne channel (:~~). '~Tlaere
provide d, these
c:o:~ductors are preferably insulated at any points ~~f contest v~~.tl~ other
conducting materials in
1 ~ o3-der tc~ avoid Plectricai energy los ses ~~ae to short-eirca~iting.
first connection ~.~inr (~J) is pros~ided for providing a connection between
the
first terrnir~al (4.Z) and an electrically conducting path (~~). ~irnilarly, a
second donnection
point (~4.) is provided for providing a connection. beer°en the sece:nd
te~ninal (~4.) arid the
2~ electrically conducting path (~2). The eE.ectricall,~~ conductir~~; p~.th
(5~provides ~ ~~ e~tern~,l
v:irc~.ait fhr carrying an external io~cc~rre~zt (~c~) laetween the first
terroir~~l (~2) ~~~d n~'~e second
terz~.~.na~ (4-~).
'f he electrically co~~daetin;~ pith (~~~) co-rn_pri6,a~s an electrical ic~ad
(W). ~.n
25 Figure ~., the electrical load (~~) a eepicted as ~. resistive loan, ~~t
thE~ electrical loaa (5~) rray
he eornprised of any type of load ~i.e.9 resistive, cal~acitive or
~a:rsductive) or any cornhir~ati~sn of
loads. nor desior~ purposes, the elec;trieal i=.~ad '5~) ~~nay also
co:rr~p~~ise the inherent resistance off'
rs~.e eectricatly :~ondvcix~~g pat~°~ (5~,~.
3~ ~uri~ag ilov~ corditio~xss a Ltseai~ning current (~i);~ is created by the
preferentiaj
do~~nstream transport ofc~-30i1s (~~). This streaming cu~rent (~i(3) in tern
res~zlts in a streaming
_~~_


CA 02437304 2003-08-14
potential (d2) between tl~e f~rs~ ~~~ir~~i (~.2) arld tl~e second tern~ir~ai
(~~.). 'i.'he streaming
tsotential (~2) provides a voltage source ~br xhe external load ~;uxrerit
(S6), wb.icl~ passes through
the elect-ricaliy conducting path (_3~) and tire electrical load ( S~) ~.jia
the first co~nn°ction point
tS~) and the second coi~ection point (SLR).
G
'Tbe external load ~urre~t (5~) is Created bar tire conversion of quid energy
into
~:lectricai energy. ~'lze fluid enemy is ~ro~~aded as tlzc arnou3~.: of
e~~ergy wl~ic~s is required to
pass the liquid (~~) through rim c~anr~el (.~'~). ~'lae efec~ariral power
co~~su~~~~~ion of the
electrically conducting path (S~) :eau be caculated by r~ultil~iyi~g the
ss.~uare of the external
iQ load ca~.r~rent (S&) by the aa~oua~t :~f the elect~°icat load (S~).
~'igu,re S pro~aide:~ ~:,. sche~:~~atic re~rcsei~tation oa ~~ eircuir~
p,~~~ridwd y a single
cl°xannel in the abscr3cc of th~c electrically cund~cting path (S~a~
provided by tt~e invention. In
~ig~re S9 the streaming current (6~) is caused by passage of they iiquic~
(2~.) througkn the channel
15 (.3~), thus resulting in the strear~~:i~~g l;oteritial (~24. jn F'igur~. S,
tl~e streaming o~zr ent (~0) is
shown as rr~oving in the downstrea~. dire~,tion in thc~, channel (3'~),
reg;ardKess of whetiaer tl~~e co-
ioz~.s (3S) are posiiive ions or nega.tire io~~s.
~'he streaming poa:e~T~tini (~~) ~nd~ac~;s i.n the liquid (24) arid in the
sold surface
(2~) a conduction current (6~-) which is in a directian opposil:e to t~k:.e
strearraing current (~~).
~'lze conduction current (64) is co~~~prise~l cf at le~~~st t~~o
sepa~°ate pa.raliel paths. ~ first path
(5~) for the conduction curror~t (6'i) is t3~rough t~xe liquid (~~;,. A second
patl~~ (6~) for the
conducting cu~ent (64) as tlzro~,gh tlse ~:oii~. s~,arfafie (22). 'f'r~e,
liq~xid (2~r) provides a buliC
esista~~ce (~Q) and the solid surface provides a surface resista~me (l2).
'flee conduction current
2S (~~) is the sup of the currents a3ong the first p~atb (6~) anr'~'. tire
second path ~;6~)~ aid is
dependent upo~~ the values of the b~ai:~ resistance ('~ta) arid tl~e suxface
rE~sistance (72).
~roxn ~'igurc 4 and figa~re 5~ rt ;°a~~ ire seerb that vhe channel
asserr~~ly (fit;) a~-~d
the electrically conducting patl? GSw~) o~' vl~e inver~~:ion p~~ovicl~; an
aczditio:~.al pa=°allel current
30 pathway between tl~e first ter~ir~~a' (~~.) and th~; second te~-~nin~ i
(~.~.) so tl~~.t tire total cu~~enL
~et~ree~~ tiae first terr.~i~~al (42) arid t~~c se,cor~d ter~W na< (~.4) is
the sw of the external loaf.


CA 02437304 2003-08-14
cFarrent (56) and the condcactioz~~ c;.zrrent ~;6~ j. '~'he mag~~ittzde of the
eternal load current (56)
end the conduction current (64) ~x~i=1 depc3n. upon she relative ~~~al~es of
tr.e elec~ric~l load (5~),
~~~e hulk z-esist~ncc (7t3) and the J~arcace r<;sista~-~ce k'~2).
fly balancing the v<~.iues of the elec;~rical load (~~), tl~e b~llc resistance
(~~) and
the surface resistance (72) and by cos~sideg°in ~ the o~aera~-5
chat~acteristics of the energy
conversion apparatus (3~;~, incl~~~ir~tine axY~o~.~zt ~:~ electrical ~w~e3~y
vahich is pz°od~ced'c~y the
apparatus (3~), the electrical powers coz~s~.r~ption cf the clectric~lly
conducting p~.th (52) can be
ontixni~e~.
i~
the value of the '~a.i~.lz~ .resist~ncc ( lil) will be d~.pe~~dc~n~; upo~a
tl~e p~-operties of
t:~e li~~,zicl (2~), and a balance ~a~~st 6e ~E~hic~re~~i in ~h~e pra~,~tice
of the iA~vez~tion l~et~veen
selecting the li~axic (2~y so that i~~ his a high electrolytic strcngtl~ in
o°der tmr~axirni~e the 1~,~~
(:~~) effect anti selecting the liczu:id (24; so chat it is aelatively non-
conductive in order to
35 minin-bi~e the conduction current (6~).
~~lze ~ra~~e cf the sy..r~~ce resista.vce ( r2) can be r~~a~iz~i~ec~ by
providing that the
solid surfacc (22) is const-°ucted oi~ ~, channel material which is
relatively an electric~.lly r~on-
ccnductive rnateriai. This may be ~chzeved either gay constrzzcting bhe
channel (32) e~-~tirely of a
2~ relatively non-conductive z~ateri:~l ;:~~ by l.i~i~rg or coating a~
ini:crior s~~zrfacc (7~) oi~~ tape chatznel
(~2) so that the solid surface (22is ~°elawiveiy eiect~~~cally z~on-
c~c~:~~.~.cti_<re.
fhe invention may _or son ~e applicatiorss be l~r~.cticed using a s~az.gle
channel
assembly (40) as depicted schea~ati~~ally ire ~'ib=are ~. h'or rraost
~~pplic~tio~s9 howevca, and in ~
25 preferred er~sbodirr~ent, t1°~e enemy conversiog_ a;~l~ar~.tLZs (39)
of tl~a=~ invention c~o~as2prises a
plurality of electrically co~ected ch~r~nel assez~~bli~;s (4~). ~'he n~.~mlaer
of channel assemblies
(4~) which are utilized in the in~:~;ntisn is dependent upon il=e az~rroun~:
of electrical energy
which is sough to be produced ~,~Tit~~ tl~e iz~zventior~. since the electrical
energy ~rlT~ich naa~ be
lsroducec~~ by a single channel assei~~bly (~~) is vez°~~ lom
(typis~~lly ire the range :of° ~bo~zt one
3C ~aano-a~nperc or less per lcilopascai crf h~rdrostatic A~ressure)y for
z~ost applications ~~e invention
utilizes ~ large ntzz~2ber of chax~~~e:l assemblies (~~(~j. 'the rrea~iynazn
number of channel

Image


CA 02437304 2003-08-14
~~a tlW.'~a~a~lE:l ~~Il:~~:~.~"atl~~a C~.~ ~''?~Llr,~,'"~7~~ ~l'~~ str<a1~3~~g
t~~Irre~'9ts ~~7~'") arm ~.dE~~tl~I6'
so that the electrically co~ductir~.~ l~at~-~ (~Z) is ~ap~blE; of sust~i~~rsg
an e~ter~al ~o~sl current
(~r~'~ ~,vhicll is propc~rticr~al to the r<u~nber~ ov'~~ar~~el ~,sse_~bl~es
(=~~~).
~ the series cors~i;;~.~ratson of Figure 7~ the char~~el assen~bfies (40) are
electrically co.~rzected so that tl~e ~~rst ~wer~ir~al (42) of a i~rst channel
assembly (~~) is
electrically cor~~ected ~uzth the secc~r~~. teisn;a~a~ (4=~) of a second
c.ha~°Anel asserr~bly (40), vdith
the resu It that the ch~.r~nel asser~~~ (ies (~ ~J) are connected "eri~~ to
end" to cr sate a chain of
channel assembiies (~0). In the se~°rev co~~~~ratic~~~ ol' ~'igvre 7y
~~~e ~'~rst ters~~i~~~' (~~) ef the
la channel asserrir~iy (~0) at one end o:f 'che c~air~ o~ cl:~~.r~r~el
assen~~~lies (~~) is coected vvit~"~ tl~e
3 rst co~~ectior~ point (50), while tire second ter~~i~~al (~~) o~ the channel
assembly (~~) at the
ether er~d o~ the chain of channel asserr~bl3es (40) is corn~ected Edith thc~
secor°~d co:~uectior~ point
(54~ so that the electrically cond~:cting pate (~~) ca~~ be established
bev~xreen the first connection
point (~0) and the secoacl coanectiorl point .~~~. In the series configuration
of Figure i, the
streaming poteatiais (S2) are additive so that t:~e First conrzeraion point
(5~) aa~~ the second
connection point (~~) hare v potential di~~erer~c~~ wh~cl~_ is ~ro~ooior~al to
the ~~urnber of
~~ael assemblies (4~).
x~igures ~ through l.~ are grapl3s ~epi~;t3ng thEoret8c;al relatioz~s~~ips
bet~reen
2~ ~Tario~as parameters pertaining to ~~~.; desig ; c~~ ate e~rurgy
cor~versio:°~ apparatus (3~) according to
the i~zventiorl. she data for the graphs o~ Figure ~ through Fig~zre l~. has
been generated from
equations derived from physical relationships accordira.g to the
;~R°inciples of electa-okinetics arid
hydrody~arz~ics. t~ thorough disv~~ssion ~f the development of th a equations
wl~~ch served as
tlae basis for Figures & through l~'f i,y provcded below.
~5
Nig~re 15 is a sc~.aernatie ;-e,preser~t~.tio~~ of ~z pr ef~rred ernbo~.:ime~-
~t k~f' an
°xperia~ez~tal a~.paratus which has E~eera built and has been used to
~~w°ify the treads o'ser~~ed in
the graphs from Figure ~ through la'rg~re ~4. ~ tl~cgro~gh diseussio~~ of the
experimental results
from3 the use ofthe experimental apparatus of x~ig~~°e l~ is pro~eded
belova.
3~


CA 02437304 2003-08-14
The experimental apl~arat~.~s depicted in Figure 1 a incorporates preferred
features
ofthe energy conversion ~pparat~~s (~3) of'~l~e in~~~°ntion.
hE.eferring to ~ig~r~e 15, -~-~.~ ~ prefwrred e~rbo~i:~~,ea~l: tlae energy
conversion
a~~paratus (39~ includes a plur~.lit~ cpf channel assey~~blies (4J) ~w~~i.cl~
are electrically connected
i~~ a parallel conf~g'ar~tio~. In tire ~refe.~-re~ emb~~din~.e~at del~~~cted
~:~ f~ig~re g 5% the energy
conversion apparat~,~s (39) incl~t~.e,s apprs~~ii~~atea~r an es~iy~ats~~.~ ~.5
~ SOS (4.5C,4~~~) ch~.r~rlei
assemblies (~~) ire a parallel cc~n~'~g~rati~~~$ vh~s d~urraonstratiy~g that
the: ~:~se o.~ ~ ~-~~-r~ber o~~
ohannel assemblies (40) in the order of 1 ~ 1 ~5 ~ 1 CC~,~O~) and l~gher is
feasible in the practice
1 ~ o~ the inventian.
W the Figure 15 ernbodime~~t, the energy conversion apparatus (39) is
comprised
oC a porous bilk material (7~) and tP~e cla~.n3°~els (3%) are defined
by pores in the bulk material
'l'he use of the balk material ~7ci) a~joid s the oecessit;y of fa.bricati~ag
the pl~rali.ty of
cl~~nneEs (~2) ind3vid~all~r. ~ 11e ~a~El~ zr~a~erial '7f~) rnay be
cc~k~~a°ised of any suitable poroa~s
~r~ateriai ~vhicl~ has s~,~fncient ~er~x~eab.lity to ~ex-mi'. the 'iqtrid
(;~~) '~o pass t~rougla the; cl~an~~els
(3~) be't~een the first axial posi'cic~:~~ (4~;~ s~~d ~l~e secor°~d
axial positiork (~~)9 including bofh
nat3.lra~ a-d2d 3'?'1an-rrl.ade ~'~2~'tC~r~al~. :sir t~'.E; ~~''1~~I::~E, i5
C°~":~17~CillCEaent, ~',~le ~SL~1G ~'l'=ater9.aE (~'~) us
cr~rr~prised of glass arid is provic~ecl ~~. the fc~~n of s co~~~.erci.~wi~y
available poroaxs glass filter
~~~aterial.
'fhe first ter.~inal (~zarid '~dhe second ter~i~inal (~~; for each of the
channel
assemblies (~.C~) are shared a=non get all ov' thEr chaarrel asse~~blies (4~D)
and are located at
opposite ends of tl°Fe bullmraaterial (lay). ~ he first tcr~rninal
(~.~) and i:ze second te~ir~al (44-) are
~5 each separated from the b~.l.k material (7~by are ~-ring ('~8) ss~ that
t:he fret axial position (~.6)
and the second axial position (~~; are eaca located adjacent to~ ~:~e ends of
the chanrleis (~~) bnt
are spaced fro~~~ the ends of tlae ch~,n~els ,;~~) bar a. distance eqr.~~~1 to
the thiclcam~~s a~f o~~e of the
~-ri.ngs (7~).
i:n tie p'ig~.re 15 er9~bodirraent the ,first terrrsir~als (~2~ are comprise~~
of a first
electrode (~.'7) and the second ier:a~ir~als (~.~&) ~~re cov~~prised of a
second electrode (~.9~. 'fhe first
-Z7-


CA 02437304 2003-08-14
electrode (~.7) corn~~°ises a ~'~rst con~ectior~ ~oinc (~G) ~n~ ii"e
s~;t; c~r~d e~ecfi~ode (49) ccprises ~
second connection ~oxnt (S~).
'fhe channeis (32;h~~~ye ~ iength ('~~) vrhioh in the eW ~od~rnen~ oi°
Figure ~~:~ is
defined by the vvidti~ of the bvl~ ~~~.a ~~,riai ;°7~. ~:he =.eng~rx
(7~~ ~~i°are ~ha~~~els in the l~':~gtax°e 1~
e~nboci~~ent is aboLCt 3 rr~iliietes~s.
~ he ~nrst electrodd (~i'7) ~n~ tr ~e sec~~:,~~ eiectro~.c-~ (~t~) are
connected to a rnete~°
(~~) for r,~eas~ring the external ioa~ cuwent (~C). "~'he ~~rst electrode,
(4.'7) is cor~~~ected to the
t; rr:eter (~~) at the first connectia~~. ~,oint (~~1) ~anc~ tl:,e second
electrodE; (4~',~ is corEr.~ected to the
greeter (~0) at the second connection ~c~int (~r~-~. '~'hs~ eiecta"~ic;aliy
co~~d~uting ~a'~ (~;2) is de~~r~ed
by the circuit between the first coy~~ectio~a. point (~~~:9) arsd the s"Vcond
~;on:zectior~ point (~~) and
tl~e electrical load (S ~) is comprised of the rr~e~:er (~~~),
'_5 'she t'~ui~ energy ~s rovider~ ~,y ~ :dt~id e~~erby~ sovrcfu (~1Z. ~'he
fluid energy
sc~a~rce -(~i) is eomprised of a lid r.id reser~aoir (~~). .~~s c~ resu~it9
.the ~~t~.id e~~e:~gy 5s ~:on~prised of
a hydrostatic pressure or head (~3:~ ~ from the rese~woir (~~). 1=~~ring
testing of the figure l~
e::~bod~~nent, the hydrostatic head .d3) v~~yas ~ppro~:ir~a,ceiy ~G4
~L,er~ti.xr:ete~-s and was se.ected to
e,~sure that the liq~~id (~4) has su~iacien'=: fi~id enc~s°gy to pass,
t=~~o~t~h the brut x~aterial (76)
2i~ under substantially ian~inarP flo~~r conditions. t~.n~~ aite~-~.ate fl~vgd
er ergy so~~ree (~ l) a~n~y be
used in the practice of the inaentior.
'fhe energy coz~r~er;_,ion a~ap~~r~,tus c~~~) of the ~.i:iyar~, lv
ernbodv~necn f~.:rther
c~~nprises an i~~Iet (~4) for intro~ucing the ii~uid (,:%4) i~~to the
a~ese~trc~ir (82) and an outlet (~f~)
~5 for vritlWrawir~g the li~nid (2~f fro~~ the ~~iaaratus (3~,~ after it has
passed thro~zgh the b~zll~
anaterial (7~). 'fhe relative elevatic~~~s of ~:be inlet (~4.) and the o~tiet
(86) define the rr~~axim~rn
hydrostatic head (~~) which carp be attained ~~wit~~ t;~e reservoi-s (~~).
both deioni~ed water and
tai water vaere used as the ii~,Lrid (~~ ~. j ciu~~z~g testing of the
er°~~:~°gy co~xversEon app~.rata~s (3~) of
igura~ ' ~.
L .o


CA 02437304 2003-08-14
W use9 the reservoir (~~) is fiig~c~ ~avit~s t~~~ Liquid (~4) d;o a desired
ievel argil tl~c
hydr~st~.tic be~~ fr~m the res~rvc~ir (~~) cause ~ressur~~driven ~~o~~ of the
9i~uid ~~~~ thr~ugh
the ~ha~~r~eis (32). The passage ef the ii~x~rd (2~.~ throa~gh t:~~~ ~;~~a
~e?s (~~) results i~r the
strearr~irg current (6~~) through ~,a.~,h t~f the chanz~ois (~~; acrd tire
stroarnir~g potential (6~)
between the first electrode (4l) ~n:~ the second electrode (4~). ,~alxe
streaming potcrrtial (62)
provides a voltage source for the electrically oond~c;ting path (~.'~),
r°es~.lting in tl~o external load
current X56) wl~ielz is rrzeasured by tizc, meter '~0,.
~i has been obser~~d duri.~-~~; ~s~ oi~ the emrgy ~~n~v~rsi.or~ apparatus
(3i3) of
l~ ~~igazr~ i~ using water as zf~e ii~~~i~(~4) that ~x~~g~r~ gas as an
~:Ixi~~.t~;or~ product urn: ~ydrogei~
gas as reduction pr~duct each ~,rmlv~ ~~o~a ore ~f t~~~ verrr~i~~ais
(~.1~,4~). ~s ~ r4~,s~zlt, one
puter~tial appli~atiorr of tire energy ~:onversic~n apparatus (~~) artd v~"
t~~ rnetlrod of the invention
is as ar~ electroche:.nical cell for the production ooxygen and hydrogen or
other oxidation
products and reduction products. ,l.epending ~~pon the von3pc~sition of the
liquid (~4) tbat is
~:aiai~ed in thbe ~;ractice of the inveratiorr.
~,lre testing oi' tlq~ ur~~rg~y c~rw~rsi~n °~.pparatis ~~~) ~s~'
iiigure l~ Eras been
serried out under steady state Lar~i.~dix~~tion~i flevr ~on~ition;; so that
the strear~ring potential
~~2) ar4d the d~ternal load current (~~) ~°~ both effectively a dreca
o~arrunv (fit:) so~r~e ~f
2~ electrical energy. ~lze inventian is not lir~itod to ~;~se irr this
rrt~,.nn~r, and rnay be utilised in an
alternating manner in order to prcdzce an a.ltoatirg current (~~) so~~rce of
electrical energy.
it is ~onten~plato~ that the use of tr~~, invention as ~~n .~~ so~arco ~~~ould
involve
an. alt~rr~atPng ~zieans such as an ~it~rnatirrg rn~~,l~a;~isrr~ ~~~) ~~ibi~h
t~ro~ld fa~,ilit~te t~=e ~~se ~f
2~ the ~lui~ energy to cause the li~~~.id (~~.~ t~ pass alternately =hra~~;l~
the clzanraels ~3~~ in a
cir~~tic~ra toward tl~~~ s~~or~d ax.iai l,ositio~~; (~d~) ~ncl ire ~a
t"ir~~ti~r t~:~ard the first L~x~~i position
~4~~ so ~~at the streaming cazrrent- ~~~is ~sta.hlisi~e~ alternately irt t~~c>
s~ppr~sing d-~re~ti~ns, this
alterr~.ately rw~:rsirrg thL strearrrzrrg p~t~r~tial (;;~) ~;~bieh is abserved
het=.rveen tire first Llectrode
(47~ and tl~e second electrode (4~). pref ra'oly the Liquid (~4) is passed
alternately ire. a rrranner
3~ such that tire streaming potential ~ ~z3 alte~nat~s sir~~soidally.


CA 02437304 2003-08-14
i~eferrir~g t~ ~ige~re ais, ~~~e er~~~,'~~:iirrA~;r~t ~~~-~~
~lt~.°,~"~~~.t?r~.g ~recl~~r~is~l~ (d~; ~,~ic~
~;~~ici '~e ~se~ t~ pr~~irte a~~ ~-te~rmting ticv~r ~a: tile, ii~~i~ (~~~
~,c~id c~rripris ~ ~~~a~e
~~ert~~~is~zl (~'~) ~.vich is cmztreiie.(~ t~ ~ite~l~te..iy :~irect ties
~t~s.i~~ er~~~rgy t~ ~pp~si~zg sues ~~
tile ba~I~ rr~~,ter~~l (i6~, t~~s ca~~si~' the i~~~i(2~~ t~ ~ite.~teiy ~~c~~
in ~ppt~site irecti~~zs
~Jft!1'~31 t:le '~L~i~~ I'~~,~erl~~ (%,~''s) '~.~',l~~r ~ y a>xti,r~l~tl~~l~
preSS:.kre ~i': ~~e~~t< ~'~1 EI'~~. e.~2~G~~~e~t ~=
~'ig~re i ~, t~~e c~ztie$s (8~~ are ~qt,:,~°~~.~tegy .~pe~~;~ ~~~.~
ci~se~ ire. ay~cx~3p~~iz~ti~al ~~ith tile ~r~ive
;~lecl~a~is. (9~; s~ ti=~~t ~°iliie a~f~re ~:_~i~ e~h~rgy is
~:~wern~teiy ~a~~;c~~,e~. ~;.~ ei~~cr sire ~i'the ~~tl~
~~A~teri~a (7~)9 ~~liy tt~e ~~tlet (~~~ ~~z tile ~p~csin~; side, ~~~°
ti~s~ b~~i-i~ ~l~teri~l ('~~is ~~pe~l, in
.,
~r'~er tv '~°i2S's~re t~l~t ~:Yie pre~S~re bs"~e~3°,~~, i~
~~ti~J~-fer' :~'ii:l.g~fi t?16~ hu~~C ':"rl~eter$c~,~ (~~~.
a,o,
~ '~e
~oeferri~zg tc '~ig~~re 1, ~ se~:~i~.~ err~~~dir"3~e~zt ~.f ~~~ ~~~e,s~~t~.r~g
rr~le~;~~r~is~zl (~~~
~rhicil c~~~ie a~se~ tc pa~~~~~~, ,:z~l site->~l~~ti~zg i,~~v ci° tie.
ir.~:id (2~c~~i~ c~:eHprise a
reciprcc~ti~zg ~pp~r~ta.~s (~2~ assc~c~~$e~ ~ air tie ~~~~r~t~a ( 3~; c~'
pig~re i 5 s~ ~ia~~4 tile ~i
t°~..ergy sc~~rce (gl~ is c~mprise~ ~~~ tf;c li~;~i~ ~~es~;~~r~ir (~~)
~l~t tic; rec.ipr~ca-Li~zg ~pp~.~°~t~rs
t~ (~2j. 'I'iae reciprs~c~tir~.g ~ppar~.t~<s ~~1~ is ~,~~~prisr.;~ ~i' ~
pis~:~:,r~ (~~;~ ~i$i~lt~ ~ ~,°yti~~der ;~~~.
~~:~e sire c~f tile cyiincier (~~',~ is z~i m~~i~ ;~~b=rr~~~i~,at~cra with
t_~e :~~~tiet (~~). '~.'~~~~ 3d~ai~ (2~
exter~~s c~nti~~~c~siy fr~~l ti"~e Ii~~3~ r~.serv~ir (~2;u t~ t~~,
cyiir~c~° (~~~) v~i~ tie ~~:~tiE~;$ (~ey~ s~
tilt tile cx~~r~a~ei ~sse~°~blies (~.~~ c~rc i~ersc~ ire tic iiq~~;:itK
(~~~.
ors tile ~ig~are y? er~l~~ir~le~~t, :ile ~;i~~~:c~el (~4~ is ~'~:c=3p:~r~c~te~
~~iti~ai~s tt~;~ ~~;yii~l~er
(~~; by ~ ~~ri~e ~lecllarais~~ s~c~ ~s <.~ ~~.~tcr (ay~t st~~~rr~~ t~
~a'terr~teiy ;app y pr~;ss~re ~r s~cti~n
t~ tire Eic~~.~i~ (2~~ which c~~ses ~~e 'isi~:i~ 2~~ ~aersaatey t~ p~.:as
ta~r~~g~ tt~e cll~~~~le~s (~~in
~~i.~~site cairectirns ns the levei cr tile xi~~d (~4~~ irp the ii~i~
~:esc~e~ir (~7~ rises ~r~ ~~ils in
resp~r$se t~ tile recipr~c~tis~r~ ci' tile p<st~:.l (~~~, '~>t~e ~~~e~e~ ;ry
~~ tire recipr~c~ti~~l ~i° tire
piston ~rg~y tie ,r~rie~ t~ ~r~r~y tile rre~~e~:~c.~-° ~~°tlle
~itc~~~a-tr~r~g el~ctric~i energy tll~.~ is ~°~~~aceci
'~y the ~ppar~.t-~s (3~~.
i ~r ail cf ~:ile er~i~~iegzts ct~ the i~ ~cnti~~ly it i,~ rm~tett~~:~ tile
ii~i~:gict ~~envy
c~e passed trc~gil tile ch~rinets ~'3~'~n ~s~y a~l~~~~~1~;~: wsli~~~°~
re', _yts ire ~a~i~~ rr~~~~e~zlevzt o~ tile
:~~ ~q~ica (~,~f tilra~~gil talc ct~~r~rleis ~~2'i, sir~c~;: ~~~y ~.ai~i
~n~vew~.e~l~: ~~ a~i~e ti~~lici (24~ vain res~.it i~
~i~e; stre~~~ling c~~-rent (5t~~ a~zd tile stre~.rzli.~lg pcte~zti~l (~~;~.
~;Q ~ rwsnit, tie p~ss~ge ~~ ii~~aic~


CA 02437304 2003-08-14
~~~',~ tI°C'Llg~c"l ti~'s.-° cirlsE~lYlC;~s ~~~s a'~~:~
~'w..° ~3,~~~~d~'i_'Pi.fa' "41~~1~~'.T~.'1~I~1 Wt~,~'~~~ I:,"~
4~"X°~~f t~ 'ff3~JIE~'c i~~ ~Z
:~iYiIIY'~~a~12 C)~ ~~~Gi Y~":~~l~Iil~2'~t t~.~ ti~~, ~~~1~?~ f~~Lry
t~;~~aic~"a :~.c'~y ~~, ~~,~'~,~c~~&~~~°~)r 2vi~%~~t~tgc~~:~s IY2
p~~'~icii~-~g ~~~° aiternating ~,~.ss~gc a~i' -~t~~J 33~~i~ 7;~~~
t~~~~g~vd vi~~, ~,~~~r~cls ~3~~ ~r ~rghe~°
~~'~cciucracics.
~. ~cscriptic~~vfcxic~~as ~~t~~ ~v~e:~c~~-~;~c~t ~~ tt~~ "~~~~,c:~;tic~~a
~°~.i~ti~~isi"~eps :~er~icl~
~.~~vc avs~ttc~ iu ti~zc g~°~p~s vi° ~~ig~~~cs ~ taxi~~.~'~=? i~
~~~~ c~~~ =I~c ~c~cl~p~~c;~'~ ~~~ tisc
ca~pc~cnt~i =.~sn c~~t~c cr~~~~ccii~~~cr~~ ~~ cr~~.~°gy ~,=~~vcrsi~sra
~pp~~°ratv3.s ~~~~ c~~'ig~rv ~.~.
1~ i~~AEC3RE~t~~~, e~!~~=~~,~~i~ ~~i~< ~ ~xi~,T~~,i=~ ~.~z~ll~ri'~Ex
C~. ~c~ntr~iti~~ ~ ~~ticra ~~~y~~~~~~e~~a~itie~~s
~%~~e ~cgi~ ~~ cs~~~si~c~r~~g ~ ~~~~ci ic~~ p~~uss~~:vc-~~i°~c~ ~~d
tix<~~;-~~cpe~~c~t
ct~~ct~~sr_inetic x'~tww t~r~~~g~~ ~ s~~ glu c~~c~:i~.~ c~~~.~~ci f3>~. l='~L
~~ i~i~Ji~~~~i ~°t~~~a~~egcs ~32~
'i~l:~t~o~li~;- ~~3 b:.~c~tf'~c~xd~~ CE7Ilu°~Ctl~?~ ~~6i? {~~J as la"P.
''lg$~~E. ~9 "~,~d'~' s~~i~S3~c~" ~i~lc ~~ai~l~~3~'~1 ?~~~tg~~
~f'o~"'~~lG.fi'T$ 1~;9I ~scl~l2J,tl~g ~'~~($.I~C~ ~~~~~ iic'"J~e~J ~~3 a~~3
I~1~ ~~t(;~~~ ~,~t~i~~P..~.~ ~ag3"~~i~C° Ca~%.a~~~~°3 ~.~'~~'~.
~ ~r~~ ~ arc tic ~;~_:~~ ~csis,sa~~;c a~7~,~, ~f ~~c iis~~i~cs ~;~~.~ a~~~ tic
s~~°i'~,cc 9 ~sist~~fcc
G~ ~7~;, s~i tic s~si~ s~~f~cc ~2~yy ~~~~ccti~,~ci~'., ~~~ ~, si~~;ic ci~~ci
~;~~~. ~ cy~~:~a~°ic~:1 c~~~°~~.r~~t~
systc~ ~~,=r, b~9 z;~ is ~~zscci ~,vc~°e tiic z-:~~cis is ta-'r~~ t~
;c~~r~ci~c ~itri~c ~,~'~~~~~c,i ~~~~ ce:~tir~i anis.
~~:,I ~~cic~. q~a~r~tities ~~c tai{cue t~ ~c~,~,~a~ c:~ ~~c
~°°~ci3~~ c~~~~i~a~,t::d ° ;~~tz~rc tv '~~~c ~:~~~ar~~~~
'l~.sic ~~3~~eI~ '','JItt1 t~l~ at;~~~l~~t lI~'t'x fa~tl~a~~~~is ~~'16~
~a~'sa~~aCli ~J cz>3;,G~i~3t7T~.s ~Y°~, ~f~sc~°i~i6~~ ~~~f5~:~.
~5 ~~. =icctAical ~icl~i
'~1~ t~'~t~.a p~tcl~ltRs;~,~ d~ ~ i~~a~~l~%"'~ ~~°~ zy ~t e~ gz~~~p.
~,E~aa:: ~' 2:3 tc'~.~r~T3 tC3 t~~>
~~1~, z~~~ ~2'~~T ~°~~o ~ G~e~~~.
~Y
~t ,


CA 02437304 2003-08-14
~it~.I'1~S'tj ~/ ~3'~ ~S -~;~,' 23C9~eTl~a~~ c~~~ tG to°ie '''.3~ .:
~,~ ~~ ~,~ ~Li.~.~~?'~5~'~L~iTl ,s~c'~.'~~, ~~.~., zR~ a1C?IE&~~ l'YYI~~I~~
'~dx~
~~c~ ~~~iivc:~ ~ri~e~r~~l i°'~~,lc~)~ fIo is q~s~,° ~~te~~:~it~i
~d z =_ ;~ ti.e., LlC~ _ ~r fir, ~y Z~9 ~~~ ~'.~~~~ is Ire
s,~:~ii~.li~r ~r~ii~'~~-ar3, r:ie-eiepe~~de3~~ ~:0.ecv~°i~~ ~°I~
sty°~,~ir. '~'re ~;~I~i i~~i-e~ii~i ~ .~~ ~r~.~i.j is
~~:2Sj~~'1~~Y1C~~°I~ ~i'zt~', ~~'Pe~% ,~ j(~'~ nS '~IY~4~ ~~lu~~~~
A?~F'~I, ~,'C~.~~ j iS IC~';:a'~I~~(d~I~3 i:~.~~.~.~ ~S ~a,S~T'l~iiC~:~
i~ ;i.~. i~/:i~sliy~r, ~leclvc~~~~~elr~ ~':~~~.~~~~Z .~~~3~:=~z~~~ur~c~
~~ir~"rq~ Vii:: ~~~,~,s ~ec;r~~~~i~~~r a~~
'~crsea~vi~ l~~ih~~iiy, i ~~~'~). ~'f°z ~~~~e--r~e~er~~e.~i xi~~r~ I~
'~e vi~~iec~ re~e is ~ssar:~e~ ~~~ Ise
s~~~'i'FCiea~;iii sic~~~ si~e,h Ir~i the r~ci~aa. ei~~rge ~isi~irict~~~ :~s
~ei~~ca.~ :~I vfs sie~ciy side' ~v~ti~e~°, iI
is ass°~e~° thai ~r~~y in~~eed ~~<~eee Iei ~s ~~~e s~
E'e~cie~niy s~~E~ii ~r~ci r~~egif~irle s~ez~ th~i the
I~IaI eiv~,irie a~eid ~~~~ still he d~,ir ~~r~ ~s ~._~r; ~se~ ~v. ~'~~d~~h-
ii~, :~ii~ .~~~~a~~~~~~t,r~~~'~~ iv~'z~~d
i~ ~'~ 9~ve~, d ~7~~ Ihas ~ef~r~zi~c~l~ e~~ Ik~~e~z tie :~~~,~ ~ ~'~k~~i~ ~~e
P~tus~~ e~~~~~~~~.~.
.~~~r= ~ ~~)
~~I~ere ;~ is Ii~ze Free ~,12~~°~e ~ensii;r ~t~d ~ is I'he
~e~°~~=~Iii~ri~:~ ~i Ir ~,~ ~e~iv~-~. ~or~ri~li~~ E~s.{l~
i~ ~~d ~2~ yields I~~e fc~li~~~ir~g ~ ~iss~~& e~~.~~ivE~~~ i~ c:~li~~~~ie~9
ecs~~r~isa~ie:
.! dp ~ ~a't~'~r;1
r da ~ d~°
he e~t~~nii~ras ir~~~~; ed ~~ w,~i~Fp~ ~h-e.:
2L
~",~~__/~~n~ Q~lc~ is ~l~iie
~l~ere ~, is the ~ei~ ~~ter~~vial ~~ I ~ ~°~ the e.~~~~rei ~3 ;l
~~z..lby r = ~ ; c~ is ~IZe ~~.i~s ~i' the eh~~a~ei
~~r hre~rir~, we shill ~ce~,~.s ~n ~ 0.,y~~~rr~=:Ixi~, h~~aell~~,ett~'~~Iie
~3~~i~ ~r~i~:~ ~~~iv~le~°~I
er~rges. rare, e~ii~n.s ~~d ~.ni~~as ~~F; ic~ef~~5.~ie~~ ~s s~eeies I ~,~ci ~5
vespe~~~i°~el~. ~~sed ~~ tre;
~s:h~rn~ti~~ ~~ theied~s3~~~ie e~;~<%ir=i~~c~, ~~_&~ ~~It~~~~r~ e~u=~Ii~~~
~r~~i~.es ~ ~~e~~~ er~~~c
~:lersir~r ~; ~f IA~e wily s~eeies. ~n~s:
_~~-


CA 02437304 2003-08-14
~I Z ~ ~yi~ ~ f < ~ i
y'~/ii~T° zt is ~'fi~ rl~icii~~ ~z~ L~'?~ i~.~si~~a,I~.4; ~.' i~F
~~io's a.-~~i"Ti<'~ ~~T~~ :,~i<~a~~~; ~2a~ is 'i~ae -~JI31C
~C~i1a~,~3~1'i~~a~Ti iid ~tl ~~ill~i~"i°fLii2'i
~~i~~°3:T6,~~II~~.1-i~~~ sC>'~LLi~s"~ ~$: L~2~ l~i~'pi°G'-i
5~~~° ~R1~3~T~% ~;, -- 't~'~ ''tZ iS
~i~~ ~~i'z~~~~i~ ~~i~stai~t; a~~~ ~~s t~s~ ~~s~~~~~ ~>~:~rr~~~~~i~~°~.
~r3~c~i~is~i~ -?~h~ ~~i7;~~~~-~~~~k~i
~~nTS~xi~~~.ti~i~ ~~r lc~v z~.#a ~~~e~~ ~~s ~~ ~',3 ~z..v~i%~c~' -:< ~ ~~ '~~
zz~~~. siz~a~(z~~~/k=~<zo~~~ll~~" aT~
~~~e c~L~~~ ~~a:g~ ~~nsi~~ ~'~il~~,vs ~-»zt:~ ~~.isa~:~~ ~,~~ ~~',; ~.s:
o=
- 2a~ z"
'~=~P~; - k~
G,~c~~r~ ~~s ~~v~ ~se~i z~ = za = z~.. ~ir~~ai~:9 ~Y:~~ ~~~'n~i;i~~~ ~~ .V~~
T~c;i~T~~~l ~f ~:i~c ~T~L ~~0;
~~i~i~~~ss f~~ ~ rzo : c~ j ~i~~~-r~Iy'~~ is ~~v~~ ~.s:
2~a G'z-
~~l
t~ ~ka''
't
~.~sr~i7i~iT~~ E~is.~~;~ ~a~ ~~s) ivs~i~s iTt~
. cr ~r ~r ~r
~'°
2~ ~IO~C~~=~ ai"~~ ~~~~~=C~
s
~a~~T~~~T~1~ ~j
~~~'i.~'J 'd,$A'i?ai ~.'~~C~I"i.~°. i2v~'.~ brx~i~'s. ~i':~~Es:. ~ ~~~~
i~31°C,°:: ,J~: z zt."s'1CP P.~~v I~lC7~lile~l 17e4JY0u1--
~~~I~es e~~.ati~~~ sec~TTiese


CA 02437304 2003-08-14
;~ a~ T ~ a~ a3f,
~r~ere ~z have taken ~l~e p~essu~~ ~°~.aien~: ~lo~---~lo~ ~t)j ~ o ~~
position-in~~pen~en~; q, is
~~e viscosity; and ~ is one kin~r~~a~~~ ~~iscosa~:~r of ri~~ li~,lui~. 'l:'=~o
~o~~nda~°~ cor~~eii~io~~s for tlr.,
~~u~~~3~~' 3.tinit.v. ~~~.
o~~
the clcc~ric cu~~=v ~~x~sic,T ~~o~g ~ir~ cs.i.a~a~gel (3'~) ~~.~y '~a:,
anv~~~°a~e~ oven the
i~ cl~a~n~l (3~) cross~s~c~ion ~:o ~ivc ~;ie r,lect~ic c~~~c:~~o
~'>.L ~ l )
_= 2~c p~» ~l~ ;- 1~
va~~o~e:
i J
__0~
"II ~ -'-.Y
~9 X20, ~, and .~ are tlae total r~sa~a~aco; '~~~k ~~,s~s~a~c~ {7J), s~~~fac,~
~-esistanc~ {~~;~) arid tlxe
channel length, respectively. ~~'f~e -=~~s~ ~e=-~~~ oit~e ~-i~i~~ sr~v o~
Eq.{~l) is d~~e ~o ~ulk
2t~ c~nvec~ion a~~ the second ~er~n ~c conda.c~io~. cu~~-en~ {~i4). :because
of the ass°np~ion oa'' an
~~~~nitc~y ex~c;nde~ channeiy t~~~: "o~~:~~il~~~ion ~o the
c~ar~°°en~ ~~,~e ~c~ coucen~~a~io_r ~~ad=enfs
v~~~isl~cs. ~Tsir~~ ~q.(5; .for a (z~, o z~,~ ele~~n~oly~e., ~~ ~~ave p;i pz =
2~zd~z~ cosl~~(zoeal~=~~.
'1.~l1e ehye-:~~~ac.kei app~o~ir~a~io~~ axx~p-pies ~~5a~ ~,os~i(zo~~r=key ~.~
anEi pl - p2 -_ ~z~~e~~~. ~i~Ti~la
this sia~pli~ic~~tio~, rl~c conducti >~y of ~a~lk ~,?ec~;oiyie. ~ ~°~~
~~Iv E~r~-i~~e~ as:
_ 2zn~=n ~ (12)
i~~


CA 02437304 2003-08-14
~e leSlSt'cIYT~~S ~~ aT~l~ izc:iC: C.~.ef~e~~ as:
_ ~, ~ 13 ~
z.n .; 9 ~ ~ - 5 a'~ l
,e~.9 ~~ ~ .1~,. .H ..
;~~ere, ~s~ is the sa~r~~ce co~ci~cti~~it~~ ~6~~ .=''lv = ;~ r~c~ ~~ tl~e
~~°~~tes~ ~eri~rute,r. 'Clue i'~cw rate c~ caa~
~e'WriLt~I~ as:
q _ 2r~~~' va~ Ll~'
~'"v"' ~..~. ~aY°ta~~lcal v~~iLsLiQ.~"°
analytical solution is sozzg~t here for a sinusoi~al perzo~icit~r in tie
e~ectr~~y~rodyraa~ic Fel~s ar;d t~Z~s is '~~sl; ~~~ressed by using cor~~lex
variables. This, a
general fiela quantity X may he ~eiinec aL tire real dart of tl~e complex
~arction ~X~~"'t; ~~lzere
~* is cc~~.~lex ~.j---~I-1); ~~~ is tk~e csciE~atiorY 1'r~;~iuency
osci~.lati~n~ ~~p~ ~ is v~~ ~~~ne. gl;~e
general field quarltiiyXis ~rit~e~ a;~e
= Re~x'e ~"" ~ (I 5~
2
'=~'i~e ease angle ~S is ~e~ r~~e~ as:
.~m~X~
~P = t~~-
~ 15~
1~e X t J
G~ "trV~erC; a3~2~~'Y'~ a~'I~ 1~~~'X'~~ t'3.rC.' -e~fC.' ~k'~2c'lgl~'~,'~:~'y
adl~~ rya"s'zl ~D~rts 6J~.~j"~ :~'f,:S~~,'~'~~~wlG:ly. ~'ag r.~'~err~atF~lP
~°epreser~tatio~, of ~g.il5~ is gives as:
~~ =.(~e~r~ ~eic"~.'>~
-~.;-

CA 02437304 2003-08-14
'pm% ~'lPf ~
~',esj=~~~ I ~I~tc ~~'~~= IJi2-~I~~~+~°~~ ~l2 a
~~~Jit~I tie I~ot~ti~I~ -~,. .~~~~~,_ s~~7 ~~; ~,° s~.~ii ~~~i~ tic
~~rvti;~a~ ~~' ~~~~ ~~n~:~~d~I-~ v~i~I~
~~;,.~~iei~r ~.~~, f~ii~~~iu~ ~p~~,i~~ ~':~~-;I~IdeI~E;i~~:
~z
i ~ ~~~~ v~s~ISid~c tile ~~w~:g~ ~~= ~~~~r~~~s ~~t~~I°~; ~~~ ~:~~ ~~ii-
~~~d~, c~~t~ ~r~~~S~I-~~ gI°~di~I~t
c~I'Id ~~.C: ~~~~tYl~ ~ila,~d ~fPL7~C~ ~~. ~s ~ ~~°~I~~ j1_~~,~3p~iu
'fit ~:, I.~.9 l~ ~~~ ~ y> '~~~J~ ~~'s&'~ ~ ~°~ =t~ ~'~ ~1~V~. ~'~1.~
uc~i~ty~I- f°~I° ~j °a;~iii t'~~I~r~ r=~Ii~m ~r~ ~~ ~,~
~~~_<~ t ~~t ~~ ~a ~T~°d.~~I ~ ,_~~. ~~~. ~'~.~s:
~f = ~re~~"Eaa;
?R~ ~ ~I'~:
~,. - l., ~'p' ~~ - vl' ~Pp% ~~~ ° ~~~ y 1~°I. ~~f % f'.iJ'f~:~
re ~ ~ ~ r .
~,~~ ~,~~ressl~n ~~~~ v~rr,~~,~~vgd ~~r~~~~ ~~~ ~~i~° ~~; oiv~~~ ~-i
tY~~ ~I~d ~~ t~:~~ se~t:~I~.
rs ~~I~ ~i~~;t~-ic ~u~ ~'IIr ~~ili f~ii~~nr i~~~_~ ~'~.~i I ~ ~I~d I~~~b~ ~~
,~sitt~~v~ ~s:
=.~e~,f'~"°'B
2~ ~~,.,~:~:
~~Y~ ~~c3l~.il~°a~~I'I~" afim~~J I'~~~ g' S ~~~;3II~~~: Ih..~'~t~.~~~,~
sald s~;r~I:~.. ~3~ ~X~D~~SS~d ~~5:
~~ _


CA 02437304 2003-08-14
= ~CE~ Via' ~ ~' ~ ~~~ .,
'~~tri'~ t~~~
,< ~ a
J ~ ° _ L~ % ~~f~ ) _ ~~ p ~~~ ~,~i ~: (4't3 ~ 'E' ~ r. S~1> ~~ ~- ~ ~~
~ (! i y
'~, f~l ~'S ~~'9~a1~~ ~~r ;'9~e~1~$~' ~ ~° " vt Li'~ ~',~.~~~~.
°? <~ii~~.
~;, i
I V 'v fl,)
~a~~.l~~eqJl~ (~G~,) '~~3r ~~~ ~~:3~~35~~~;BTi:~~ _E1L63 '~,C~"s.(Lf:~~ ~i~t~
~l~) zt~ ~°~:~~?'T~~,~~ ~~i6
~~~x~~lir~sl li~~ia (2~) ~~i~city ~~.~;,. rix~, ~~~i~;~r~~c~i~ ~~r r~~e., ~
b~~~~;~:iv~iy. ~It~~-~~~i~iely9 ~c
~~~;-~~~i~~%9 c~ai s e~s aid v~l~~n~tri~ =i~;~Rr ~~~~~ v~~i~~
~i~~r~°~~s~=~u i~~~~ i~li~~ f~-c~x~ :'~~,~s.(I~)_
(~~) '~~ ~~t~i~~~~*(v~) _ ~.
yl~~ zel~~~~~ ~u~~~~~ ~;~~ i~~i~.~;l~)-~ %I) ~pc iis~~s~~, ~~.i~~re
r
I ~ o l ~'.~ _
,,
r~ f ~ (~v)
-j~
a .;~
~°d~ ~s ~ o ~.~ ~~
~~~. ,_ ~ .- ~" ~ ~ rya ~ ~dr;; .~' ~"C~ ~ s' ~.i,~ I
°~ ',~ ~'i' 1


CA 02437304 2003-08-14
r
s ~ ~ ~--.-_ ~ 1 ~l' - -
2
;~sd t.~~c Jo ~.~~'~'~ ~~' + ~ ~~r~ '~~ ~Io ~jxcz~ ; t~ Y - j
~; ~
', i ~'~ l f
,~~ ~lcl~ =
~t~ V JC~3~r~a ? '~n ~1.J'~Cdr' i .l tL -
j
~ ;_ j~~.-
.~' ~~~U
( .~ 0 (. J 7~~d ~ ~ ~ ~ .d~
z ~' ~ i ---
L ~ ~ t'
_.~~u 1
2;~ cz- -
_ '
i z -.~~ -j~> 1
P
~:~ cas~_ _ i
i '~° '' .a' ~ i
I
zrsr~=rj~., _c~ ,l,ej ~ccd~ ~ °'',~~a ~ _. Y __._
~J .i~ ~.~-~ _
i (~
~~r,zcrc ~c" J~ ,,oa and ~ are tire ~~rct~- arse f'r.~s~c-~rdE~,: ~csac~~
~~tr~c~~~tt~3 ~f tam ~rs~ l~i~d, ~-<~taid
density s.nd i~inenatic ~isccsity., rcsi>ccti~~;~y. ~ d;~~'rrtc tic ~a~>~~
~cv~i'~~~1.:(w~ ~.s ~~''~ 9i(vv~n
can ~e c~:prcssed as
i 1
/ =,7 r~ I
__
-2TC8-X''~; i ~y ~ .,1;'~~>st~,I ~ .~,~J~'C~ ;~-j~ ~ ~
y~°w ~~ i z ~! ~~~c~~' .1~_-~:° fi ,~ (,j~c~'
- .~ A~~r , i_ « ~ _ ° « yi '
~p~ ~1 I
1 ~ ~~ ~J ~ i i
L ~ ~Ji


CA 02437304 2003-08-14
'~'he strea~in~ C;~=~c~t ~~~x .fit,. ~s ~.~:.,~~~md as ti7c ~'~~st term o~
~q.{3.~~ or ~stY =
~j~~ ~~~E9i~~' ~~Wt~ -~~~~"~f~~~N'L F
'~~~.en v, ~ ~, ~qs.~23)-(2~~ reduce to tho;s~. c~~ steady state.
,J, ~r~0y= ~ tcr- _ o~
. vp;
'fir: ~'~>~l - ET s '_I _ °~ r. ~~~~
vpa
-~~~. i~~ _ _. ~ ~', ~ca 'rc- ~~ - ~ ~, ~.I t~c~ ~ , J~ ~. i acct ~ ~ ~ ~,
vp~ ~ j rsc~ ~,r ~j%~'c~ ~ -~. y,, ~> ~ca~
~,~~~)=rea°
~vpu
s~~-~, ~ 1 ~ .7 _~; vl ~~ j
r ;-
,, t vp~ L rya ~'~ ~J lca~~
p:.r~~~- F ~.,JTC~'l~'- ~ _ G ~; ~,~''~Gi ,i_ '' 'l.jlsfX~'~'
V~, jl~ J,ua~'~) °~,, ~J~~cl j~
~rr~~~~~r ~i~T~~,~~~~~ ~~ ~ ~_ .~ ~ ~,~J~.,z~r~- ~~ ~:~~~~rer~:~,6~ t
~~~,~,~~~
-a ~~z~
~gnce ~~e strearrn~~~ cLZr~°e~~t ~~r~ of- a aia~gie chanx==~,p ~3Z~ is
sa~~ and i~ t;ypi~°~.ily
ef the order o~ abort one nano-a~~I::ere, ~v~: cocn'oir~e. ~r channeis ~3~~
i:a a ~araliei con~~buration
~:~ obt~i~ a i~r~cr c~~~°ent ~~"~s~urc ; a:or ~:~ e~t~r<~ai e~ectr~c3~
g~ac. 4~~~~ ~~~,. hor this cir«~~it, throe
~',r~ al 3~~ 3nC~a ;~ ~'S; lid(; ~~rC'~TY31YP~ C'.3~~z"~~il~~ ~~'3~~ ~~'~;
s~C~Ca~t~'V'~' ~3i~~s hC~~"sic; rG'wCal~; 11f1 a2~ ~'~Str~~
_ ~~ _


CA 02437304 2003-08-14
i'
-.t'2 -;- ~,.
nl,", _ ~..~, ~~ (31~
~~e caan salve for ~;'~'~. aso
(3~ j
Y i ----
1.: ,1
arid ~'~e °xtera~~'~ 1~ad ct~~~er~~ (~6~;>>.ss~r~g ~;~e c~terr~al
elcctric~.l "cad (:>~~ ~i ~s:
e~.'.1 _F ~i, ;
~i
a~
~t steady state, ~c~.(~ 3~ hec;ava:
a~3'~ds
_ ~,~~ ~
_ _~Z (~ '~
1~ l~Ier~nall~, '~ullC co~~~~ctivilies c~~'~ sal~ztio~~ ,~ and surface
c~rlducti~aities ,,~ are
sn~aalt. ~'cr ex~,~~~~le, the ce~~duct~~~r:~~ ~1'I~~'~ ~~,vatc;d is ~i the
c~~°~~~~ ct~ 1 ~~ ~/a~ (~;e 1J.~. e~~,
~,~. :~,i and '~7.~,. ~u, J. ~cllcid l~reci'ace ~c:~. 2~3, 1~ (2001~~; tie,
cc~ud~ct~vity ~l' ~.l l~ ~~l
is of the order ~f 1 ~/m (see ~.5. l~ e~za~, L~ee~~oe~~e~~~ec~l ~'ys~es
(hrer3tice Mali, ~n~;leva~ad
;n (;
~Iifzs, ~~ ~.~~1~, ~ . ed.~~ s~~f~ce co~:~vw?~;~,zvity ~~ c~ ~;he
~~~e~° ~f 1~ ' :~~ :~(~-~ ~~' ;see L.~~. 'r~en, :~~..
2~ Li arid =:ALL.. ~~, ~. ~~llcid Inter~zace Sci. ~~3, l~ ;2u01~ a~~d ~:.
er~er, 1~. l~c~rber, l~.
~ir~rr~e~:~ari~ay ~. l~akhir~; aid ~..1. ~~~ccbas~~;li, v. c~~1'.=cid
iraterf~c~~~ ~~~. :~~~, 329 (l~t~~~~.
_~.~_


CA 02437304 2003-08-14
r
~?'1 a~~Itlo~~ ~C~ ~~~. >lY.~ ~~a ;;~°c~~SS '~'~~i'.~.3~, t"3~5~
Ed~k~"s~S ~z~ z~~1''~'~x~~~1 ~"~I~~~~ t~l°
~~;sist~~~e ('~~,°7~) ~~ ~iZ~~~~ls (~~.; xc~~~ ~z ~~~~T~ ~~ci~.~~
i~:r~~r t~r~.~ t~~ ~i~~t~i~~~ i~~~ (~~~ T~~ ~~aa~
°w:~~~.'.L"3'l~.a C'.,~~'~td'7'~.°,~~~f~ ~~~Q3T~~t~Yig ~.'Y~~T
y3.w'i~ ;~, iia:.~ ~Cj, ~~~''~ ~S >~...'s~r:~~'~~$~ "~'~$l~~a, ~.~,'
S~i"~~1110
~Sc~E~~1'eEai (v~G,~ oE",e'3I1'(3C:C~.~ Y1~~~3~3~;;r~~~ SIYia~fi. r~31$'s,
J'o'b "iit~5~ y-~'5~,~,~'~'~. ,r'~ ~3~I"~ ~~ wa~'t~' ~G~r~~~~t~~913
~~.~a~°~I'~L a,'~~~ LIe~~Ca..C~ ~~~j St~°~c2i'~l~xt~
~~~~1"~i?cci ~~1~, s~,l'z%~'°. t~'6r % ~~i~ v~~'3ta,:Y~ t~9~ ~%t~"~'3~~
~~9c~t~
~~z~cer°~~ ~5~,~ ~~ ~ria~I'~ ~ass~s t~r~a~y.;:, >m:j~~tr~~i.~;;~~ (~~~
, use
(3
.~~~. -t- ~i
~~~~I~A~ ~/i~ » ~Y'~. ~ ~'l, :-, y~~'C~(. ar:,F ,~,,e(.,~ylwt= '~,~~'le,l1 F'~
'y ~ e., -.c'~1L'~~f.f 4L'~<,..r~rJ~ r~, _ Y.t ~S
~I's~l~'l~~~eJ~ 'o'i~~~ t~~ lii?sp~.Iil~~~l~t~ Csr Fa;i~~~l'~'dis ~~~"s:d
~L0.~'~°L.',ie~ (~~~ r',C, e~~=.~'s iii S~gI~~~~~3'",. ~~~2 > Cue,
6~f;~~I'~C~f~l~ ~1~ ~'~~~; ~'2cti~ C3~ ~/~'C~, ~~Ai~ t~t~~ ~~~5~5~1 ~5~
~~T2~F~~ (J ~;e W:~'~~1. ~~. ssS~C'1 ~A~ ~'i~°(3~j, '~iJ~
stv~y ~~~e hs~~,~ tie ~x~:~~i tt~~~ ~~~:et (:~~~ ~, ~~~~~~g~s
°>~~~t~v:,sp~~,t ~~ t~s~ z~t~. ~~t~_~~i~i (his
5~~~h t~~ r~~i~rc~v~l ~t: ~e~y~~ ~e~y~~~ (~~ ~i~~, ~~~~.~i~~~~ss~ ~j ~~,~~
s~C~ ~ ~~c~ r~ l~~g~~ ~i
iJ ~~:~az~~~el ~;~>2~ ~:. ~'I~~ ~'~:l~w~ia~$g ~~,_°~-~c~t~ru ~~
~°~ ass;~r~~~~ ~~r ~~~ ~.~~s~~~~~et~i~ st~~l°~~ a a= i.~~~~ i
= L~~all~ = G~pl~,, ~1e
4
~"x~= ~p t s ~~ ~ ~ _~s~..
~~ ~ig~~~ ~, fc~r ,k =_ ~ ~ i ~~" ,~: f ~~~. ~, = -. ~_7 ~~:,~., ti~~ ~;F~e~c
c~~ t~~ ~~~a ~L (~~i~ is
~l~~te~. ~l~ez~ ~~ta ~~st~rEti~i (~a;~ ~;~~~-~~s~s -~i~Y~ ~~~~er~~i lc~a~
a~~~~~t (5~i~~r~;~~9ey iir~~~~i;~.
~E;(16C~; ~13~~'',.f,'~° Z~z~ ~C3t~;~?t~~Zg (~ ~~ ~.ei.3S~,S
~~~~a1°' ~ a,, ~-~lSlt' i~~'z ~~~ :~~l~~g Yx?~~°~ dal~~~t~~~;
a,~l~~'~~S wI' 1~~15 '~~i~ 3~$~11~~ ~ ~~~'b~;~" S'~fa ~~3da'1~ d;i.~,~'a~?~i
(~'°,~~i~.
~~. ~i~u~°~ ~, ~~~ ~Ji~- = t ~~ ~r,'~~ ~~~.~ ~ - i ~-' ~~., t~~
~ai'~~~p: ~~ x~.ci~~~~i ~aL~~, (~~~
ri~s~,l~~ess r~ ~~ ti?~ ~~~terr~~I i~ad ~tBv~~~t (~~~ ~~, ;;~~''~~~~r~~~.~~
i~~ err'-' ~~~ i~~ ~~-' is ~~~k~~~,~. T'~~
~~c-r~s~~~~di~~ ~~,~~, (~,~3~ thi~tcr~sv vj~~~s ix°~x~ i~ r~ ~~w i
r~~r~. ~'i2c~~~~~~g~;rlcil~~3~;~r~~, ~Kl~~t~
SEJ.':~?t3f3I~ ~~~5øS % t~lY~~~~~ 3J~ ~~~.y a~;i~~l~za"eia;~i~ S~~~attl~i~l
d~5 ~ ~,t~~~3:~1~'3° ~',~~, ~~~~. ~3 ~'':i~t~~°~ ~,
~~%cv see ~~z~v L~Z~ ~~t~r~~~i I~~~ ~~~-~°~>~t ~~~~ ~,,
~~~~°e~s~s ,~s :c i~-u~~~~s~;~ ~~,3~ ~c~ tl~~; ia~~~~~~s~; ire
~. rr~ y


CA 02437304 2003-08-14
Sa~~?.t~lc'3A~. C~?lC~:iLZ°a~lC3~i. ~t~~1~~1~,2, ::cS d,
~1~~'(~"~Czd~:° ~ ~ ~'°.~~ 1~3 , ~..b(~ 6;~LC~"~a1 ~S~aC~
C~.l~f"~T~~ ~~CSj
'.~fi.~aC~dCS a ~~~~C%.~b.~..~,
~~~ ~~g~.trC ~ ~, ~=~~ tGs. - = ~ ~~ ~r~~:.~ a~~~d '~. _ ~ ~ ~'~_ ~' ~~ ',
~~~C ;f~'CC~ ~~° C~~~~~~~,a ~C~g~~ ~~
~(~, ~:a~~ ~~~C~'ia~ ~~ad C~Y~"C11~ (~~) t;; ~'~ ~~~'a'~a;~'m. ~~x'(CC till
~~~'CSSLl~"~g~°adl!~~1~ ~~ / (~~ ?S ~~~3~~?"'(y~~lEL~
~~ ~d 3C ~~:~C?~ga~ ~~ad ~~I~'CYtt (~t'3~ :~.~ ~~.~C~ (~C~,..~e: ~SCS ~JVaL~3
ft~C~~aSiwl~'! ~, ~f.C e%J~~a~ ~X~e;C'~ ~,~ (~(~) ~()
~c:C~easC ~~a~~ar~~y ~~i~~ .~. ~'~~ ~~:--~~~~CaF ~~i~a~r~(~~:r g:~~~: iii
~~g4~~e; ~~ Can ~~ 4~~r~~ai~aCd as
~~I~~~s.
~i~CC ~1~~ 5~:~:p~~e~ ~~~;SS;~rv~ d~°~~~ ~n ~S l~cld C~~~~~an~, ~e
~~~CSS~rC ~;~~d>i~n~ ~~ /
~3~~ dC~z~,as~s aS ~~r~g~~ ~ in~~~~sCS a-:~d ~C~~CC ~j (~~) dc;~~~~5(;S. ~n
~I~C ,~~~~i ~~a~xd,
'''c _ ~G'~.~"~~~t~"~'J t~~~J. ~(~sr:'2 ~ ~~ >~le,~. a .d3g~~ ~~~~c~.~~n~~
~~.~S~S 3a~"g~s" .d~ , y ~~,~~,) pai~~'CaSeS ~'~Tl~~,'~
~'',. T~1'aC c,~~~CC~S .~°~F ~~"~SS~Y° gI°ad~r.~:- algid
~°~,Si,~~~,~'9~~ ,~ ~~L (~~r C(~~la~d~iiE~~ ~ae~'',~s~~I2~~~'. ~Z~C~;
~~C
fc~~,:C ~i ~CCt'CaSC IfF .~~, (3~~j Cai:SC~~ ~,j%~ ~'~°vS~~'~~s'
,~i~3~'" LS 'A'siS'~:C~° LF?,o 1 :~'sC 733C~"C~S~ng :~,~C ~;a~ISC~ ~9~
a~ , IL ( ~~) d~:,°~CasCS ~~Cn-~in~arl~ ~~~ .~.
'~'~~~~r',~~.~~~, ~~~:~'~~I~;i~,T~~Gj .~~T~~,
-'~s~r~g a t~adi~~~n~~ ~:,_i~~~~~~_~~~ ~~ ~~~; ;~~r~(S~~ ~~~.~. ~~-nn~ag, ~.
~~-g~:&a~d~C a~~d
~.s.'~. p'T's~~~ICsl, z L~~2'~Ls~2~'b''t~fd~~ G%~
~r°a~'7°3e?~Li~s~~~~pel~.~', .~'~~~i ~'~~l~~Es'i-L ~~~~ti'2 ~~I-
als,~ ad~(~. ~vi°315, iYlC.,
~~~~8;), ~rvC d~~~r~e d~C Cf~'~C~~~.Cy .;~,as ~~C i~.=~~~ ~f '~;I~~ -arC ~~
C~~~;~~~(~aa ~~r(~~~ ~~~~~~C~d ~e~ tr~C
~pa~C ~f r~(~~~r ~~~r~c C~ns~ed. a~f=~ srCa(~'.'~ s~a~~, ,~~~~~~ng ~3;C ~~n~~
a~~d s~~~~ ~~"~:at~~n ~~''
~,c~.(3~), ~5.(~~) and (3~-) L~r ~f~~, ~rC~~n~~i(~~.~ ~r'by~'~v ~~(~r~.
v,,~CldSe
id'~ t°C(i~ ~f~'. ~~e~~~°~~~i !:v~Y~C ~ia~"~~rdt~'E'~l a L
(~~t~', 'y' (v)~s',
- __ ___- - ,~ -
L~~Z~ P°~~C't)~ ~O'JV W~~'~ GOr'3~'Gl~~.?~G~ - ~~!i
J 3 $_
___- ~ ____-~ _.____(~ ~,)
~~LI E,1 ~~i ~ ~' * .,< ! ~'i~ ~A
_ __- ,
P P
~ ~Ey ~~~ ~ L~~Z '=~i~~~


CA 02437304 2003-08-14
he upeci'°lc c~l~s~~.~ts ~~a~r~~ ~beclY gi~~el~ ~.;ariie,:.°
a~~d v~rr-;re ~rr~p~~~cd i'o~ r~~e
~,~xc~:.~atio~~ of c~ficic.~zcg~.
~~ Figl,lre ' l , fo r ~, _ ~ 0-' ate, :~~ = ~ C c~ and ~k = ~ x i ~~~ rr~ ',
the effect c~~' chaz~l2el
tadins a (fer a circ~.zlar ohannei 3~on the. ef:~lcieY~c,;~ of an ene,rg~r
col~~ersic~n app~.ratus (~9) is
~iotaed.
~'he~~e e~~3sts a 1T~~n~urlz~~Y ei°b~cierc;~ het~eera ~: = O.a9i ~~xl
alld c~ :_ ~3.:~ rlrY.
'~C '~~szel~ ~ --~ 0, she c_~f'rc~e,lZCy aop~ovciics ~;el~o as ~.~.c:;
so~ici/s~q~:~~~i ~z~avela"ace approaches zero algid
~e,llce the Y~zlr~~:~er og rrlo~aabic loe~u i-z~~ this ~~sca., there is ~s~
il~,~zloecul-~erlt ~~l~d r~~e~ e~'~ciez~oy
~eccr~es zero. W'L~lclz c~ > cue, the, surface ~~aea of ~~~ ~ (~0~
il~z~;~eases ah~~, because th~:, sa~rfaoe
area is of the order c~ arld that of ~:1~~; oar rate is of the secoY~d
~:z°-dez° ova, the fio~ -irYOreases at a
faster rate. ~'h as, ~roportit~r~.atei~ zrlore ~lo~,~r 'JOrI~ must be
p=rrz''or~~ed to drive the i=nova and
i ~ iYence the efficienc~r approaches ~o~o.
~'he r~.di~ ~ of a c~d-~,a:~~as~ ::YZa:Y~zel ;~~.~ lrz~~ he zzs~:;P~ to
~;~kou~ate she cY-o;>s-sectional
~.rea of a circzn:~~r c~arYl~.e~ (32~. h~ ° exan~pi ~, rc;ferrr~g to
i~~gr~l i :~ 7 _or a ~,irc~.Lar cross-sectiol~
~, radios o~'' 1 x 10-s riaeters cor-~~~spo~ds t~ a cra:~ss-sec~iona~ area of
s~c~ut 3 ~ iOw sq~~are
~0 microns, a radi~.zs of I x 10-' rneteh-v ~orresporl~ts t~~ a cross-
secv:iorcal area of ~boz_v '.9.03 square
rrliorons, a radius o~c ~ x 10-6 ~~ecers corresponds to a cross-s ect:ioY~al
area of abo=zt 3 square
r~~icrons, a radius of 1 x 10~' lnete.-s oorrespal~lds t~s a cross-s~:~aior~al
area of about X00 sqzaare
Za°11C~~~tS, a Y'a(~'~'13~5 C:~ ~ x ~ 0 '' rYie''.~:C::3'S
C~(°Y"'~".5~~12~5 1E~ ~, a,roSS-s-C.'C~IOY'iu.l area Cf a~C'3~~ ~i.~l~
Square
r~~il.iil~eters, a -~adiz.zs ot: ~ x i0' z~ ~tev~, co~Y~esponcis ro a cross-
~eotro~al ~:~ea s~f a~out 3 sq>xare
r.~ilii~-r~eters, arid a radius of ~_ x ~ ~-' l~~eters correspoYZds to a
~4~oss-s~~ctaollal area o~ abc~zzt 300
sqzzdce xrr,ilii~rlevers.
~t lna~ be theori>;WV tlEaz there rr~~~T lie solTie c~~hr~eatiol~ irl the
practice s~~~ tl~e
il'l~Ierltio2l ~3et'~~,eT! C~llaT'.nels (~~;~ ~avir~g a CirCLYlaI.' GrOSS-
SeCtiLn Cf : partcular C.roSS-Se.~°.~loYlal
6!rea and s,~iat~l~ elS ~,~~) ii~'~rlllg a lifil-~;YY'Cl?lc'Li" C:ic"~SS-
SeCtlol2 of ~:!'ie SaYTa~: G~iOSS-SeCtYOI'lal area, hY,Yt
~y°~IPS pC~eilt~~.l ~'JirGIat10I3 ITla~ ~C, i'-.-~il~.el2.'°,G~
~3~ ~c~:C'~~srS SUC ~ ~S tai, x~r.~:lLl, C~~'t_'.le Sllrf~t;,e area.
~t3ft'~'le
_~~3_


Image


CA 02437304 2003-08-14
~7 r~a~It~, pC3rC~a-s ~~~~. ~i~rl~-aC~~lfJ ~PII~ :~'r;:atCd°id~S
~,i'~), s~C~. as ~°t~:7S °~Pl$Cr,
PrZCIT'~~3rarPC, rt3C~'~, ar'~~~ Soil, CO~~~~i lm3e CGrisICiiCrvd as a
riatLlral CiCC$ro.~il2CtPC h~.t'$Cr~1 (i.e. as ail
C~iCr~~y% C;~~I~~rSICII'i a~~Jar~~;LIS (~'rj. .~ ~C d~s~ '~~~ 3'~a$~?l."E'cl
~~ie'~$Cr7a=s S~IOL~s ~,~I3I~1C~
rilicroiPPanoi'a~cricatior_ procedures ~o prod:~acc, cl~.ai~rPel (3'~) arrays
~~~i$h a large st~rfa=~,c area to
~JOlue retie. ire ~,dditi~ri, ~~tur~:x ~~c~-c~is r~~~tv~~ial:c~~~ h~.ve =L
higl:~ ~orosiv~ ratio ~.~~ to ~~~/~.
~'o explore this, the ex~eriz~ental d~mrg~r curPVersi~PP apparat~:u (3~)
sho~s~~P in Figure 1~ mas
~.~~ns$r~c$ed tc illustr~~e the c~~~ce~~~: e~ aia ;acctro~=i~e$ac
l~a$~nr°~, ~~::si~~.g a -~,o~~rirrr~~;rcvval p~,ra~:.s
glass alter as ~ ~~uik Priaturial (76) td~~ provide $lie pl~.~ralit~~ of
cha~~.rEels (32).
l.~ g.-~ the experii~Per~t~~ ~~~p~.rat~.~s (~~) o~~'igure 1~.' the pc~rou.s
gl~.ss alter (76) vaa.s
%~ rr~P~Prz iri diaP~~s~ter aPid 3inni te~icl~: ~~itlz a ~~ei'e si~.~r frorri
l~ ~.rr~ ~~0 16 ~~r~. (~ch~$t t~'ZJF~I~r,
l~.l~ir~~, ~~eri~ar~~). '1'vm Te~or~ ~ui°°rEgs (7~j ~l°~.
i~b:~ $~~aicl~>~ess were Wised ~~ hold ~l°~c; f~lte~ disc
7 6) iii pcrsitioPP. Te~rc~ r~3eshed l~g,'H gel e:lectro des (~.7,~~) vrere
used as the first terr~~inals (~2)
gild tli° seco~~d rerrrrr.ir~ais (4af). xhe ~:~e$er (~~:i~.~ortsisved
of a lgc7Ll~te~ 2~~~ digit~a i~u.ltii~eter
l~ (~Cith$e~l ~t3str'~IFTICiIts, ~3Cr321Cr1I2g, ~i.?~'ilal~.~T~ ~J~.s 1'rsCd
to rCCtSr(~ t~~, extCi'2lal load v°~='r8rit (~J).
3~ c~-.~ ',hcig~$ difference in the li~s~.~t~ rese~~,,,~1~° (~?) ~~as
a~i°ev~d~;~i het~,veera f~Pe ~=r.ie$ (~4~ ~r=d
the outlet (~6) to rrial~e tl~ie liquid (2~) pass tlzrcj~gh the filter dis;
(76) udder hydrostatic
gC Css'di3 C.
2~ ~eioi,i~ed wai:er (~~~,~~~~~~,, a'il~~zic~., ~~lass~~ch~ser$s, 1_i ~~~.)
a~,d yap vJ~ver
were both used as the testing licl~~id ~;~~.'. 'l he experir~mnts =~~c~zCed
~rP stea~d~ state z'~c~v passing
in ~, s~.~gle ~irectioii $hrough ~h~~ iait~;r d~s~ ~'~6), l~P this case, rs~c
digi~~:l rn~zr~ir~~e$er (~~)
r~i°asured the ex$errral 1~ad cL~rrea~t (5~) ~li~-o~.~;h the ahurat
:~esis~~c~~ (~~) in 9:hc rr~eter (~~). since
one s~PCin~ resistor is l~ ~~ for 1~ ~ ra~~ige:, ~rhich is srP~all corr~pa:~ed
to the surface resistance
X7,2) cf ,glass niter (76), the str~;~~~~irsg ;c~c~ :f;~$i~,l i~2hecor~~~~.;s
~-e~~.~~ivcl~~ salt ~v~e to ~iPe
re~atively high external load current (56). ~ h:,~~s, ~rre igP~ore the
;,<o~~ducrion current (6~-indxced
'~~ the s$:r°earriing potential (62), ~;~,~ =J'~, sc; tiz~t.r~.fc~~ ~:
~~(~~ / ~~~v,
's he i~~rr~z~er c~~'peres ~~~ $~e gl~~ss xlte~ ~ ~=gas ~:alc~.lat~;d
~°orr~e
~C
~'~7)
_. ~.


CA 02437304 2003-08-14
~nh.ere ~ is Ore porosity of gi~ss f~~~e~- ('~~;~ ~~~d .~I is ~~e ~;~'a-
~~~i.~e ~~ea of ~aiae ~~er ('~~).
~.'onside.ring the thickness of ~-r:~vgs ( i ~), the efP bcti~re area was
calculated to be ~e~,10 - 2)z
r~lrri2. ~~or the ptpose o~ caICI~i~txons., a~~ ~~3~er~~.gc c~fa~~ravi raci~~a
of rx = i~ ~,~~ w~.s selected.
~irice ~ vas ysot aaailabie ~°rorxx ~~.oclu~:~ desc~~p~ion., ~ ~y~ic~,
pca~o~~';;~ o~ r~ _ o
- ~ ~~ ~ = 30 /o ~nr~s ~ss~~ed,
~~ai~ic~ resulted in ~ _ ~.3r~(S x I~'~/(~5.~'j ~ ~.5 x ;~~5.
Since the bulk ~o~.~vcti~rst~r o~° p~~~e wa'~er ,~t~ es J.~ ~.35/algid
tire sur:~~ce
co~.duc~:i~Tity ~; is the o~-der of ~~~'' Sii~ or =~-s Si=~ (see L,.C~. ~.e~,
~.. ~,i ~~d ~'.Ir,. t~u, ~.
l~ ~~'olloid h~ter~ace Sci. ~~3, 1~ ~G~vl)5 . v'~e~~er, <I, .orber, F~.
.~i~2~z.~errnar~~, ;~. ~ulchir~ and
ma:.J. ~~e;obasch, ,l. colloid Lriter~~~~;e ~~:~. 2G~, ~~~' (.~9~~~ a~~~w ~.
f~~°ici~sora, ~.~s '~~,x aid ~.
'~ler.~er, J. colloid Interface Sci. -,,:~v, l8G (~~~~?)), ~r = ~~~~ ap I' ~z)
is e~LpLo~~ed to predict the
a~.eas~.~~-e,d cu~re~t.
t~ 'ho predict the rr~easz~red exte~~~.I load current (~'), the following
constants were
elmploycd v~rilicb co~respouded ~o =~~.;~ e~perin~~~,h~tsl ~;~~~~ditao~~IS:
;~w ~ /~.._'= x aI.~S ~ ~ ~= l~ ~ S/r~~, ~~cl
m= ~ x au-s S/; .~ - 3 rnfrL, ~.= ~z ~: ~.d~~. x :_~-'' ~-~r-~~~-I , ~
.°= ~:e~j ~ lyc l.~zs->> ~ ~~ ~ ~~ k~;I~~ J7
and a = I.~~21 x l l3-0, -~p ~ ~~ =~ ~.g x I~~ lea ~~_-'. ~'or sir~paicity, it
was assned that all
ll~~dros~~tic p~°essure drop occa~r°~ed r:~~ tl~e ci~ar~~I~.~;ls
(.'~2p.
It should be noted ~~;~t the ~ralae of p~~s depends c~~~ botl:~ the
concen~ation o~y p~
oI'sollztion. ~I~d cha~Ir:el r~ateria~. '~:~~e ~~trger t~~e re~:~ poie~-s~~s.r
(~~~°a airs, tie Fore ~oti~:eabic t~.e
L~=.rctrol~i~.et~c effect. Thus, one a~tro~.~ld expect to o'osee s. =E~vge,r
st~-ea~.ning c~ar°~ent ~~t3),
strea~~g potential ~c~2) and exter~~al lo~.u ca,~ro-exit (5d) i~'or larger
Jets poteY~tial (3l) ors.
~J
'I~I~~I_.E
_~redicwed ~~~.errla~,oad ~,~~_°rer~-~~,.Dfo'=~ p~ass~v-3e ~'~l:.Ies
e~: ors arid yI
~s=SO mV ! ~s=IOOrn~! ~ ~s=i~Jm~' ~ ~s-?pOm~i
i'r-' =I ~,~, ~ l~~l r~l-~ ' :33~)I rI~'~ I ~~~52 .iA~< ~ ~t~t~~ r~~
- ~.


Image

Representative Drawing