CA2437304A1 - Apparatus and method for producing electrical energy from fluid energy - Google Patents

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.

Description

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~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~,$;L;G e'~~; z S~i:;c.'95~:~ ~~~a~
~;3SY~~~n Srl~ !a ~OrI~Ii~.L)11~a~~~ n °~~llt~a -~~~.~; ~~:at'~a'~el.
.°~-MIA a V~~f~~ld ar'Ci~~~~~a ~;5Y~3Cr~~., ~i~'!~ iil~:'t_'.r~~:l~3fi 3S ~, L~~~z ~Jd ~~~I i'~ui:9~bi2g ~~~a:-3~ra~a~
~,Y~~erg~y i'~~~rrr~ ~~L~id energy ~~~r:~ris~.~g i:liv f~i~~:~~i~g ~,~ ~~5:
~i'~Vi~ii3,'g'- ar3. ~3~~' a~'~ ~ ~I'x'~l~Y~>:143Y~ a~y~5,s~.r~~~:zS, ~~lxls~i~sY1 ~~v 4:,l~~rg~J L:~YI'J~ISg~iYi ~~'9~5~ra~;LiS IS ~(3~1i'35~~~ e~3 ~, ~5'ia'~'~~i~' <ISS~ii"°g~~~, ~i''i~;a~'iY~~YF' ~,~~ ail3~~~ a~'S~:~T3~~J "aS
~'.J3l~rlS~d ~i~:
a ~~1~1~~9 .~~i ~i3~y ~ PrS~ ~:~rY3~ir~~;.a ~.C3~~~~>' dL a. :::'lrS~; ct.~la~
~(~~Si~:;;~3i dYid iY~ Cvi.;ir~~xY11~~3~1~TI
~'Jx~'fl ~~i~ ; ~~,~~M~gn ~iil~ a S~~'~9ri~: A~.',~.°allz~: ~v~,~->~~,~~ a~: ~ SP':%~Y?~ aXi2~
~~S'~EQ» aT'~Ci lfi ~~~.'1~,.L~YliCa~l6~~ ':~IA~!t. L~;~ ~~,~ial'°a3~~~~9 ~i~d 1~
~s~; ~aSSi~lg a~~ ~le~Er~~~-"d~, ~~~~~c? ~t~n°~Lg~ 6~1~ ~a~a~~~ei.
-_.~~ Laid ~r~~,Yg~ ~~<gj~ ~~ v~r~:rid~d ~~ a _~~L~id _r~~,rg~= Sc~F~r~e w:~i~Y~ ~r~~~ideS
~:~Y~.SSLI$'~, .~~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 ~_ >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_ 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, a ~

'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 ._ ~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$.aer°~tion r.~a,~ be scaled. to inclr~~de any :~ur~her o~_ channel asse~n~'wes.
if the, inve~jvion includes a ~1~~-~~°alitgr <.~f channel asser~~~hlies, each o:~tl~a., channel assemblies ma.°~ be identical or n xay be different. for era npie, ~ac~
of the channel ~sserr~hl~ses ... '1 ~s may ir~cla~de ~: separate First terrrsi~al and second terrrainal, or ~~;~o or tr~ore of tb~; ch~.r~rlel asse~r~blies may share terrr~ia~als.
'~'he plurality of ch~~-4~~e1 asseanblies nay be elec~~rically cor~r°3ecte~ in a parallel con ~~~uration so that the farst terminals of the channel assemblies are electrically c;oa~nected, a series confi~uraiion so that the first terminal oi° o~>e of a pair oi° channel assemblies and the second ~errninal of the ottzer of t1-~e pair of c,~~arlnel asse-r~~blies are electrically c,on~~ected, or some cornbinatiori of parallel aid series configurations. ~on~~~3rin~ the channel asso,rruiies in parallel provides additive currents .~hile conii~u~°in~ the, s.;l~arm~"1 ~5sse~~~~lies irf series provides l~ additive poter~tiai differences. tr ~ f~rei'erred c~~i~od_~rrie,nt, tlae plurality ol"cl°~anneF as:~ernblies is ~,oraa~gu~-ed in para11e1 and the v~rsv .erf~~.i~~als arid the sec=ond tc:~i~~als of each cf tl~e ch~~n~el ~ssea:~bl=es are shared.
1:1' tj~e first te:~arsals and v.~~e se;cor~d terrri~~~a$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~_ ~~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%
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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_ '~'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.

~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_ ~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 ~ -~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_ 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~_ 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 (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 _~~_ 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.

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 ~~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~

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 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 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.

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~

~~~',~ 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 , ~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.:

~",~~__/~~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:
_~~-~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 ;~ 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~~

~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~

'=~'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"~.'>~
-~.;-'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:
~~ _ = ~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 r s ~ ~ ~--.-_ ~ 1 ~l' - -;~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 '~'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~~
_ ~~ _ 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~~~~.
_~.~_ 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~$g ~~,_°~-~c~t~ru ~~
~°~ ass;~r~~~~ ~~r ~~~ ~.~~s~~~~~et~i~ st~~l°~~ a a= i.~~~~ i = L~~all~ = G~pl~,, ~1e ~"x~= ~p t s ~~ ~ ~ _~s~..
~~ ~ig~~~ ~, fc~r ,k =_ ~ ~ i ~~" ,~: f ~~~. ~, = -. ~_7 ~~:,~., ti~~ ~;F~e~c c~~ t~~ ~~~a ~L (~~i~ is ~l~~te~. ~l~ez~ ~~ta ~~st~rEti~i (~a;~ ~;~~~-~~s~s -~i~Y~ ~~~~er~~i lc~a~
a~~~~~t (5~i~~r~;~~9ey iir~~~~i;~.
~E;(16C~; ~13~~'',.f,'~° Z~z~ ~C3t~;~?t~~Zg (~ ~~ ~.ei.3S~,S
~~~~a1°' ~ a,, ~-~lSlt' i~~'z ~~~ :~~l~~g Yx?~~°~ dal~~~t~~~;
a,~l~~'~~S wI' 1~~15 '~~i~ 3~$~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 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~~~

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_ ~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) _. ~.

~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~~
- ~.

Claims (46)

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.

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.

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.

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.

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.

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.

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.