EXTENDED CHARGE ELECTRO-OSMOSIS AND ELECTRO-CONVECTIVE INSTABILITY. Isaak Rubinstein. Boris Zaltzman Ben-Gurion University of the Negev Israel
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1 EXTENDED CHARGE ELECTRO-OSMOSS AND ELECTRO-CONECTE NSTABLTY saak Rubinsin Bois Zalman Bn-Guion Unisi of h Ng sal
2 Conduion fom an lol ino a hag-sli solid ion hang mmban o mal lod Eli doubl la -- - ψ C C - ψ Elo-nual bulk Sid bulk Chagd Sufa of Caion- Sli Mmban Diffusion La
3 . Malki al 99 lim olag-un u of a C-mmban Elol C-MEMBRANE Cun pow spa
4 Classial piu of onnaion polaiaion mmban: ou dg of diffusion la: < <. and lim. ln Elol Cun dnsi lim? C-MEMBRANE olag
5 olag-un haaisi fo amalgamad opp Poopial pimn. Rubinsin 7-h _ Cu ahod A and mmban B wih lol immobilid b aga-aga. Malki al 99 CuSO 4 δ MEMBRANE Cu Coni miing MEMBRANE.< C <.N < δ < µ < Ra < δ No Gaiaional Conion No Sufa δ C C Elo-Conion No Maangoni Conion
6 5 / / S.5 4 P : S P P < < < < < < π ν πη drt D D D D D d RT D L p p D Bulk Slip loi << OUTER SOLUTON: BULK ELECTRO-CONECTON NNER SOLUTON: ELECTRO-OSMOTC SLP TWO TYPES O ELECTRO-CONECTON N STRONG ELECTROLYTES Bulk lo-onion Elo-osmosis
7 BULK ELECTRO-CONECTON NO SLP : S P P < < p D o low-molula lols:. Conduion - sabl. Eli fo - sabilis lik gaiaion fo sabl saifiaion. ln
8 Rubinsin Zalman P Lind [ma/m ] [m A /m ] [m A /m ] /. µ m [m A /m ] /. µ m [m A /m ] /.3 µ m [m A /m ] /.4 µ m [m A /m ] /. µ m [m A /m ] /. µ m [m A /m ] /. µ m [m A /m ] /. µ m [ma/m ] / oiginal U [ ] Cun-olag us of a C-mmban modifid b a hin la of osslinkd polinl alohol U[]
9 Tho of Eli Doubl La and Elo-Osmoi Slip Hlmhol 879 Guo-Chapman 94 Sn ψ Eli doubl la C ψ C - Hlmhol-Smoluhowski HEURSTC THEORY O ELECTRO-OSMOTC SLP Assumpions:. Laal hdosai pssu aiaion is ngligibl.. Eli fild supposiion of h ininsi fild of EDL and wak onsan applid angnial fild ς u Σ u ςe ponial E E dop bwn h infa and EN Bulk
10 Mahd asmpoi pansions Dukhin 6s 7s u p p w wj ui ± fild on h applid dpnds osmosis hag ndud onsan maial appoah Classial u u ς ς ς ς ς ς ς ς ς ; ln ln 4 ln ln / / / / /
11 Quasi-Equilibium Elo-Osmoi Slip. u u ς. mpmabl Chagd Sufa ln 4 ln ln ς / ons u ς. Chag-Sli Solid Caion-Sli Mmban Conna ion Polaiai on lim ln ln p ons u ς u 4 ln 4ln ς / D Conduion sabl: Zholkoskijoons Saud 996
12 Bakdown of Quasi-Equilibium a h Limiing Cun > < alid fo fails a h limiing un. Rubinsin Shilman 979 Enihd Dpld mmban s ufa: mmban sufa: p p. < < Elol C-mmban
13 .6. C - C.8 Tansiion fom Quasi-Equilibium o Non-Equilibium Rgim oni onnaion pofils. 4 C _C - 4 O /3 - h iial lngh sal fo O4/3 ln - h ansiion fom QE-EDL o NE-EDL. o > O4/3 ln a whol ang of sals appas fo h n of h spa hag anhing fom O /3 o O. o suh olags O /3 is h lngh sal of h ansiion on fom h ndd nonquilibium spa hag gion o h quasi-lonual bulk.4. Y Lih 959 Gafo Chnnko Nwman Sml Buk 975 Rubinsin Shilman 979Lisonih 989 Nikonnko Zabolosk Gnusin 989 Buinsma Aland 99 Chaalil 99 Maf Mananas Muph Riss 993 Uno 999 Chu Baan 5 Dukhin 989 : NE-EDL Elokini Phnomna of h Sond Kind
14 BASC D PROBLEM N TERMS O PANLEÉ EQUATON / 3 / 3 / 3 3 / 3 - nn aiabl / 3 Eli / 3 p fild inasi ng funi on of ζ << -- QE-EDL O - T ansiion >> - E ndd Spa Chag
15 Em Non-Equilibium Elo-osmosis >> >> 4 3 u lim u ln - NE-EDL Endd 8 Spa Cha g Domina n d ζ < < 3 nsabili of Quisn Conduion < / 3 u u < limu < < < P D D P P D S p S p : u w 8 Quisn Conduion Connaion Polaiaion a h Limiing Cun <.
16 Mhanism of Non-quilibium Elo-osmoi nsabili u 8 o luuaion
17 Olimiing onduan
18 Nual Sabili Cu 8 PD D sinh k osh k k 4 sinh k osh k k oh k 8 P D D k Sho-wa singulai: k
19 ull Nonlina Elo-onion Numial Soluion fo. W nd a unisal alid fo all gims gula limiing lo-osmoi fomulaion
20 3 /3 /3 /3 s s s s s s O p un h limiing Na Basi Singula Painl Soluion ζ ζ d / 3/ 3 ma ln ln ] [ p U U u Dukhin s omula fo ζ O - fo ζ >>O /8 ζ [ ] 3 / ς >>
21 LOW DREN BY NON-EQULBRUM ELECTROOSMOSYS Unisal Elo-Osmoi low omulaion Elo-nual bulk P D < < < < P p S U [ ] ma ln ln p / 3 u w U ζ ζ ln ln p 3/ d ζ w. u 4ln.
22 Compaison of Nual-Sabili Cus in ull and Limiing omulaions Dashd lin -4/3lnons D 3.4 k Dashd lin k-/3lnons k
23 ull Nonlina Elo-Osmoi Conion Numial Soluion fo
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