Glenn BacaL New
ond R. Dean Hill' Mexico Stole University Lor Cruces 88D01
I I
A Modified Moving Boundary Method for Determining Transference Numbers
T h r moving tmundnry mrthod".' for thc rlrtrrmin:~tion 4 , f trnnxfrrrnrr ilumhrrs hns hcrn rmployc~l11rrnwr of its simplirity nncl grentrr prcrision ovrr t h r llitte~rfmrthocl. ;\ modilie~lmoving houndnry mrthod is proposril hy whir11 t r x ~ ~ ~ f r r r 1111mI)rrs ncr mnv Iw drtrrminril prrrisrly ill sol~~tions whrrr it iu cliflicr~lt t o clrtret thc lm~tnclnryhy opticnl mr:rna. This mrthocl Irntls itself I I Su d l ns I I O I I - : I ~ I I W I I ~ very wrll for work in : I ~ ~ I I ~ :IS solutions. T h r moclifie:~tiot~ proposnl h r r r is 21 rcwlt, of :witI-11nsr studiw in I I O I I : I ~ I I W I I ~systrms, iu whir11 nricl-lnsr indir:rtrtrs w r r wml to Ior:~trthe Im~r~rd:rry I I n o i n g I M I I I I I I I~ ~ I It wns found thnt t h r t r : ~ n s f ~ r r n 1111ml1rr rr of t hr ion I~ringst11din1lvns a/~ra!/x s l i ~ hly t I c w \vI~tw:III indicntor \v:w prwrnt tlr:rn xv111m 1111- t r : ~ ~ ~ s f r rnr~mhrr n ~ r r 1vns drtcwnit~rflin the snmc s o l ~ ~ t i ol1y n npticnl nlrnns. This indir:~torrfTret IIC came. moreBp r n n o ~ ~ n r n.s n l t h r cor~crntcrlion of :I p i r r t ~ s:\lt hcr:~nirmore. clilutr, h r r n ~ ~ s r ~inrlirnlor thr :rcid itsrlf xvo~~lcl contrihutc~to t h r trnnsfrrcnrc. 111ln11)rrof the r i o . 'I%r mo~lifirntio~rwhirh o l ~ v i : ~ ltlrr n wr of inclirntor nricl.;, htw-c. rliminntcs this rrror, is t h r ronstrllrtinrl of n moving ~~~llnd:Ir.v tllhr with tlw ghxv ~ ~ s t r i t i o :n1s1 t - 5 rrntinirlrrs : r t nrtnils in the! cnnslr~~rtion of this t1111e.nrr g i v r ~in~ t h r rxprrirnrnt:~Isrction.
F i g u n 1.
C i w i t diogmn
T h r rlrctriral circuit shown in Yigurr I i~tilixrs:I conslnnl volt:~grsourrr s ~ ~ p pwhilr l y t hr currrnt which p n s w t h r o ~ ~ tghlr~ moving I)or~ntl:~ry tnlw (lahrlcrl nn t h r vnri:~hlrrrsintor N?)is hrlcl ronstnnt hy rn:m~nlnclj ~ ~ s t m r nnft s srrirs rr.;istnnrr. :\ graph of t h r rhnngc in rrsistnnrr (I?,) trrxtcn tinir na shown in F'ip~rr 2 ~ I I nhlw o w l o lorntr t h r time :11 which the- movinp 1muntl:~rypnww t h r ronntrirtio~~r in the tub. This. thrn, :~llowscmr to drtrrrninr t h r time of tr:lnsfrr )>I-' trvwn mnstrirtions with n good rlpprrr of prrcision nn t h r grrntwt rhnngr in rrsistnnrr will occur ns t h r ho~tncl:rrypnssrs :rcrosn tlw ronstrictiona. (':tiionic trnnsfrrrner n ~ ~ m h r rsho\vn n in t h r tnhlr inclir:rtr thnt rsprrimmtnl (T,)anel litrrntur? rnlr~rs
nrr in good ngrrrnwnt. I.'or :I givr~isoh~tion,t h r trmsfrrrnw n ~ ~ n i h rnu r r In- rrprotluml to +0.001. Experimental The m n v i n ~Iwu~A~ry wll i* I Ii i : Thr c n t h ~ ~ l ~
i-h:~mIwr e a n & I s of :I I I , x I 3 n m 111. I I ~ W . whil.h WSIE in II 2 X i n nI A platinum wirr r:lthrdr i~ plnml in thr smt~llrr: 8 h , SINI is wpprtwl I,? Figure 3. Cell d.sigm I f t I 'I'IIP R I I I ~ P rhnmlwr i.; m n h hy using R m m I'yrex tuhinl: i n w h i d ~t w o omrfriv:itmr R ~ Cmnde hy wc o f n s h n r , ~R:tmc surh :hnr the alw* I I n i ti tf I 2 n . The wnmi conr1ric:izw ihoulll lr aI~w11:{ tcv I, ~~n~timt-erw frcm thr AN. S e i l h ~ the r c l i ~ ~ n w lgd~ m 111- wwlrirtiw~.~ u t rthe diwtnnw spar1 r i l i l :\ p l 8 k l i t ~ u n lwire S C I n1101tt ~ 2 ( ( I :{ w n l i n , ~ Iwlanw I~~~ thc IOWPT w n ~ l ~ i o ~isl i m ~ nn d ~IWI t h 111he ~ IVCII: w ~ I I I W I Ii n I"igurc 3. Thr voI!~nwl ~ ~ l w wl lnw tw> w w t r i c l i ~ ~ nmst r . 4 he : l i l t IL i tL I . Thr- IN- 111nwnwr?. dw.; nut givr a* pcwd rt..ultr 11.; Ihp na~lhodill lhc use of a rat: of known 1 r : i n 4 ~ ~ r wnumlwr, w if ow i- willing l n wwme !he trnnsfcr~n~+ n u m l r r of t h ~ t\:dl from lhr l i t ~ r n t ~ ~113r clw m ~ r m r ~ I. h : h n w l h ~ "d w~ i n ngrwmen: with e:d%o:hw en *ll.:i';.
Prww~tnl,i n 1,arI. nl lhc I:T,lh Snlicmnl i l n t i n a d thr hmcri('hwniwl Swie!y, S m I"r:mcisw, ('aliforniu, >\pril,I!lG\. 8 l ' r ~ w lw l d ~ w d lmlh n111h
