l’} H 1 . . ‘,‘t‘ II. I l ‘. ’l w M {l THE EFFECT CF PARTECLE SHAPE ON SOLUTE 01$?ER550N {N MQUED‘SQUD CI'SROMAZ'OQRAFHIC CQLUMNS Thesis fer Hem Degree of M. S. Mia-{EGAN STATE Mé‘JERSiEY Jaseph F. fianfifie ‘ W693! h l IIIIIIIIIIIIIIIIIIIIIIIII L I B R A R Y , Edichigan Sta «2:1 University a MICHIGAN STATE UNIVERSITY LIBRARY v ‘- ENG?“ LL! I (J ._J‘ W . fl .‘J-"flx’. .b i I {f ;’ :1 f: . ,-. ‘EE Ig‘fif MAR 1 7 1912 ABSTRACT m EFFECT OF PARTICLE SHAPE 08 SOLUTB DISPERSIOH ll aqua-«noun canomrocwuzc comm by Joseph P. Gentile A. part of a continua; affort to dual” a raliabla acala-up procadm for liquid-00nd chromatographic aaparationa tha affect of particle aha” an axial diaparaioa in packad Sada baa baan invastiaatad. m pulaa input aathod m and in calculating tha axial diaparaion oaattiaiaata. Tbaaa calculation var. accomliahad by obtaining aoluta (liaCl) mutation varn- tiaa data at two poaitiona in a bad of irragulnrly ahapad claaa particle. Coocantrationa vara manna by alactrolytic ”data.“ at tha two aaaaurin; points. la Otdat to ”nah“ tho data from thia work vith thoaa obtained in a aiailar imtigatiaa involving bad. of apharaa. it vaa nacaaaary to datarlina maria-null] an attactiva diamatar for tha mapbarical particles. 111a attattiva dimtar Iaa dafiaad aa tha diaaarar a aphora would and in ardar ta paaaaaa tha aaaa aarlaaa araa aa tha irragular particla. Uni-a thia,aaaia for diaaatar aaapariaaa. it vaa found that for flow rataa ham am and m—hundrad faat par hour tha axial diaparaion ooafficiant for a bad of My on.“ particle vaa aisnitioaatly hiflxar than that for a ainilar bed of apborna. a. u . o I a . 4 ' . _. t t , I a ' . ‘ d . I a ‘ ' ' . ' ' .1 ’ l I I ‘ ' l ' I l. - .‘ o « . . . . a . ~a . I . . ,1 . _, k: . A . o ' .a' . .-. . . . _ , v1 L) .-' - .' . ' I C 9 . . l “ ,‘.. 1.. . ' I’o f ‘ I I . '. . ‘ ..' t; a a. ‘ ‘J ) .- ', ' , . w: l‘ :3 .1. .3 1 : -v ' Dr- \ J " I: r -- ‘ -'( t - 4‘ .5 d t “at ’ ' i. . "‘. ' t " f ‘ "h t I . . .: ."‘ — . '. - -l. _ o . 1.“, . _. , l . v ,. >9 _ a _ ‘ I. ~ g - ... . fir ‘ I ’ ‘ ' "l 7 .3 '3 h a. f \ . , . a I ' - «,1 'fi. .1 . . -' . - 4‘.» J ‘ 4 - v v. I ml EFFECT OF PARTICLE SHAPE ON SOLUTE DISPERSION III LIQUID-SOLID CHROMATOGRAPHIC COLUMNS 3! .4/ If“ Jooaph If dontilo A 1311818 sub-ittad to Michigan Stata Univoraity in partial fulfill-ant of tho roquiromonta for tho dogroo of MASTER OF SCIENCE Dapartnont of Cho-ical Enginooring 1966 P.-- i .§ To Hy- Hotfiot and hthor b a: -11- ACKHOULEDGMENT Tho autnor gratefully acknowledgea tho Upjohn Company and tho Rational Scionco Foundation for tho financial oupport of this work. Bincoro approciation io alao extended to Dr. Martin C. Hawlqy for hia‘ilrlluahlo aaaiatanco and guidance during tho couraa of the projoct. -iii- , o- .' f .. . ‘nt ' 3;; MSTQ IABLI OF CONTENTS WWW? O O O O O O O O I O O O 0 O 0 o 0 o 0 O 0 LIST 0' mm 0 O O O O O I O O O O O O O O O O O O O 0 “ST OF FIGURES I... 0'. O I O 0 O ; O 0.. O O 0'. O O O ImonumONo'ooo'OOOooloooaoooooo‘oa. THEORETICAL DISCUSSION OF THE PROBLEM . . . . . . . . . Diaparaion in a HoneAdaorbin; Bod Mixing Coll Modal and tho lifoct of Particlo Shapo on Diaporaion mmm “man 0 O 0 O O I O O O O O O I O O O I O Tho Flow Syatoa Conductivity Calla Tracar Solution hoaaurin; and Rocordin' Apparatuo Tho Packing Motorial Dotoruinatioo of lfioctivo Particlo Diaaotor Packing Procaduro Calculation of tho Diaporoion Coalficiaat “we" or mu 0 O O O O O O O O O O I O O O 0 I O Corrolatioo Mbthodo Calculation of tho Effoctivo Particlo Diaactor Diacuoaioa of tho Dioporoioa Coalficiont Data mmmlom I O O I O O O O O I U 0 O O O I O O O 0 O O “Pmlx O O O O O O O O O O O O O O C O O O O O O O O O 'num O O O O O I C O O O 0 O O O O 0 O O O O O O ~iv~ U 11 25 32 33 38 Iv. 11an . T. .1. . . .. . . i C O a ' o ' a . o C . a a a . Q Q I ’ I O ‘ ' , V( Tabla I. II. LIST OF TABLES Effoctivo Particlo Dialotot mu . . . . . . . . . . .' Diaparaion Coafticioat Data . ... . ... . .-. . . .O. , 5 a . .4 , A . r.. V . o. v or . n .. t 'a .a r . . c . Am». pc I V. r A o D P '0 :a .‘4. or; .I . ‘. ‘0. . -t .r. 5 . ad. 4 x a 1 . U ‘— — I w.— in. .0. .a _. 1|. I . vrj- Iv- I. II. III. IV. V. VII. VIII. 1!. Conductivity Coll LIST OF FIGURES Du'm Cf B.d O O O O O O O 0 O O O O O O O O O I'crmtcfl.d0000oooaoooooOOO FMWaIphlrl.............. 11.. About in Irrasular Particlo . . . . . . . . 8choaaticot!loolyotao............ O O O O O O O O 0 O C O O O O V Echo-otic of llactrical Circuit for Conductivity “W M at m him-g Circuit. . . that mu: Partial. alto mm m‘ Goldaoooooooooo M‘maooaooooanooooaa ‘ ! Soho-atic of Equip-out to Mooouro Praaoura Drop .I Typical Coucantratioa‘vo Tina Curvaa for muttwmao-ooadiootooaaao all/Divan“v mmummq.......... Wattaatimolm farticiaa . .3" ' "maC'IVanoaooa'ooa W of man-m lard: firti‘oi'a. " law of tutorial rartieiaa‘. .- . '. ’. Iionphotouaph at Irra'ular'rarticloa‘ ; "-. . ,. Pogo 13 16 17 18 20. ' 2A "26 27 ’3‘ as '- 36" or 2"! I“. k/ .- 0‘1 1.. I .qu ....- ' 7 ~‘ r: v‘ ..a.-‘. I. 8.}..g-‘J‘J . A .‘\. - r ..'_“- ‘,4 . .~ ' .‘4’ !.'.'...V ;J\‘-.'~q"}~...b-. ' -r— (. 3, £1.11)? a. $244.. - C . ‘ ‘3 “t l ‘ .LJ‘); '.‘.f\'. ' I ~ . 't’ ‘0"“ ‘ ".}v ‘1‘- .. 1.-' »‘..- .l.‘....,u . , kv unu¥39na;u v 0H i I ~-. ~ \‘~ 4 " Q . ‘- LQ¢J;VJULCGIHH . 7 1_I ' ,~a~.cucrwutuLfi IIITRODUCTION - Dioporoiou in fluid {loo throngh porouo uodio hoo hoou tho ouhjoct o! intonoivo otudy by ociontioto ond ouinooro for uony yooro. Smrol 9 11 tronoport thoorioo. ouch oo tho lining non nodal, 8 tho diffuoion uodol. ond tho ototioticoi opprooch. hovo rooultod trou thio offort ond hovo hocouo involunhlo in prodictin' tho outcouo of yoriooo moriuooto. ‘rhooo tindinp. for mu. hovo oidod in tho dovolopuont of ouch procooooo oo oxtroction. drying, ond ohoorption. Hovovor. tho phoruocouticol indnotry. which oooo tho ooporotion tochniquo known oo chrouotogrophy for iorgo-ocoio production. hoo hoon noblo to ocoio—w chrouotrorrophio ooporotiono roiiohly. m: io. tho curront thoorioo did not ootiofoctorily occount for tho oovorol procooooo (fluid :1... ohoorption. ond dooorptiou) which occur oioultonoouoly within tho hod. It voo thoroforo nocoooory to rovi- tho voriouo hypothoooo in oo for no thoy portoinod to chrouotogrophy. furiously. thooooticiouo trootio. tho phomuono o2 uooo tronofor ond fluid flow through porouo uodio hovo workod only uith pockod hodo cowriood of tiny ophoriool portioloo. Io chrouotomphy. honour. tho ohopo of tho ”chin. uotoriol uouolly qloyod io highly irrogulor (nicrophotogropho of too of thooo uotorioio. octivotod corhon ond diotouocoouo oorth. onoor in tho Appondix oo Intro 1-! ond I-II. roopootivoly). For thio roooou o otudy of tho offoct of porticlo ohopo on fluid flowing through o puckod hod uoo initiotod. -1- 1'11. if i--.‘ l I .6 ' )3”; ..'\ J - . (a c. . ...4 n 73'. \ v.16: l" l . w .“ uO. ‘ 1 3‘1 ‘3 r‘ r ’5) .r -2... An invuotiption of thio noturo io nocoooorily onpiricol. That in. tho nth-otiu doocrihing oxiol dioporoion in fluid flan through o column fillod uith on W); ohopod pooling uotoriol io outficiontly couplicotod thot tho prohlou hoo not hoon oolvod. Hanover. o quolitotivo thooroticoi diocuooion will ho prooontod. o ‘Io O ‘l‘¢ u . {Sui - 6 I: ‘- 1. .st¢ . .. ‘J.:J , Q lit: $4.0 ' D u. IIIOIIIICALFDISCUSSION 0! THE YRGBLEH A ‘ T o. It io firot noooooory to prooont tho nothonotiool trootnont o! oniol dioporoion in plug tin through o pockod hod. I «:9‘ Tho oocond ooction .1 thio dioouooion will dool with tho nixing 1.10 coll nodol o! dioporoion in pockod hodo. Although othor thoorioo howo prowod oquolly oopohlo in onploining thio phonouonou. tho nixing coll nodol io oopociolly onnwoniont !or tho quolitotiwo prooontotion giwon holow. A lottor portion 0! thio oootion will oonoidor tho thoorotiool offoot o! porticlo ohopo ‘5. tho oniol dioporoiou in pookod hod‘o. o n' 1o a - Dionroig in o Hon-I-odogrhigg g5 Conoidor o poolod .“.. «ah-mud o! d Ion-odoorhing notoriol. um oonoontrotion nooouriog dowicoo loootod ot x. ond 11 (Figuro l). ‘o "1 _L l T T ad :1... .‘Ibl\ ‘* w “rigoro T. i flogron of Bud .*::',‘:‘L 7.: lolwoot io continuouoly flowing through tho hod with o woluotric 5": tIn onto ‘1. A poloo o! trooor oolutiou to injootod into tho colnn upotroon u-O !ron x. ood ollowod to polo through tho bod. Aooooiotod with tho pockod 1:. I I & oootiou in on oniol dioporoion coo!!ioiont. D. .t‘!(¢-«( -. -3... . < H! “ ' ‘l '. . .| a A . . .1 . . - -_ . . —. .. .‘ .i A . . o I ‘ . ’ - ' . . ,‘ , ’ .. ., - _,,. ‘ .4 ‘ . -. ‘ ... l 4.5 J I -' ‘ o . ' . ._ . , (a , . - I . ‘ - \ #4 .‘ ‘2: HI, .._ ‘ 1 _ I l ‘ ' ~ ‘ $ 7 , . Y - v, . v - . .. o ._ . ,-‘ - _, . . « ‘ o . - . ‘ _ r .1 \x H.-‘ ’u‘ . " ‘.’- {in I 7 n v , g o ‘ ~ g _ - , n 7 . ‘ ‘ H; ~, 'V o ' ' A * ' o'- -v\» _v.--‘ c “-t " 'oU ‘) 1.3". ~ A p ‘ Io o h . o ' ' - ' . ~ ' I ‘ " ' s " - ' I ‘ . - 1‘ - o . J’ I. ' ’ ‘_. , , ' . Hid}, 'j \ .J .3 .t J' “I. '4 n.) . o.‘.s t-“ o V . .. v I - ‘ 0 l I' ' A o‘o- ,- 4 . . I ' ' - 3 ' -— a > I— ' :3 t . t.‘ .1 J 4- ‘Offll 3b k 40.} o. i a ' 4_.1"\I 1 J I O t , , . t- . ' .. f-u ’. D v.1. -0 on- o '— .. - ' ' ‘ ‘ ' ' " Y ‘ q.“ ' n- '1'.» " r I? {“1 J"; 3 ': s~ I ‘ - ' r" - o- -- ‘ r--\ _ . V \ l 5;; '. o , " , , . .(- . - . - . = ' ’- - o “H : -, “I. l I.) no I ‘ p ‘ g .. , I ,J. r. -. w,-PL,'.;~' -_2 .. OJ H23 I . I ‘ t l--1U~.-' ’ 7- w .t , \ -‘ I a ._ 2 > a“ ' t r . '.. o. ' ' « l s l w '0‘" . ‘ "' o \ - ‘ 1'} o , - ?'.,. oz}; -. J-. ".‘510 ia—a . ' q 1- u' oils slow uLJ ‘ c I! .— 0r I pol. ‘ (u L , ”3 {r u .. . n - ‘ . o a- g o .‘ -oo—~—._—..—-.—< + V l"'w 1.4;. . - - o. - - _ ..- - . . ,- on .— on -- V ' r ' ‘ I } "‘ ' - 2 7- . J. C ' ‘. . - l 0 1 - u I: Q ‘ . r "'-‘.". In - r *7 w r.‘ ,' «r y \‘g I:' I ~' ‘ g '; ~* I (. I~ r '- fur-s - J I." ’8 v ‘. "‘u." '3 .1 ' i . 1 '7 . . .4 ' ‘ ‘, . I I‘ J- { O 4‘ " 'm‘) o - - - ‘ . , . o ‘. o- I _.I . . f'gl “- l ‘ *4 , i I | ,“ -' . l "o‘ a. I!)(, o O ’ - n P r. r ‘ ‘ , , .p 0” ‘ ,. ' g a. ' .5- .. '2‘ ‘_ . U ‘ , . ' lo , 3 g’ . . . ,. C. -.. - “ 2., -' . l._v .‘. ‘...) ‘ _‘ Id 1.: ~~s’..- ..1." - . o , J — ,. ‘.- -A r- v .‘ . . IV . I _. o g i I _.‘ ‘o I.’ ' r 4.”. ‘ Fir) l'z .4- Itto ooeooooty to out-o: 1. Tho trooor 1o tuoetod uniformly oorou tho bod. ' " 2; Tho flow is {uniform ovox .tho ctou‘ooctton’ of tho bod. 3. Tho-mt of mo troutot by dioporotoo 1o proporttoool to 39 ax c to tho ovotogo onuntrottoo of trooot ocrooo o oocttoo of tho calm; tho nu: mutation pullout. m mutton «touting tut ohm 1o ohtotood (too o ootortol boloooo o! tutor on on toot-”ootol load of pond bod (than 11): wc + + wc .. 3.9. 3.9 m,.ax " 1 " "nix x... , . ,.x~+u ngooou. Imam-toil“ 233 1.2.;29. u, “2 pa 1: D}: .‘...‘.. ”g..g.m’...m*;.;;,u. t-ttu . ' t I! void faction of bod A O trooo ooctioool oroo of «1m mama emuuo- oro: ' I o-ovhoot-olotx>x otXI-X‘ COCO“) tott>o otx--C(t)'£1n1tofort>o Halo” hot upon thot ZtAD ”I . o . :5 a ‘ »| ,- p‘ I ‘u-‘ ‘0 .n , ‘ ' o 7 A -‘- o\‘ . . 3- 1-3, .{c : ’3. vi \ 1 I J 1 ‘b V 1' .' l‘. ? r f 4- ”I n (—0 k. I II. J :3 i (’2‘, 8 | If i. J ”‘ g ‘ J R '5 L !o" I’ I .4‘ A. :3 f. I. f ‘7’ ‘3 ,5... It.- . ‘ L'XI-Xo ' (3) II." Ihoro t it o uooouro of tho oprood of tho poloo duo to oxiol dioporoion ond io Minot! ont . (112* a , p ....._................l 0’ ' <4) 1. ._ “)2 . _ oi it tho tint miuco of tho tonoontrotioo ot x1 and 3‘ to tho noon ti-o coocootxotioo ot I“ _ P . No.1: otfoct. ototoo thot tho oprood duo to dioporoioo io proportion]. to tho oxiol ditpotoioo ooofficiont. Thi- nodol it hoood oo now-in. plug flow with oxiol diopotoion. hon it tho nu dooo oot opproniloto plug flow. it it ooouod that thooo nigh-rum m otcountod for by tho oxiol dioporoion coofficiont. ’ toy pooh-o too. of may. in «myriad of o "riot oi rota-1y «intuyousoyoooo; tho-o void-totally rota-rod to u m «11-. onwothimohoodool oiooiu .m.. itvilluhttomioot to con-id“- o to].- mull' 0! onion ton- ot-mtoxiatoly. ”minim. lhofllldpuotllw mm to union: Woo-sly litigant]. M-“ um ”III-Ilka coo void to «othor. tho mu of tino o sm,mu u ”not 1. tho i"? m «u u dofiood to tho rooioooco tioo lot thot portieulor void ond it doootod by 0‘. for tho oooo oi piston no! thtoooh tho bod vith pottoot lino; in ouch-ton 61.92-...'61-....9n.m0mt * (S) 4).} in. u I {:11 WW) 11"":; ;) {\ .5... m: to. tho midnnco tint for oooh void in o amount. bio oitxotiat Infill. tho oboonco o! hook and forward fixing, to in ofloct for n-NI,tho diopotoiooiooono.‘ . ~ ,. e 1.. Hum ”111. W unouuotpmm. tho W'fll malt-ltd; ”nut to. («thou-oofoo-poaod. ant-cm fixod mm 4W Ionhl‘bo infinito. can“? u. upmod mm mu an «MM-u tho mm and I. In to W to nfinonoto thoo‘ thooo moist-onto afiid only “M 5‘. m porfoct 1181!. 8.11. with mmt mid.“ til... it mtm M m fill! “minutol Cu? ‘ 9"Okmlik, (or in gonotoI. ond o touch-co tint diottihntioo “rude-J x. thiofi diotrihotion hoe-nu .‘m pronouncod {tho moot of intorcoiinlor fixing. ‘ ~ond contoqoootly. tho dinoroion. inttooooi." his. oitnotion it mini crootod vhon intro- mmn um“; «flaw. u‘. m.“ - -‘ ; ‘ ' ‘ ' " ' Tho' tor-Toning officioncy it ”1.5.4” no. on indinotion‘ of tho dogroo 'of an... occurring within o void opooo. Tho fixing officionoy. z. u o noxiou- ihon porioct‘ fixing in ptooont." Cioorly.' thou, tho' coll fixing offloionoy “in mm; Emotion of tho coil in. on! io diroctly tolotod to fluid turhuionco." Sooo'oooooto of tho tolotivo ton oiooo' at two or ‘ loin pockod hodo on ho ohtoinod hy “Bria. tho void froction of tho ”china. 'M'&$ohm will thon. in offoct, ho ditoctly rolotod to tho is. ma ftoetion.‘ " “:Tnthnlonto viii ho oono‘ cooplox function of tho fluid voiocitioo ond‘ yolooity' grodionto fithio tho bod.” Unliho tho volocity‘ gtodionto tho flfid‘ volooitioo con «molly homolo‘ooly opprofiootod by tho ovotog‘o ' ‘41. 1.51 L’ .. ._ law- ;‘&i£ a VI too 3., .. “-- i) -7- intototitiol velocity through tho column. Volocity grodionto con only ho obtoinod it tho flow profilo through tho bed in known. Such o profilo in not ovoilohlo oinco ouch o nothonnticol nulynio nonld toquiro o ptocioo doocription of on orbitrorily ohopod porticlo. Bovovor. it in poooiblo to diocuoo tho chorhctotiotico of flow ohont o oinglo inogulor particlo tolotivo to thot é: o ophoro. Tho otroohliuo a: flour oronnd o othoto'oto than in Figaro III.5 Signiiicont Volodity grodionto con only ho ionnd on otroonlinoo noon tho ourfoco of tho oplhoro. .‘l ‘ Figaro IV in o oinilor droning oi otroonlinoo ohont o non-oyhoricol porticlo. fio notoll oiioct oi tho ittognlot pntticlo on tho fluid in oooontiolly 'tho oono on thot of tho ophoro. Bonnvot, noor tho ontfoco of tho porticlo thorn in o ouhotontiol incroooo in tho onount oi otognont ilnid pronont. thin in prinotily nonood hy ontioco otockn. toggod odgoo. ond projoctiono iron tho porticlo. It in oloo poooihlo thot tho tnthnlonco donoottoon iron tho itrognlot ”melon would to oonuhot grootor thon tho I ‘ n-—~ turhnlnoo ountod by tho ophoro. I If tho offoct of tho inctooood onount of otoguont fluid prodoninotoo, in o pochod bod thoro fill ho loot turbnlonco in tho voido nodo by ittognlot porticloo than in tho void collo crootod by ophoroo. Conooquontly, thorn in loot fining within onoh inogulnt colL Ao diocnoood ptnviouoly. thin tonnlth in o broodoning of tho tooidonco tino diotrihntion to: tho n fixing oollo within tho hod. mimroll ofioct in on incroooo in tho ononnt of intoroollnlor fining ond io ohootvod onporinontolly on on incroooo in tho dioporoion cooitidiont. lhio it two oinco fixing. ond than dioporoion. in tho nixing coll nodol it rolotod to tho dioporoion oooiiiciont in tho dioporoion nodol. ... . .. ‘. ‘ . ...o o . halt W. A P. .I.» v... in o . . . . Co a on o . x o .3. u ‘ i s . o . . . ”I V Y .(n. ‘ . p x .... .oa I‘ a . a o \ . . o r u f ‘. v v r , p ‘ o. . of. o a . o. J k . . o. v , A . f . ; . a v n . r 1 .f I . v. 4 o t ‘9 t. . 1. I . . 1.. I. .. . n I .o. n A . . t A . . t C o . . .l o \ 1 / ‘o \ . I l . o A . 1 . , ‘ . r o . o ’h o w n on.. . o a . i t A l v w e .f . f ‘o- to ,. ‘ o , . . _ 1 fl . . V I I o ' .. . . ... .I II I. . » oi . v I. u. A or I u o' . .4 .l _ L V A h 93an < 925.2 30.3 .HHH ounwfim oauwuumm unannouuH an unon< 30am .>H ounwwm vosam unmawmum m -10- Convorooly. if tho incrooood turbulenco it onto oignificont thon tho oxtrn otognont fluid. tho dioportion coefficient for o bed of irregular porticlon will ho loot thon thot for o bod of ophoreo. Thot in, tho oddod ogitotion'nithin o nixing coll producoo o grootor introcollulor mixing officioncy conning loot intorcollulor or bulk mixing. and conooquontly o onnllor diopornion coofficiont. ,. \I.Q. IL A o l‘v‘o EXPERIMENTAL METHOD Q _,,,,_'1'ho opporotuo hood for thio onporinoototion couoiotod of o ono-holt inch dionotor glooo colon. o prooouritod flow oyoton. ond two conductivity 1 . . _ collo which. togothor‘vith on outonotic rocordor, nooourod trncor _ I _ . concoutrntion ‘vorouo 'tino. § ; : i Tho flow Iyoton (Figaro V) 'i'ho mlunn no on 18-inch longth of {longed pyrox pipo. Ono- .Quot‘tor inch task-in; not nood to connoet tho rotor nnd trncor oupply tonko to thd_colunn. A golvoniood otool took woo uood to otoro tho rotor nhilo tho trout oolution not hot in o otoinlooo otool mool. Nitrogon not uood to nointoin pronouro throughout tho oyoton. now rotor voro odjuotod uoing o gfioronotor volvo locotod on tho doonotroon oido of tho colunn. i Coinductiflg Collo (Figuro VI) 3 Conductivity collo idonticol to thooo dooignod by Howloy6 noro ohhyd.‘ Tho coll woo nochinod iron ploxiglooo to tho opocificotiono in- diontod in Fignro VI. Tho niro not no. 25 plotinun viro. It won oloo nocoooory to ploco o onoll circulor ooction of filter cloth our tho coll to provont tho potting notoriol iron ontoring tho nooouring dovico. -11- i. I. .' “j a n '- o no 1. F o o ‘i ., . _" I l l I 4 “I J» ' u .. .-- . .- .. h . -I 1‘ i - fl” “1.: J .7 ‘1 3‘ i M ~ ‘ fr - ‘ - I. V ‘ P 3 - "r ‘9 J -‘ Y ‘9 'r. 1.} o " . I. ‘: 'q ' .' -J L'; i .J-‘a v. .. . ' , . g‘ a _. .. A ('7 loJ.'.l'~ . o. x ‘ ~’-’ "0 '..: ‘I ‘5 . 0 ‘¢‘) .'-.-3' “3... . " 9". - ~'- . J 31.1.1.3 LL .,. .5n", rJ -- {.-. 1'." .‘ .;~~' ‘LLC‘J ' «‘ 0 rr' 'vw ' -.o ,3, ‘ f 'r ' t '— - (‘3' 5-: A. I‘. {5 ) I - v I ‘. . f‘ .1. ' . :- _ _ ,t ,. . r . '3 .1: 1 Ho‘ :1. o .. fl'on ; .' .l‘ ‘ f9't. ... ; 1 ’- ' x s ‘ ., . I - ‘ ‘ “I .7 j ‘nrr .... i a ‘i ~vf (I ‘ ‘ - o o .. }. up" .’ 'o. .. to or; A ’o.‘ ~-o".l. ..I. , -._o ~ , 5‘ ”.7 .-‘ ‘2: .... f L “as. g A .5. .‘ .--_2 1'3. J :J - ’. 4 \ I o - o .. , - n o h In : ' I ' r 2 Lu W “‘3 31: ‘ 0 I ’1". .‘ .. 3 "‘ t I '3 .. 1-1-11 EofisgPH-Tzi filo. :r. »» ? 03 : P - ‘~ . t ' 3.. ‘K‘ \o I on C r. an. r... : 73.x .~5., 1.. Sufi t’ I 3 .I..- Put)! J 1.1 Po ‘ - "" . r ‘W .. o $ " '\ “ o 1 nj no; .0. I ‘P .. — .1 ' h " ...! ‘ ‘-.‘ .1 . ~ .. . ' . . - ‘. .- .. " 3.3 ’ u I 3": .r'} v.21 4'; ' ”5.. .2.'.‘.‘ ." t . “ r - T 7 7 r . - r - - °. .-..~, i . 537 .J'IJ i .9.) ‘.o i .... “ ?".":I ) ; ' Tv‘ ‘ )" a I’ g. > u u 3), ‘I' a, 5-5.‘ -. «on a J. J ~3F“.' J ‘ ‘7 ; .’-L' ‘3"; \.J 1", ‘ ._ i' ‘ .‘ - :-o I. I“. I to 1“ o n “D T h v' .1 4' . ‘ i -. I ’ (i ‘ 1 ‘- l ‘o ‘ - n‘ s-O‘ - 7 ‘ ‘1‘ or .-.‘ - h R I .‘ ,' ’ it ‘ ; ,. ') S .. 4 g u‘o’rJ J‘Q‘Jd. I .,~ l. I... or. .‘* 9“,; .'L‘ J '31. A. [Lt-‘-.--'.:1 [\A W $2: . \ a] — A \\ \\\ \ § Rm ._____J. Water Supply Tracer Supply Tank 7 Tank E: I Nitrogen Pressure Cell 1 Nitrogen Pressure Packing 44 Cell 2 ’1"! " Micrometer Figure V. Schematic of Flow System -12- Plexiglass - - - -—»- - Wire lad ‘ ‘1" a . I Figure VI. Conductivity Cell -13- -14- Tracsr Solution An aqueous sodiun chloride solution.was chosen as a tracer since NeCl concentrations can be readily determined by electrolytic conductance. Also. the specific conductance of aodiun chloride is proportional to its concentration in the range of 0 to 700 parts per million.6 Tracer concentra- tions for this ears were approximately 0.5 g./1. or about 500 parts per nillion. ' Per a concentration of 0.5 eel/l. at 30.0 the soleculer diffusivity -5 7 I)' is 1.84 a lo cal/sec. flgggggigg and Recording Apparatus (Figures VII e Vlll) In order to neasurs and record the tracer concentration as a function.o£ ties the circuitry designed by Hawley.6 and shown in Figure VII one used. _ The voltage drop across resistor R is proportional to the reciprocal of the cell resistance lo’ and is given by r - I x (7) uhers I - w/(R‘I l R) (8) 'nm.huau1peaubemch1mmrc so that nave/ac . (9) 4. .leth V's-d I are constant so I is then proportional to like for new. ' the voltage was supplied by a variable frequency audio oscillator. The.A.C. voltage across l.eas than saplified, rectified, and eessured with a u. erl. .1. .i. a e - e uw>auonvaoo pom ufisouao Houauuooam mo owumamnom .HH> enough _ umvuooom . — umemfiuumm can umnmnaaa< . <<< noun-Houmo oaoa< \/\/\/\ JLo/ souosm -l6- uwsouflo wafimmama< mthMHuuom mo owunaonom .HHH> ounmwm > oom+ .U.> ”.9 n u Po.- 8. m M h...» Tllla V: 5 m E ...-N. , F u a a a .2 2 m. \<<(~ J . H Pc- 8. o- 02 H - a PE 8. V- 2.. — -17- unma mumumamfla anaflxmz Hwnvm auwa meoHuHmm nodaaamman mounh .NH ouamfim KGB. -13- g 4.9- J exposed to the flaring nediun. Consequently. it was decided to calculate .H a. ..p... ....— an effective particle disaster uhich was defined as the diameter a sphere would need to possess the some surface area as the irregular particle. A bad of spheres with disasters equal to the affective diameter (d ) would effec than have a total surface area identical to that of the bed of irregular particles. ' Detersination of the effective diameter was facilitated by the ’ 2 if Illshe-xssaay relationship: .2 150vu-(1-o2 d .. .3- A! a gc l . a ! shore :d.- disaster. feet (10) v. - flee nets of liquid through bed. ft/hr. . L I length of bed. feet u,- viscosity of fleeing radius» lb/ft.hr. a - void fraction of bed or - pressure drop across bed. lb/ft.2 g' 0 gravitational constant. lb force ft/lb. uses see.2 This equation relates particle surface area to the pressure drop across the packed bed. Since Equation (10) assuees the packing particles are spherical, the effective particle disaster is obtained directly. That is ' 2 2 a - (a an effec) a.schenatic disgras of the apparatus necessary for this deter-ina- tioa is depicted in Figure 1. .As before eater ves needles the flaring sediuakand nitrogen was eaployed to pressurize the system. L +33 . . Iv A , , - _ . A . - I ..r. ’ t..---._.' - a' I \ . I o, 1' " pl . h‘ / ' - I L9 - .. ..s\..-r - . . e g. , . , .. ..... _ . . . u u , , o. g _‘ o l . i J ‘, t .1 I b4~ l - i l .‘n '00 L \ I ‘ o a ' “‘., e e x J , ' ' I - ‘ 5 s ... , ' ' | ~ -~p‘r ’; , ~ . - . - . 1 at .4.“- 8 f a I ‘ '. " . — I -’ J .l ' -‘ a ..s.a ‘ . '..l . a ‘ \ , - . - ‘ ' g " :‘.. v. l ‘ ' ' ‘ 3 I b .'. 3 ' I C ' - ~ , -.. - 3. ,J r - _. U e ‘ ‘u ‘.a_ ' ‘ 4“: ‘ r s l ‘1 ‘ t s. b I .o ' J A a a v o ‘ . ‘ .' ‘ e ..O“ ' \JJ L 'I . .J O . . _ :_ ' . ~ v.1 .. ~ . . .s.‘ 1-... , .‘ ,. . _. _. ) 4 7.9 t I —o I ’~ ' ’ . t .J...’ ..; “V a ' -..- o -:J.-)--4( .1 . ‘ 'a‘ . v "s h ‘ A ' ‘9 - 1 J V'f‘o'fl' :3, , . .2.’ I. (1 . " 7 . -'. "f '_ g t' ‘I . .. ....-- a .) h *7 ,.>--: 5‘ {a .. r’oe). .l..'4 ” .. . A} h l 11‘." ..' c 3 O sf 'rl -, r f. Li w. ' t a ' '1 ) a . V __ . '4 ‘ .- ‘s. .‘a {OUi,-‘ ‘3 f.9.n. . v ‘ i. . .-l _e-I- .s..: e . 1‘ . ‘ I . ' .p . 1 I . In. ‘ f.’ r a , .J I ' .3 T‘r J I. ->l a! \ I. O . ' l s - ' V V - t _. 5;.- JG. ‘3 4 . as, '7 .._ . '1 f' ..i .I . 3 . ‘ -- C- .eJ JlJ : . ' .1“ .s. HR .1: ' h: ___J. Water Supply Tank ,___'_- Nitrogen Pressure Packing A Micrometer valve U-Tube Manometer U Figure X. Schematic of Equipment to Measure Pressure Drop -20- ' -21- 2951;. noceduro for'effective operation.it use essential that the column be free of trapped air and unpacked channels. Air cntrsppment was eliminated by slurrying the packing netsrial in.weter and channeling was prevented by vibrating the colunn as it was filled. In addition, each portion of the column‘wes filled with water before packing was initiated. After the button section was satisfactorily packed a conductivity cell. together with ito filter cloth cover, was fastened between the top of this portion and the bottoa of the neat. Having repeated the above procedure for the second.segnent of the colunn. the third and uppermost section'wes packed to a height of two»inches above the top conductivity cell. finally; a einculas piece of 60*nesh screen. which served as a liquid distributor. was placed on top of the bed. 9" K. .. - a . a ... L w. Ia‘ .‘ Distilled water was permitted to flow through the bed until constant ssro readings were obtained from each conductivity cell. The water level wen then.sllened to drop to the top of the bed. at which point the flow‘wes '.!£.1.. stopped by closing the nicrsneter valve. A pulse of tracer solution. which wee carefully introduced into the colunn. was allowed to enter the bed by regulating the liquid flow rate. The water supply and nicronster valves were than.opened to obtain flhe desired rate of flow through the bed. As the tracer passed through the column conductance versus tine ' b ‘nessuroeents were recorded fron.both cells. To insure that conductance ‘l ‘. was proportionel to the scale readings resistance versus recorder readings were obtained prior to and after each run. ..- I‘LJ .‘ 0.1 [1‘ e I. ,7 :5') I 5% .1“ .v ‘. -s er. J; [I in) t L.) Leilijzi 4"} I‘ V.’ )3 I a. J I 1 ”'0 'r '1' -. -21- lcula e fiicient Barley6 showed that the dispersion coefficient D could be calculated iron the relation 2‘ 2 G - G 2 f 12 " 373 (12) ("2 " "1) where u is the interstitial velocity . un - I. c: dt I 1': ca: (13) ai’. /: C(t - H‘)2 dt I f: Cdt n ' 1,2 (14) The subscripts l and 1 refer to the upper and lower conductivity cells respectively. lunatical solutions to the above interrels were obtained through the use of sispsoe’s Rule and a Control Data Corporation 3600 Digital Computer. The oeeputer input consisted of scale readings obtained tron the recorder chart at equally spaced ties increnants. The values used were sisply the actual seals readings sinus the sero point. lines corrected scale readings were proportional to tracer concentration they could be used in place of c in Equations 13 and 1‘. Also. newlsy‘ reported that since a: was independent of the reference tine utilised the ties could be considered as sero at the‘beginnin; of each cell. the ties between the beginning a! the two neeaurinp points was noted. however. and.added ts u2 for the final ealculstiss of D. -. ...—.... VI) ‘ n . ,r. ..... o e . r. .l . .- . I. . a. n .4 .... 11 \U .. el \e «N. we. I‘ ,l: . A» ., I a 4 0. 4 i t ..’A re 1 ‘J ~23- ‘l‘he interstitial velocity was calculated using 0 - LI ("1 - "2) ' (15) .‘ q - i i I 1 The conductance versus tins neasunsaents for a typifil enperinental run are plotted in Figure 11. ; .i‘)' ,..e N van H mHHou How mo>u=u mafia m> doaumuunmuaoo Houamha mag .HN ouowfim 1101391 QUBDUOO 924- PRESENTATION OF DATA a t etho It has been reported that for fluid flow in a packed bed a log-leg plat of DID' versus ‘c ulD' should be a straight line. this is due to the sinilsritiee in the relationships for the eddy diffusivity tor turbulent 1! flow. and the asial diffusivity i'or mm: new.“ in a tube (locations loendm. n - 3.7 at u 5' < (16) n . d: «2/192 0 (17) where v - resistance coefficient d. C tube disaster To facilitate proper data correlation (or thelpecksd oslunn it was necessen ts substitute {our tines the hydraulic radius (er the tube disaster. than. for a nu m with m... d‘ '."‘ -35 75-? an“ (18) It is correct to use the hydraulic radius for spheres since “.11.: is calculated with the mass that the packing particles are spherical. ‘a plot of leg DID 'vursua leg Elie/Dv is depicted in tigers 12 for thedateebtaiaed iraathisisvestiaaties- rues-seasontbadeta reported. by Baulay‘ are also presented on this graph. In.eddition. a plot oi is. D versus log u for the seas sets of data. is presented in Figure llllt -25- ... -‘ - e . ~ I a ‘ e' ..a "‘ s “ ‘3\‘4 Y - a I , l c.“ r. ~ ., -7 ~ _.. , . a f. r n I . '05 is . v '4 n . - ' b ‘7 ‘ _-.4. ' " rel f" .L-« -i'.,e. 'c. .31 - 3 - ' . ‘ 1‘ y . - .. .I l' o' .) ‘i‘i‘n ‘ .' 11" a a '- s § . I w A. 4 : x.) t-duj . ' .. r J . v r 0-. . ..n I ‘- J- 1 lurk! p» ..- . a e 3 ‘ ‘ -O ' - Q n i 1 ‘ a 3 -- 2 ,, v fi 7 v v Q ‘ . ‘ "'I 's ‘f 3 1 1‘ I A v -v " .1 .- . ' :- I h ‘ u , s . p. .' ‘ i ‘ i . I l . .J ’ n}- . . I ' I ' 1 . J .'/-'_' p L J i‘ a _. . , ,- .. .. ._ '. - {J's - 4-’ I i'e‘ ... ,4 . fi' ., , L . ’ J A - “a e ...... Q/Dh mumwo chance [0 ' ":3.ml'r_ 1 X I Curls-e 3 2 (Mu/Dv Figure XII. AM'u/Dv -25- 2 3 4 ll Logarithmic, 3 1" 3. Cycles 5 6 7-89fb Figure XIII . Z 3 4 5678fi60 u, ft./hr. Diapersion vs Fluid Velocity -27- Z 3 4 ° ° ’ io‘bb’ .2 8.. leculgtion 2f the Effectizg Particle Diameter The apparatus used for this determination was designed and built by D. users. a Graduate Assistant at Michigan State University. The results obtained are presented in Table I. As shown. the value of d was found to be 0.00491 in. This was effec very close to the disaster of the spherical beads (0.00416 in.) used by havlq.‘ Disggggigg of the Digpgggigg Coefficient D55. The data collected for this study can be found in Table II. figure XIII shows a significant increase in the dispersion coefficient for the irregularly shaped particles coapsrsd to the spherical beads. The actual difference is the diffusivities is soaowhst greater than shows since the userspboricsl particles have slightly ssallsr disasters than the spheres. That is. the diffusivity usually decreases with disinishing particle sise. This increase in.ths diffusion coefficient is substantiated in tigers :11. This graph takes particle diastsr. and packing void fraction into consideration and it has been reported that the data for sinilsrly shaped particlse of varying eiss should fall on one straight line.‘ It is inortsnt to note. however, that these results do not con-- clusively answer the question regarding stagnant and turbulent fluid presented is the theoretical discussion. One reason for this is the possibility that the proper date correlation ssthods have not been considered. lot eaaspls. the concept of the effective particle disaster used in this work. has not been derived free a theoretical consideration of the probles uador investigation. It is therefore conceivable that sass other. sore a.‘ 's r... e . 'e. I . a- n .3 a .. ‘0 o .u e . lo‘ a . xvi . .. n .7 ... .. 7 . I: a . I ... rm 3 . ‘- I a d o. r? l\ -29- appropriate. neasure of particle size should be employed. Pressure Drop. A! Flow Rate, V vs,” o a-.~s.u~.un a» U~N H ‘g 10 11 M; : EILLnin. A ; admin. in. fig, ’19.1“ i i '37.0 1.93 18.9 f 97.2 1.97 17.3 35.0 2.02 17.3 . 34.7 2.00 12.0 23.0 1.92 'H12.0 I 24.5 2.09 12.0 24.0 2.00 "11.3 "22.3 1.93 ".7.0 .1 13.: 1.93 6.9 14.4 2.09 ,5.2 10.1 1.94 (V./“)." .'1e99‘.1e/.13e 111. “go mu 1. ' "-Iffsetive tarticls Disaster Data 1... g... (7 P's .322 n - £1.10“, 1 0.533 2 0.630 3 ’0.350 A 0.075 3 0.213 s . .9»2°‘: 7 0.0333 3 0.0532 9 0.0553 10 0.0230 11 0.0211 12 0.0193 13 0.0099 2131: 11. g "’ ft./ht. ' 112.0 91.3 39.3 37.3 . 46.5 ,23.31 16.5 11.8 9.03 5.54 5.08 0.00 1.95 0/0' 7080 8900 .4990 6660 3060 23.6 1170 788 777 393 296 278 139 Dispersion Coefficient Data bun/nv 355 289 (280 278 107 75.0 52.3 37.0 29.9 17.5 16.1 12.7 0.18 ..IQ .1» . U I.) , . PH 0 . . 1- A ... . .. ..\b a .s. .l‘, ~ '.75 \. v a * . _ 7‘1. ' o ‘ s I I /. a ,1 i .. nth v.74 DI!“ ’ . .9. n O 0 If I.“ .n . n. 9 ~ 1 p; U. , 1) flu. 2 O O 1 \. . . .. . at r . s a . L . 0 (j P... PIL ' . a" I. CONCLUSIONS for flow rates between one and one-hundred feet per hour. the axial dispersion in.a packed bed is affected by the shape of the packing particles. More specifically. for particles with disasters of order of asgnitudo 10" 1... the diffusivity incrsasos as the shape of the packing asterial beceaos aere randoa. -31- ..,. it u. 1': 1 r) . . I I ‘ . O .7.) .. .wn mum}: nous I-l. hisrephosegrnph of Activated carbon tartiolee 0.". o — . 9' ,Ic’o, ..— ... \ V-"I . 'I a“ 'ijfjg’éiw “a? ....”z'. 2",. ._ *‘fi'ffg‘ .7,‘ J o' . 1 ,.-.- 24-2,“ #:1910105 um 1-111. flicrophotograph of spherical Particles ...”- ‘ 0 nm 1-“. Ricrephotegraph of Irregular Particles 1. 2. 3. ‘o 5. 6. 7. 9. 10. 11. 13. 1‘. BIBLIOGRAPHY Aria, 3.. and Ammdson. H. D... A.I.Ch.E. Journal, 1, 280, 1957. bird. I. 3.. et.al.. Transport Phenomena, John Wiley and Sons. Inc., has York. 199. 1960. “”W. Jo Jo. AeIeCheEe Joumlg 3. 13M, 1958e Carbsrry. J. J.. and Bretton, R. 3., A.I.Ch.E. Journal, 5., 367, 1958. lshinsai. 8., Principles of Fluid Mechanics, Allyn and Bacon, Inc., Boston. 291. 1962. ' Haley. Ii. 0., Solute Dispersion in Liquid-Solid Chrmstogrgghic £91m Doctoral Dissertation. Michigan State University. 1964. International Critical Tables. McGraw-Hill Book Co.. Inc.. Ncw York. Jacques, 0.. and Verneulcn. 1., Mudiml Dispersion in Solvent Erection Columns: Peclot Numbers for Ordcrcd and Random Packigfig. University of California, Berkeley. USAEC, 1957. Ira-era. 11., and Alberda, 6., Chen. Eng. 301.. _2_. 173, 1953. bIcHenry. K. 9.. and Wilhelm, R. 3.. A.I.Ch.E. Journal. _j3_, 83, 1957. Prausnits. J. 14., A.1.Ch.E. Journal, 3, 14M, l958. loner. 1.. et. a1... 1. and 8.0. Fund" _1_, 287, 1952. Taylor. 0. 1.. Proc. Roy. Soc., £1333, 446, 1954. Taylor. 0. 1., Proc. Roy. Soc.. 1219, 186, 1953. -33- . p O Y; _ Y9 ... . .. I I a .. .a. . o‘ ' ‘9 ...f s ...... ... r1 u . ‘ l‘ .u IL 0 \ I. U . .‘ he :1 e 'gvfs s s‘p I“ [vi ‘ \|H|\\\\\|\\\\||\“INN|\\\||\\\\|\\|\N\\|\\\||\\\H\|H\| 31293003836