Conclusions
From consideration of the spatial distribution of equalsized particles in a randomly dispersed and 10 ryere derived for determining th sample required to observe the bulk mean volume fraction of a dispersed component with a prescribed degree of reliability. Two examples are preseiited, one of which deals with the particle size diutributioii analysis. I n the case of the particle size-weight frequency distribution anal> size must be determined for the maximum-sized particle ase of the particle size-number frequency it must be determined for the ininimumsized paiticle groul). The spatial distribution is also discussed in a randomly packed bed of equal-sized spheres and a measure, denoted by DIR in Equations 17 and 18, is introduced to express the degree of irregularity of the random systems. 13y use of the measure a.: a ciiterioii, a r:iiidonily packed bed of equal-qized spheres i* espreawd by a random mixture model of two r e g u l d y packed hy, space rolume ratio of saniple and populat’ion number of times of particle distributions defined in Equation 8 defined in Equation 8 standard deviation, defined in Equation 8 shape factor of particles ( = d 6 for spheres)
References
Bartlett. 31. S.. J . ROT/. Slatist. SOC.Siiml. 4. IS1 (19337). l)avid, F. S . , Bartoil,‘I). E., “Combiti:;t‘oi,ia~Ch:ii;ce,” Chap. 6, p. S.5, Griffin & Co., Londoii, 1962. Fry, T. C., “Probability mid Its J’iigiiieeritig 7T.5es,” Chap. S, p. 20fj, Vaii Yoatraiid, Princetoii, Y.J., 102S. Haiighey, I ) . I’,) Beveridge, G . S.G., Chcm. Eny. Sci. 21, 905 (1966). Leek, L: LI., lleshpaiide, P., Coiiper, J . It,, I N DESG. . CH1.M. FL-xD.\M. 8 , 340 (1969). J I a r c de Chazal, L. E., Hung, Y-C., A.I.Ch.E. J . 14, 169 (196s). JTason, G . , .\‘oticrc 217, 7 3 3 (196‘3). Scott, C;. I)., .\nture 194,936 (1962). Sriiiih, T. K.) J . Fluid .Ilcch. 32, part 1, 203 (196S). I~I:CI;IVI;D for review LIarch 13, I970 ACCI;PTI:LIOctober 29, l 9 i 0
COMMUNlCATlONS
Phase Separation in liquid-Fluidized Beds Macroparticles of differing density, size, and shape were added to fluidized beds composed of water and glass spheres. Extremely sharp phase separation was usually observed between these large particles (“solute”) and the glass spheres (“solvent”); only mixtures containing Fiberglas yarn were partially miscible. Miscibility criteria for phase separation of dissimilar fluidized particles are discussed, and a parameter 2 i s tentatively proposed as a means of correlating the observations.
111 ’
iii
:I recciit lisl)cr \vc rcliortcd d:itn oii the expailsion :ind wit\. of \v:iter-gI:w I m i t l fluidized beds, and succeeded correhtiiig tlicsc 1)roi)crticswith :Lfree-volruiie theory of
tlic liquid state :iplropri:ite t o molecular rn:iterinls haviiig a glass tr:iiisitioii (IIetzler :uid V.illi:inis, 1969). That effort 1v:is originally iiitciided to produce the m:icro~copicaii:ilog of a liquid solvent, for the ii1tini:ite I)urpoxe of ,hnulatiiig polymer solutioiis. This latter I)ortioii of the work eiicouiitered iiit,erestitig 1)li:i-c sclwratioii p1ieiionicn:i ~ v h e n the “polyiner” 1):irticlcs wcrc :itltlctl, :i*rel)ortctl here. Experimental System
The lied, roiitaiiietl iii n glass column 9 inches in diiimeter, ~ ~ ~ i n i p cof~ ~unifoi,ni cd aphrricnl gin+ beads (“solvent Inolcculc~”).13cads 32 to 4 8 i inicronq iii diameter were awil:ihlc. To .inuil:ite polyincr boliitcs, fiber-. of v:irious lengths :iiitl dpii-itich were choseii (Table I ) , Their Sh:ilie duriiig flnid\v:i*
164
Ind. Eng. Chem. Fundam., Vol. 10, No. 1 , 1971
ization was invariablF rodlike, rather thaii coiled, so in this regard the 1)olymer simulation was ruiiuccessful. Fiber coinpositions up to OAy0 by weight of dry bed were tested, the hope beiiig to examine the dilute regime where interactioiis between t,he isolated Polute particle and its eiiviroiinieiit predominate. Phase Separation
Total Immiscibility. Initial tests showed that’ phase separation was P O coninion t h a t it \vas iiot possible, in general, to obtaiii a solution. Saxton (1966) observed a similar immiscibility in bed? containing iiiistures of spherical glass beads of differiiig diameter. 111 general, t h e plictioiiiciioii of 1)xrticlc acgrcgxtiutl iti fluidized beds ia r:ttlier \veil kiiowii>h i t h:i. :il)l):ireiitlyIiOt been bro:itlly studied. In the l ) r r w i t ,tii(ly, the firit :itteiiil)t t o *irnul:ite ii rodlike polyincr utilizetl iiyloii fisliiiig h i e . IIon.ever, liyloii fibers
~)i,civcdto he tot:illy i i n i i i i d d e ill all sizes of glass beads used, over the entire raiige of fluidizing velocities ( L T m l to T h e ~iii:iller-di:iiiieter fibers fluidized :is a sepirate phase be:ids, while thicker fibers siml)ly col1:ipscd :is :I iiiiitted layer on the upper surface of the fluidized heads. 111 the case of iiyloii, then, the deiisity i.; too loiv to permit fluidized niisciliility i i i gl more likely solute, from coiiderntioii of deiisity alone, w:i-: gl:i\> f i l m . ]eiited qualitatively iii :t fliiidizcd-bed ph:iw di:igrani, plottiiig “teniper:iture” against Iiulk cwtipositioii, 7. For these sy.iteni,*, “teinperature” ~ i i u s t b e mtiic sitnplr fuiictioti of cyo> as slioivii 1))- IIetzler anid IT-iI1i:iiiis (1969) :iiitl others-e.g., Pastoii et nl. (1970). We have p r c v i o u ~ l x1v:iiicetl ~~ argiiiiieiit-: tliiit the bed aiinlog t o (IiT) i* 7 . 0 5: n-licrc i is t h e :iverngc void fractioii. Tliu.; the h t l lih:iw i1iagr:ini i i i Fig1u.e 1 plot-: i vs. C.
Figii1.c 1 rc1)wseiits :I systciii Iiavitig both :i l o w r :iiid a11 ul)l)cr coiiwlutr teniper:iture. Aklthougii r e d liquid-liquid systeins of this type :ire iiot c o ~ ~ i ~ ~es:inil)les i o ~ i , :ire kiioivii (Fruticis, 1963). For tlie fluidized bed, thc loi\.-tetn~)cr:it~ire regioii of itiiniiscibility represents case h :iiitl tlic hightemperature regioii case 15, with mi iiiversion of phase 1)ositioii in tlie bed being itnlilied betweeii tlieni. T h e iiiteriiiet1i:itc region of miscibility correq)oiids to C. I t a1)pe:irs t1i:it the 1 0 w - 7 - ~ phn.;e separatioii results 1iriiii:irily froni buoyatit effect-, ~ h i l ethe liigli-I-O separutioii is :i coilsequelice of geonictry (relative size and slinpe of 1):irticles). T o t d l y imlieads) \voulcl have miscible systems: such as nyloii iii t-7nf n i i d i) both iii :i tvio-ph:i>e regioii, :is slioivn iii Figure 1 by :I brokeii line. Iiegartiiiig allape effects, Onxiger (1949) showed tlieoreticall>- tli:it higIi1~-:isyniiiietric 1)urticles niay slio\v pliase separntioti without the presriice of attractive forces, t,lie transition being eiitirely entrollic iii iinture aiid related to volume exclusioii i i i tlic particle vicinity. This has been tnkeii to explniii the pliase sel)arntioii observed in dilute solutioii-: of the rod-like tobacco mosaic virus (.idnmsoii, 196i). Segregation Parameter. Iii the absence of an applicable Ind. Eng. Chem. Fundam., Vol. 10, No. 1 , 1971
165
For systeins having particles of equal density but uiieyrial \-oliinie, z > 1 and the niodel predicts that segregation iiicrr:ise4 with Thih suggest. that glass “iiincroii~olt.ciile~” iii beds of small glass heads will al~vayslie icreasiiig with : i i d that pe enis niny never be niiscil)le when z >> 1. This boriie out iii the 1ire;ciit study, for the iiioiiofilament glass fibers in glass spheres.
ro.
I
Conclusions
Fluidized beds conipo.ed of noiiiiiiiforiii 1):trticalc.: di>i)lay very lirnited iiiiscihility of these liarticle.? in c x l i other. Only iindcr :I iiarrow raiige of coiiditions, dcfitictl by tliffcreiices i i i particle density :iiid voliiriie :is \\ell :is by flriitliziiig velocity, c:iii lioniogeiicity lie :ip~iro;ichecI..I tlirriirotlyii~iii-iic aii:ilug li:ih Iieeii 1irol)osetl :riitl a i i e v pu:iiiicter~ 8, (lefitictl in :iii effort to unify the \-:iricty of (1u:dit:itivr oliserv:it,ioiii. ’l’1ie.c colicelit.: dioultl Ijc :ip1ilic:iI)k t o the delilierate plia-e se1i:iratioii of gr;iiiiil:ir >olitls, which might lie :rcliievcd by careful regulation of C-o. I .o Reduced Temperature,
T
Figure 2. Schematic representation of use of generalized segregation parameter
therniodyiianiic model, it is espedient to generate an empirical measure for fluidized bed miscibility. T h u s \vc a t t e m p t t o f i i i d a generalized .segregation I)aramcter, 8, ivliicli iiiiint be a fuiictioii of re1:itive 1):irticlc (Iriisiticn : t i i d voliinies :uid of iiiterstitial velocit!-, and niii\t :ilso tsl)rcss the observed doniiii:itioii of ( l e n d > - cffec>tsover gcoiiictry effect.: at lon. velucitiea :ind vice verza :it liigli velocities. 1-tilizing dimensioiiless p:ir:iiiieters,
Nomenclature
n
=
c
= =
I) k I,
= =
mf T
=
[ i o!
c‘“= ,)
I
=
T7
=
z
=
GR1:I:K
5’
7
where 8, :iiitl B , m i y coiitaiti properties of the fliiirliziiig ~iirdiiini: \ i d tlie solute coiicentr:itioii. IYIieii 8 iq wfiiriciitly I:irg:c.--;:iy, z > z’-pli:ise sc1)ar:itioii slioiiltl occur, and for 2 < 8’ iiiisd)ility ~lioiiltll i e oli.:erved. Surh :I rel:itioii.:Iiil) is givcii i i i Figure 2 for a 1iiii:rry hybtcin n-11o-c coiiilioiiciits nrr Of utiequul dciisitj- and (&I p l ) < 1, : i t i d wliosc lighter ixirticle> :ire also tlie larger of the two. This W:I> Ixcci-ely tlie c:i*e for mixtures of v:iriiislied Fibergla- y:irii i i i gl:iss be:ids, :is well as 1)l:istic bead.: in glass 1)c:ids. T\vo lirnitiiig c:ises c a n lie considered.
L1:TTIIRS
bed average void fractioii den.;it,y of compoiieiit i scgreg:itioii parameter and its critical value = reduced “temperature” for a fluidized bed
=
e
e:
coefficients iii Equntioii 2 bulk solute coiicentrntioii, weight, per ceiit diameter of sphere; a i i t l fillers I~oltzlnallll’scollitnllt lellgth of fi\,ers miniiiium fluidizing conditioiis t ein1)erature -iipcrficial fluidizing velocity, and its value when particles are carried out of the bed p:ii?icle volume voluii-ic ratio of two solutes
= =
Literature Cited
Adamsoii, A . LV., “ P h y i c d Chemistry of Stirfaces,” Iiiterscieiice, S e y York, 1967. IV., “Liquid-Liqiiid Eyuilibriiim,” Iiiterscieiice, Kew Frailcis, A4. Turk, 1968. IIelzler, G. lt., 1I.Y. thesis, University of California, Berkeley, 100s. Retzler, Itohb, LVillianis, 11.C., ISD. EXG.CHI:\$.FUNDIM. 8, 668 ( l < l f i ! l,\. \ - - -
Otisager, L., Ann. A\-. Y . Acatl. Sci.51, 627 (1949). Saxton, J. .4.,Ph.T>. thesis, Ulliversity of Califoriiia, Berkeley, 1 Of3A
For systems having particles of equal volume (z = l ) , 2 , always has its minimum value B , and the r-tlepeiideiice of 8 is determined by 8, aloiie. If ( L p : p J > 1, then 8, is monotonically increasing with U , and miscibility may iiever occuras for esaniple, in xnisturc; of lend and gin+ licnd.; having equal dinrneters. If ( 4 p / p l ) < I , as for d l the system- studied here, S, is ~nonotoiiicallydecreasing with Co : m I niiscibility m i y lie attniiicd over a Kiveii velocity raiige if B, a i i d B , :ire dficieiitly small. If . I p = 0, then 2 = B, niid ii~iscibility110 longer dcpeiids on L-,,> which is of course iiece.ssary, siiice :ill particles are then it1eiitic:il. 166 Ind. Eng. Chem. Fundam., Vol. 10, No. 1 , 1971
Snxtoii, J. A , , Fittoii, J. B., Yermeuleii, T., A.I.Ch.E. J . 16, 120 (1970).
ROI313 HETZLER lIIC,HAEL C. KILLI.\X3
C?1irersit!~oj’ Crr lifor 11 iri Berkeley, Cnlif. 3.4720 l l ~ c l i ~ v for i . ; ~review ~ F e b r m r y 24j 1970 ~ : I ~ : S U B \ f I T T I ~ November D 2, 1870 a \ ~ ~ I ~ December ~ ~ ~ i . : 7, ~ 1970
