rate? can be varied over desired limits and the type of flon- seen at a glance. Thus, the influence of flon- rate on flow type is readily seen. Rubber tubing is convenient for connections betiveen pump and model. However, new tuhing n hich released sulfur by 11 hat is known as blooming caused some difficulty in this 1al)orntory. Evidently, some sulfur-eating bacteria entered the system, yielding hydrogen sulfide :IS by-product, and corrosion of the metal parts resulted. -il\n, the suspension coagulated and had to be discarded. Consequently ‘l’gpn tuhing is non- used. The stream double refravt ion prore39 is n valuable tool, having the advantage of iimplicity, accuracy, and -peed of operation.
RED1ST111BUT1( I S OF XI >SO11ILl‘l’l~ 131- L)IF F L7SIO S EDWAHD LEDOUX Attapulgus Clag Company, Phzladelphia. PennsillLania
Received September 6 , 1948
Since the efficiency of tlynamic adiorption in a lied ii-hi(al1i- itartetl up after an interruption in the adwrption rycle depend< consic1cr:thly on the distribution of adsorbate in the bed. it i- of interest to htudy the redi.;tribution of adsorbate during the pcriocl r,i ~tllcnc--. For t h i i purpose, a semigraphical procedure for plotting the vapoi p w w i i ; m i concentration curve> is pre-ented. e.;trcmcly slow a3 compared The concentration cliungei due t o tliffii-ion t o siich change> hiuiiglit a h u t hy a flon of giii p:twna through the bed. In the luttcr cate, a w h t r i n t i d difference e&ts bet\\ een the vapor pressure in the gas and the equlliImrim \.,rpor pressure of the iitisor1)cnt a t thr wmc point (3, 1). In the r a s e of d i f f i i - i o n . ho\i (’1 e r , the changci i i r ~-0 -hi\\ th:tt thi- v,ipor-pre-tiire (1
11: \vhicli 0,i h the t1if'i'usivit)y for the system considered. Its cxsperiuicntal deic.rmin:itiori \vi11 l , ~t1isciis.d latei,. If \YP ( d I I, tlic I c q g 11 of the heti, antl make the follorving r1i:iiige.- in variables
962
EDTT.iRD L E D O U S
in which d P / dc is the slopt~of the iaotherm. Since d P dc > 0, the equation s h o w t h a t when the constant 0 curve ia conc:ive upnard a t any given distance S, the vapor pressure increa3es n i t h time a t tliut distance. This equation is similar in form t o that solved graphically by Schmidt ( 5 ) in the case of heat conduction but, -ince the factor d P dc is variable, this graphical method cannot be applied to the aolution of equation 4. HoTT-ever,this equation can be solved by a finite increment calculation rehting on the same basic principle as t h a t of Schmidt. ChLCL-LATIOS PROCEDCRE
Let AX and A@ represent finite increments of distance and time; AP the finite variation in pressure for X constant at the heginning of interval A X and corre
Distdnie X
FIG. 1. Finite increment vapor-pressure curves
sponding t o increment A @ : A ? P the finite variation in slope of the constant time curve due t o increment A X . Relation 4 then becomes
g
=
(E) iLZP dc
Consider no\^ figure 1 in u-hich the curve 0-10is l a o w n zinc1 the curve 0 has been determined up to point A’: the nest point A is t o be determined so as t o satisfy equation 5 . Figure 1 shon-s that AI‘ = (C‘--lj. The slope at the beginning of interval AX is (DE‘), n-hile at thc end of the i n t e n d it is ( D E )j thus, A2P = ( D F ) - ( D E ) = ( E F ) . If ( D F ) > ( D E ) !as in the case shoTrn in figure 1, then A ? P is positive, the curi-e is concave up\\-ard, and A is higher than C ; if (DF)< ( D E ) .A?P is negatiye. the curve is conca1.e don-nward, and d is helon- C. It vil! also be noted that A2P = B(BC1. \\-here the ordinate of R is the average of those at C’ and D. If n-e sciect an interval n for AX and 11’ for A@, equation 5 may be m i t t e n
I:):( AP=
- T A P
REDISTRIBUTIOS O F l D S O R B l T E BY DIFFUSIOS
963
and therefore
where dP/dc is the value of the slope of the isotherm for the preasure at C. This graphical relation determines the position of point -4. K h e n the bed is sealed at both ends, the slopes of the pressure curves a t X = 0 and S = 1 are nil. Indeed, at those distances, there is no flow to or from the surroundings and equation 1 s h o w that d p dx = 0. Thus, in the finite increment treatment, the segments are horizontal in the first and laqt increments XI-. .In alternative method is to apply the finite increment procedure to equation 3, the correspondence betn-een Ac and A P being giiTen by the isotherm. The concentration and pressure curves must then be determined aimultaneously, but the necessity of the .lope curve is avoided.
D italte x FIG.2. Vapor-pressure curves SCMERICAL EXAMPLE
Consider a closed bed of carbon a t 20°C. and containing ad,orl)ed water. The initial vapor-pressure distribution is that shown in figure 2. The 20°C. equilibrium isotherm for n t e r vapor and the carbon conbidered, as determined by Barron- et al. ( l ) , is shown in figure 3, Tvhere it is plotted as a function of the dimensionless pressure P . The bed is 6 em. long. The diffusii-ity is D, = 0.04 sq.cm./sec. and the apparent density of the carbon is d = 0.571 g./cc. The slope of the isotherm is plotted in figure 4. K e have
RTd _ _ _-_ 82.07 _ _ x 293 X 0.5il - - - 767 atm, ;M
18
rhus, the actual vapor pressure p in atmospheres is p = 76iP.
The rcdistiibuticin ~ ‘ ~ i r vup e - t(J @ = 300 :11’(’ plotted in figure 2. ly’hen the pressure is brlo\v about 1.3 x it I \ Iieccswry t o adopt bmizll interval values for cnlculation because of the rapid i k l in slope of the isotherm (see figure 4). ,111 ciirve~n e r c calculated n i t h = 0.1 hiit uitli incrca*ing F-dues of n’. Up t o 0 = GO, tt’ = 10; then ) I ’ = 20 1111 to 0 = 100; thcn IZ’ = 3011p to 0 = 200; then )I’ = 100.
EqJ
libnun Cunrrntrdtion c
FIG.3. Isotherm at 20°C. for carbon-water
:ou
.$
r c r , ~ 2 5
FIG.4. Slope curves
Calculations for a. typical point, such a4 point -1 (figure 2) at S 0 = 300, are as fullon-b: The ordinates of the preceding curve (0 that rcgion are hcttcr shon n in figure 1 . Tlic ordinatc of point I3 i- (1.420 -+ 1.322)/2 = 1.371 The ordinate uf point C i y 1.333 i f 3 C ) i- cqiinl t o 0.018 =
1 333, (11’ J c = 12.3 X 10-3 (yet figure
=
0.8 and 200) in
0.036
A2f’ is eqiinl to 2(BC‘)
i’
=
A), \ \ M e t i ’
’ti? =
100 0.01
=
REDISTRIBUTION O F ADSORBATE BY DIFFUSIOE
965
+
lo4. Thus AP = 0.036 X 1.23 = 0.043 and the ordinate of point -4is 1.333 0.045 = 1.398. Other points are determined in the same manner. Once the vapor-pressure curves have been determined, the corresponding concentration curves are readily plotted by means of the isotherm. This has been done for the initial curve and the curve 0 = 600 in figure 3. The actual time 0 corresponding to any curve 0 and the actual distance corresponding to X are given by the variable change equations:
e = - DL2 @ V
and
z=LX
For instance, the curve 0
= 600 is that a t time0 = (36 X 300)/(0.04 X 3600) = 125 hr. The actual distance corresponding to X = 0.7 is 5 = 0.7 = 6 = 4.2 em.
f$:!a*i:e X
FIQ.5. Concentration curves EXPERIRZESTBL DETERXINdTIOZi O F DIFFUSIVITY
Since the diffusivity of the system is defined b y equation 2, comparison he,ween calculated and experimental curves will determine the value of D,. The experimental points of BarroJy et al. for e = 160 hr. are shown in figiil(1 .i. rhey correspond satisfactorily to the curve 0 = GO0 except the first one at S = ).116. The authors made no determination of concentration in the iriiiial 1;iyrirX = 0 - 0.116, and the fact that the concentration at S = 0.116 drop. more lowly than calculated shows that thc experimental initial concentriition in thc nterval AX = 0 - 0.116 mi* m u c h grpater than that tiiken in the calcu1;ition. Iowever, the concentration tli*trihution before S = 0.3'75 doeq not grc:ltly ffect that in the portion of brtl a l m - c . because thc curi-es practically pivot round the point S = 0.373. c = 0.093. The time correspondence being 0 = 150 hr. for 0 = 600, thc \-nl.1(> oi tllc iffusirity for t h e systcm cwn~idcrcdi* 600 x 3ti D, = _____
150 X 3600
=
0.04 sq. cm/sec.
966
Z O L T ~ Nsz.1~6ASD
LADISLAUS K ~ B E D Y
This is considerahly l o w r than for the diffusion of \rater vapor into air when no adsorbent is present and the redistribution process is very slow. It r d l be seen that the rapidity of redistribution depends essentially upon the shape of the isotherm of the system considered. Since the diffusivity D,, as defined, depends only on the friction of diffusion in the gas phase and against the outside surface of the granules, it is reasonable to assume that it would be about the same, or at least of the same order of magnitude, for adsorbents of the same mesh iize and granular shape. On t h i q assumption, the diffusional process ~ ~ - o u he l d even slower for hausite, for instance, since the vapor-pressure variation A P is shon-n to he proportional to the slope of the isotherm, which is much smaller for bauxite. SUMMARY
The equation for the redistribution of adsorbate is established. It is expressed in dimensionless variables by appropriate changes. A calculation method for plotting the vapor-pressure and concentration curves is presented. These dimensionless curves will permit the experimental determination of the diff usivity for any system considered. REFERENCES (1) BARROW, R . F., DAXBY,C. J., DAVOUD, J. G., HINSHELWOOD, C. N., A N D STAVELEY, L. X.: J. Chem. Soc. 1947,401. (2) LEDOUX, E. : T‘apor A d s o r p t i o n . Industrial Applications. Chemical Publishing Company, Inc , Brooklyn, New York (1945). (3) LEDOVX,E.: Ind. Eng. Chem. 40, 1970 (1948). (4) LEDOL-X, E : Graphical Sulutzon o j Heat an? I-apor Transfer Problems. C h P m i c d Publishing Company, Inc.. Brooklyn. S e J y York (1949) (5) SCHMIDT, E.: -4 Bopples Festschrift, J. Springer, Berlin (1924).
ON THE SWELLISG OF CHARCOAL ZOLTAK SZXB6
ASD
LADISLhUS RGKEDYl
Institute f o r General a n d Physical Chemistry of the Cniversity of Szeged, Szeged, H u n g a r y Received October 1, 1948 ISTRODUCTIOS
According t o Zsigrnondy’s original definition a solid substance on swelling takes up liquid, as a result of which its volume and elasticity increase and its density decreases. Biologists have very often investigated this phenomenon. Katz suggested a distinction between intermicellar and intramicellar swelling. In the first case the swelling liquid is adsorbed on the surface of the particles, so 1 Present address: Institute for Inorganic and Analytical Chemistry of the BoIyai University, Cluj, Rumania.
