ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Table V. Values of Constant in Equation 1 1, Developed b y van Krevelen and Hoftijzer (6)
Nomenclature
(1 = H / R )
Material Amine hydrochloride
R u n No. 3
Constant 0 ‘72
4 5
Calcium chloride Sodium metabisulfate Mineral slag Urea Cocoa sludge Photographic chemical Polyvinyl acetate
characterist,ice, an assignment, of certain equat,ion constants to these groups, is n o t feasihle.
10 1 2 3 3 1 B
1 ’7 3 4
(c)
O(
c
2 1’7 0 369 0.333
D P G
0.868 0.541 0.435 0 197 0.290 0.077
H K k
1 66 0.374
k‘ L ?n .V I?
I ,033
2 029
dryer construction and that Equation 11 has applicability only in very limited ranges for most materials. Conclusions
As earlier workers have stated (a,5 ) there really is no substitute for a pilot plant test on a material to be dried. The studies reported in this paper have indicated the critical importance of the material characteristics and also the profound effect of sometimes small changes in dryer product characteristics upon retention time and fillage. Friedman and Marshall ( 4 ) found that the heat transfer rate vas only slightly effected by changes of dryer slope and speed of rotation and, therefore, these factors are not critical from a thermal dandpoint. Any equation discussFd in this paprr relating time of passage and retention time or holdup to dryer Characteristics has a limited range of application, and this range varies n-ith thp material being dried. From the standpoint of practical application, upe of the equation should not require the determination of material handling characteristics with dry material with no air flow. For semiquantitative purposes, this author prefers adaptations of the Friedman and Marehall relationship (Equations 7 to lo), the Smith equation, Equation 5, or the van Krevelen and Hoftijzer equation, Equation 11. Estimation of dri er size based on classification of materials into different groups or types according to drying or handling
sd T e
V X Xo
angle of inclination of dryer, degrees constant of Equation 11, devcloped by van Krevelin and Hoftijaer (6) = dryer diameter, it. = solid feed rate, cu. ft./(hr.) (sq. ft. of dryer cross section) = air mass velocity through dryer, lb.l(hr.) (sq. ft. of dryer cross section) = dryer holdup, lb. = constant in Equation8 7-10> adaptations of Friedman and Xlarshall cquatioiis ( 3 ) = dryer constant in Equation 4, developed by Prutton, Miller, and Schuet,te ( 7 ) . = constant in Equation 5, developed by Smith (8) = dryer length, f t . = material constant in Equation 4 = rate of dryer rotat,ion, r.p.m. = feed rate to dryer, lb./hr. = dryer slope, ft./ft. = time of passage, hr. = dynamic angle of repose of material, degrees = air velocity, ft./min. = dryer holdup, % of dryFr volume = dryer holdup with no air flow, yo of dryer volume = =
Subscripts a, b denote different operating conditions Literature Cited
(1) Bayard, K. A , , C h e m . h M e t . Eng., 52, 100 (1945). (2) Friedman, S. J., Heating and Ventzlating, Reference Sect., 95 (February 1951). (3) Friedman, S.J., and Marshall, W. R., Jr., Chem. Eng. Proor., 45, 482 (1949). I b i d , p 573. Rarrigan, H. IT-.,and Boyd, J. A , Chem. & Met. Eng., 4 6 , 214
(1939). Krevelen, D. Vi. van, and Hoftijzer, P. J., J . Soc. Chem. Ind. ( L o n d o n ) , 68, 91 (1949).
Prutton, C. F . , hIillei, C. O., and Sohuette, W. H., Trans. Am. Inst Chem. Engrs., 38, 123 (1942). Smith, B. A , , Trans. A m . Inst. Chern. Engrs., 38, 251 (1942). Sullivan, J. D., Maier, C. G., and Ralston, 0. C., U. S. Bur. Nines, Tech. Paper 384, 1927. Thomas, E. W., and Weisselberg, A., “Suggested Recornmended Practice for Testing Drying Equipment,” S m . Sac. Llech. Engrs., 29 West 39th St.,New York. RECEIVEDfor review April 23, 1954. ACCEPTEDKovetnber 29, 1954.
Continuous Ion Exchange with an Endless Belt of Phosphorylated C. H. MUENDEL AND W. A. SELKE Deparfmenf o f Chemical Engineering, C o l u m b i a Universify,
IN
New
A continuous ion exchange process the exchanger should be circulated countercurrent to the feed streams, passing alternately through an exhaustion and a regeneration section. The advantages of this method, which are of special importance when the regenerant is fed to subsequent processes, are well known. Although the problem of continuous ion exchange has received considerable attention, the results of relatively few investigations have been published. Patents have been granted to Kordell (11) and Wilcox (1.6) for continuous water softeners. Stanton ( 1 8 ) and Hiester and coTYorkers ( 5 ) have studied the separation of ions by continuous means. Keister also demonstrated the use of a mixer-settler apparatus that consists of a consecutive series of batch separations. Selke and Bliss ( l a ) ,
374
York,
N. Y.
\Torking on the reclamation of copper ion from very dilute solutions, used count,ercurrent moving beds. Their work was continued by Crits (2). Recently, other methods of continuous ion exchange using commercial resin have been proposed by Higgins and Roberts ( 6 ) , Koenig, Babb, and McCarthy (S), and McCormack and Howard (10). McCormack and Howard employed an endless tube of cloth filled with resin and tied off at intervals. On the basis of this esperience it is possible to dralx- up a Bet of conditions to which a successful continuous ion exchange apparatus must conform: 1. The apparatus must give positive and predictable displacement of the exchanger relative to the solution. The im-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 3
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT portance of this has been shown by the difficulties encountered in the investigations described above. Furthermore, if a fluidized system using freely moving resin particles could be designed to function properly with a given exchanger, it would be so sensitive t o particle size and solution density as t o be virtually useless if either of these conditions were changed. 2. The geometry of the apparatus must produce good solidliquid contact-i.e., all the solution and all the resin must be equally exposed to each other for optimum resin utilization and optimum separation relative to the size of the apparatus. 3. The exchanger must be rugged enough to withstand the mechanical stresses imposed on it without excessive degradation. This restriction strongly limits the use of the presently available resins. They are not strong enough to be molded as tapes and used in the form of endless belts. Mechanical handling of the particulate forms results in degradation. With some types a rapid change in ionic strength of the solution t o which they are exposed results in differential swelling to such an extent t h a t degradation follows. 4. The exchanger must have a sufficiently high capacity for exchange and a sufficiently high tolerance for internal diffusion to restrict the total amount of exchanger used and the rate of exchanger throughput to reasonable values. 5. The apparatus must be sound mechanically in useful ranges of operation. That is, entrance and exit losses through "drag out," poor closures, dilution by wash water, and similar effects must not be large with respect t o the total throughput and separation.
9
The object of this research has been to explore the possibility of fulfilling these conditions by an apparatus using an endless belt of cotton cloth, treated to act as an exchanger. Such an apparatus would fit the requirements listed above. It would result in absolutely positive displacement of the exchanger relative to the solution. It would provide good solid-liquid contact; since a cloth may be treated as a two-dimensional solid, the geometric problem of equal contact would be greatly simplified. A cotton cloth can be made strong enough to withstand reasonable stresses. If necessary, it could be reinforced with stainless steel or other metallic screening. However, it will not resist degradation by acids; therefore, it may only be used with neutral or mildly basic solutions. Much attention has been given to the problem of fireproofing cotton (9). It has been found that, if cotton is esterified with a mineral acid, it becomes flame resistant. The acid normally used is one of the phosphoric group. The resulting compound is stable in pure water, but has been found to undergo readily the following ion exchange reactions: Cell-CH2-0 \p/oH"Hz\C=O
OY \OH
NaCll
.NH/ Cell-CHz-0,
,0--Na
.
P
ON Cell-CH2-0,
\O--T\ra
,O-Na
P ON \O-Na
-c*u s o 4
While these reactions have hampered the work in flameproofing, they present the possibility of an ion exchange medium in a physical form not previously available. Specifically, Guthrie ( 4 ) mentioned the use of ion exchange cotton in the form of a belt. Feasibility of phosphorylated cotton exchanger i s tested by capacity, equilibrium, and rate measurements
The feasibility of a continuous countercurrent ion exchange process using an endless belt of phosphorylated cotton has been investigated by means of capacity measurements and equilibrium and rate studies. The results of this work have been applied in the construction and operation of a continuous countercurrent apparatus.
March 1955
The chemical system used involves the concentration of copper ion in dilute copper sulfate solutions, using concentrated brine as a regenerant. Although the system copper-hydrogen is not commercially feasible because of the hydrolysis of the cotton by the acid, several measurements were made with it for the sake of comparison. The cotton material used was white toweling, which combines strength with a relatively open weave and high weight per unit area. No attempt was made to investigate different phosphorylation methods or to develop new ones; the method used is the one reported by Jurgens ( 7 )to give the highest exchange capacity. It was found, however, that treatment of the cotton with 20% sodium hydroxide solution before phosphorylation improved its exchange capacity by as much as 50%. Exchange Capacity. The exchange capacity of an ion exchanger is the total number of sites available for exchange, usually expressed as equivalents per unit of weight in some standard form. CAPACITYDETERMINATION. Treated cotton fabric in the sodium form was exposed to concentrated copper sulfate solution, allowed t o stand for several days, washed with distilled mater, and exposed to fresh copper sulfate solution. The cycle was repeated until no more sodium was found in the equilibrated solution. The cotton was then thoroughly washed and analyzed for copper. I n this and all subsequent work, the analyses for copper were carried out by the photometric method of Crumpler ( 3 ) . The air-equilibrated weight was used in all the measurements rather than the weight after a standard drying treatment. Although the former procedure is less accurate than the latter, it allows a nondestructive analysis which was required in some parts of the work. For uniformity the same method was used throughout. RESULTS. The value of exchange capacity obtained was 3.39 meq. per gram of sodium form (air dried). For the sake of comparison with other materials, this may also be given as 3.66 meq. per gram of hydrogen form (air dried), although this form is not stable. Commercial sulfonated polystyrene resins, which are used for essentially the purposes foreseen for phosphorylated cottons, have capacities in the range 3.5 to 5.0 meq. per gram hydrogen form (oven dried). Hence, allowing for the difference in moisture content of the basis, the exchange capacity of the cloth is effectively in the same range as the commercial resin. Guthrie ( 4 )reported a capacity of 2.6 meq. per gram hydrogen form phosphorylated cotton (oven dried) that was obtained by extrapolating sodium-hydrogen equilibrium values plotted as a function of pH. Equilibrium. The relative concentration of the various cation species present in the exchanger a t equilibrium is a definite function of their concentrations in the surrounding solution and of the total cation concentration of the solution. This latter condition is sometimes overlooked when equilibrium values are reported, EQUILIBRIUM DETERMINATION. Samples of sodium form cotton were exposed to solutions made by mixing copper sulfate and sodium chloride solutions of equal normality in various proportions. After equilibrium had been attained a t room temperature, both the samples and the solutions were analyzed for copper, as described. A series of measurements was similarly made, starting with hydrogen form samples and combinations of equinormal copper sulfate and sulfuric acid solutions. RESULTS. The equilibrium values found for the systems C u f f - N a + and C u + + - H + are given in Figures 1 and 2. Values for the cotton side are expressed as q/a, meq. of C u + + per meq. of C u + + Na+, while the corresponding values for the solution side are expressed as C/C,, meq. of C u + + per meq. of Cu'+ 4Na+. In each plot a line has been drawn through the points for C, = 50 meq. per liter.
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
375
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT The copper-sodium equilibrium curves for phosphorylated cotton are similar to those for several commercial exchangersthat is, they show a m-ide range of q/u for low values of C/C,. This makes for easy copper pickup but difficult regeneration. I n contrast to the case TTith resins exchanging ions of different valence, the equilibrium in phosphorylated cotton is evidently only slightly affected by changes in C,.
l
I
l
The concentration of the effluent solution was measured as a function of time. The results of the latter runs were calculated by the shallow bed approach that has been used with fixed resin beds ( 1 ) . The inass transfer coefficient, R D X , is defined by the equation
gq - K n S ( C - C*) dB l
:
(1:
of interface concentration from the relation
4
A knoxledge of the interface liquid conccntration allows the evaluation of the interface solid concentiation from the equilibrium data. RESULTS. The results found by the perpendicular flow procedure have been plotted in Figures 4, 5 , and 6. They are, respectively, the concentration histolies of the effluent solution, a Wilson-type plot of the 02 04 06 0 8 IO OO individual mass transfer coefficient, and CIC. a plot showing the internal concentration Figure 2. Copper-hydrogen Figure 1. Copper-sodium gradient of the exchanger as a function of equilibrium equilibrium the total copper content of the resin duiing a run. When phosphorylated cotton is used in the form of a cloth, The copper-hydrogen equilibrium curve shows the effect of the there are tm-o limiting cases of fluid flow geometry-gross flow dibasic acid structure of the exchanger-that in, the first hydrogen parallel to the cloth and gross flow perpendicularly through the is almost completely replaced a t low values of C/C, n-hile the cloth, ,4n approximatian to the first of these cases has been second is replaced a t high C/C,. treated in the discussion above. In the second case, diffusion Rate Studies. Four mechanisms influence the rate of exchange: recistance by stagnant fluid between the fibers of the cloth is Diffusion through the solution external to the surface of the cloth Diffusion through the stagnant fluid between the fibers of the cloth Diffusion within the fibers Reaction a t the active sites in the fibers Since the behavior of the exchange rate as a function of the external conditions is largely determined by the identity of the controlling mechanism, it is of value to establish this identity in addition to finding the order of magnitude of the rates that may be expected. PHOCEUCRE. I n order to obtain a rough idea of the late of exchange, a series of batch runs was made. Several small pieces of sodium form cloth were soaked in distilled watei, blotted to remove excess moisture, and simultaneously dropped into a large beaker containing 50 meq. per liter copper sulfate solution. The beaker was rapidly agitated by a propeller aiianged to prevent the cloth from moving nith the solution. A t definite time intervals, one of the pieces of cloth was ienioved froin the solution, washed, and analyzed. Curves of the type obtained are shown in Figuie 3. The data obtained by the batch procedure are not suitable for quantitative interpretation because it is mathematically difficult to desciibe the concentration of the solution and the hydrodynamic conditions as functions of time, although qualitative interpretation is possible. The slope of the curve over the first 30 minutes of exchange is low enough to indicate a considerable resistance to ion exchange. The data for copper-hydrogen exchange, which TTere included for compaiison, reflect the difference in diffusivity and equilibrium betn een the copper-hydrogen and the coppcr-sodium system. ,4 second, more quantitative study m-as made by fastening a double thickness of wet sodium form cloth over the large end of a Gooch funnel and running 3 meq. per liter copper sulfate solution through the cloth a t various rates. The cloth on the sides of the funnel vias so masked off that only the circulai area equal to that of the opening in the funnel nas exposed to the solution.
376
0--
' 0
20
40
60
80
C"+t-H+ 100
120
140
i i m e lmin.)
Figure 3.
Batch rate study
effectively eliminatcd because the fluid is forced right through the cloth. This \%as done in the perpendicular flow procedure. However, as shown by the run history curves of Figure 4, the rate of mass transfer is still low. As before, the driving force is high. I n view of this and the fact that values of the mass transfer coefficient for parallel flow fell considerably below those for through flov, it may be said that the diffusion resistance of stagnant fluid between the fibers is important but not controlling with respect to the over-all resistance. Diffusion resistance on the liquid side is Ion, if the above stagnant fluid is eliminated, except a t very low liquid velocities. Obviously, the relative importance of the four mechanisms may be expected to change as the operation proceeds. Solid diffusion and chemical reaction rate remain to be examined. At the very beginning of an exchange operation with an
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 3
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT ated cottons as a whole. It is possible that both could be improved by modification of the preparation technique. Operation of continuous countercurrent apparatus
The primary requirement of phosphorylated cotton as an ion exchanger is its ability to perform satisfactorily in a continuous apparatus. A simple countercurrent pickup operation without reflux was used for this work since it afforded an opportunity t o study the basic principles of continuous ion exchange with a belt of phosphorylated cotton without involving excessively complicated apparatus. Procedure. The continuous apparatus used is shown diagrammatically in Figure 7.
ooO 500
1000
1500
2000
total throughput (cc./g.)
Figure 4.
Concentration histories for perpendicular flow
exchanger for which p = 0, solid diffusion resistance is nonexistent, Thus, for this point the calculated mass transfer coefficient is a function only of the liquid-side resistance and the chemical reaction rate. The values of this mass transfer coefficient, ~ D Sdefined , by Equation 2, have been found as a function of fluid velocity by extrapolating the over-all coefficients, KDS, defined by Equation 1, back to time zero. B y means of a Wilsontype plot (Figure 5 ) , ~ Dhas S been extrapolated to infinite liquid velocity or zero liquid-side resistance. The value found for
I I V
Figure 5.
-
-‘-I
2.4
Wilson plot of individual mass transfer coefficients for perpendicular flow
~ Da S t infinite velocity is 0.25. This is large with respect to the average values of the over-all coefficient, KDS, which ranged from 0.05 to 0.005. Thus, it may be said that both the liquid diffusion resistance and the effect of chemical reaction rate are small, though not negligible, with respect to the over-all resistance during the major portion of an exchange operation. By elimination, this leaves diffusion resistance within the exchanger as the most important rate limiting mechanism. This result may be confirmed by further examination of the data obtained by the perpendicular flow procedure. Figure 6 is a plot of the difference between the solid-phase interface concentration and the solid-phase gross concentration as a function of the solid-phase gross concentration. This difference is a measure of the solid-phase concentration gradient during a run. From the curves it is very apparent that large gradients do exist in the exchanger. The effect of liquid-phase resistance is shown by the displacement of the curves corresponding to different velocities, from each other. High resistance to internal diffusion and the particular value of capacity found are not necessarily characteristic of phosphorylMarch 1955
The apparatus consisted essentially of a 5-inch-wide endless belt of phosphorylated cotton that was pulled countercurrent t o streams of copper sulfate and sodium chloride solutions. The belt was washed with deionized water after regeneration by sodium chloride. The actual exposure of the belt to the exchanging solutions was carried out in shallow tanks, 30 inches long, containing baffles. Two types of baffles were used. The first type caused the solutions to flow across the surface of the cloth; the second caused the solutions to flow through the cloth. It soon became apparent that the first system led to extreme stratification in the solutions; therefore, air jets were introduced between each pass t o provide agitation. Thin sheet rubber was used to give reasonably good closure between the belt and the baffles. All those parts of the apparatus that came in contact with the solutions were made of Lucite or Tenite. The solutions used for all the runs were 50 meq. per liter copper sulfate and 4N sodium chloride. They were fed to the apparatus by a constant displacement pump and a constant head tank, respectively. Flow through the apparatus itself was by gravity. The belt was prepared by the same method used for the material in the equilibrium and rate work. For the crossflow baffle system a double thickness of cloth was used, while for the through flow system a single thickness was used. I n all cases the belt rate was 1 inch per minute. Runs were approximately 10 hours in duration; this length of time was required t o reach steady state. At steady state, samples and rates of all the influent and effluent streams were taken. I n addition, samples were taken of the solutions at intervals along the exhaustion and regeneration tanks. The copper content of the regenerated belt was determined by direct analysis. Sodium chloride in the regenerant feed was determined by dry tests.
O b
0.4
0.8
1.2
1.6 4 (mcq/g.l
2.0
2.4
2.8
’
Figure 6. Internal concentration gradient as a function of copper concentration in the resin for perpendicular flow
The apparatus could be adapted t o separational operations by the addition of a third exchange tank. Part of the eluent would then be used as reflux in the enriching of the ion preferably held by the belt. The value! of C / C , and q/a for the different streams were calculated directly from the data or indirectly by material balance. Local material balances were made t o determme q a t particular points in the cloth, using the values of solution concentration taken a t intervals along the length of the tanks.
INDUSTRIAL AND ENGINEERING CHEMISTRY
377
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT ratus used was designed uithout the aid of any previous Orer-all n-ork in this field, hence cerelements were based simLiquid Flow %a%Exchanger ~~t~ f ~ r ~ ~ e $ $ ~ ~ tain ; Run Flow V, u, (E) c/co d a ( K D S ) ,L./ ply on convenient laboratory NO. Pattern cc./min. cin./min. G./hI'in. (leaving) (leaving) (iUin.) (G.) operation. In particular, the, 0.412 0.00040 111 Exhaustion Cross 295 42.2 2.56 0.587 solution flow through the sysRegeneration Cross 10.5 1.74 2.56 0,0362 0.249 0.00036 0 00040 tem is by gravity with very 0.950 0.331 2.56 030 104 Exhaustion Cross 0.0040 0.138 19.8 2.56 Cross 120 Regeneration 0 00028 low heads. This prevents the 0.857 0.595 4.10 1.28 235 vII Exhaustion Through 0 0010 use of high local or over-all flow 0 00043 0,0304 0.203 0,202 1.28 11.7 Regeneration Through rates and also sets a lo\\er limit because surface tension effects do not allow smooth wheel operation at very low rates. I n the second place, f pon-er is applied to the belt a t only one point; therefore the baffle closures cannot be made tight enough to prevent leakage without slraining the belt. Both of these features are limitations of the particular apparatus employed, they could virtually be eliminated by better drsign. w a h water overflow reganeront overflow ef f Iu en t The apparatus has not necessarily been shown effluent (d) in the best light as regards over-all performt b) ance. Operation a t lower solution rates, highei Figure 7. Continuous ion exchange apparatus belt rates, or loTver C, would improve the degree of pickup with this particular equipment geometry. Thus it was possible t o calculate K D S a t points x along the length The three continuous runs presented have been chosen parof the tanks from ticularly to illustrate the effect on KDS of liquid velocity in crossflow and of through flow as compared to crossflow. Over the range covered, liquid velocity has little effect on KDS in crossflow. The coefficients for through flow should be higher than those for crossflow. A dye was used to test the operation of the through Results. Seven runs were made with the continuous appaflow baffles on the continuous apparatus. While the major ratus; of these, three will illustrate the progress made and will portion of the solution did pass through the cloth, enough leaked show the effect of fluid flow geometry and liquid rates. The around the sides to reduce someivhat the contrast between the results of these three runs are shown in Table I. McCabetvio cases. However, in an over-all sense, operation n-ith the Thiele type diagrams for the runs are given in Figure 8. The through flow arrangement gave essentially the same concentramaterial balance equation plotted in these diagrams may be tion factor as that obtained using tnice the belt rate (by m i g h t ) given as Edy, = VdC,, which integrates to with the crossflow system. Selke and Bliss (It?) reported values of K D S for a continuous moving bed of exchange resin using a chemical system similar to the one used in this work. Their values of KDS for exhaustion are one to t w o orders of magnitude higher than those found in where E and Ti are the cloth and liquid rates, respectively, and the present study with the continuous apparatus, but they are x and zo are any point along the length of an exchange tank and about the same as those found in the rate studies. Their values one end of an exchange tank. Exhaustion and regeneration for regeneration are in the same range as those found with the have been plotted side by side with equal q/a axes. Thus it was continuous apparatus. It would thus appear that continuous possible to connect the exhaustion operating line and the regeneration operating line for each run with dotted lines, as shown in Figure 8. Points a,b, c, and Exhaustion ( C e ' 4 8 . 5 rneg,/l.) R e g e n e r a t i o n ( C e = 3980 rneq,/l.) d relate points on the diagram to the correspond1.0 ing points in the apparatus, as shown in Figure 7. The C/C, axis in the regeneration diagram has been expanded for the sake of clarity. 0.8 The results in general show that the apparatus has not performed at, the level of efficiency that might be expected from the data given in the 0.6 first part of this article. Specifically, the valucs of the over-all mass transfer coefficient, K D S , 4 /a tJhat have been found are more than an order of 0.4 magnitude less than those found by the perpendicular flow rate study procedure. This would indicate that the degree of solid-liquid cont,act 0.2 varies widely within the apparatus-Le., that the mass transfer coefficient on a gross basis is .... reduced by channeling and st,agnant corners. 0.2 0.4 0.6 0.8 1.0 0 0.05 0.10 OO This leads t o a low number of theoretical conc/ce CIC. tacts and a consequently low pickup. Figure 8. Operating lines for runs with continuous exchanger However, this does not, mean that the method o, b, c, d correspond to points in apparatus (Figure 7 ) in general is limited in this way. The appaTable 1.
Results of Continuous Operation
~
378
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 3
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT ion exchange with phosphorylated cotton could a t least be brought to the level of operation obtainable with resins. The course of this development should include a study of the relation of the chemical structure and preparation of the cloth to its eapacity and resistance to internal diffusion in addition to refinement of the apparatus.
V
= liquid rate, cc./min.
x
= superficia1 distance along liquid length of exchange cm./min.tanks, cm. = end of exchange tank, = time, min.
2,
zo
e
literature cited
Acknowledgment
(1) Bieber, E., Steidler, F. B., and Selke, W. A,, Chem. Eng
The aid of the United States Atomic Energy Commission in supplying the apparatus used, under Contract AT (30-1) 1108, is gratefully acknowledged.
(2) Crits, G. J., M.S. thesis, Columbia University, 1950. (3) Crumpler, R. B., ANAL.CHEM.. 19, 325 (1947).
Progr.,
Nomenclature
a
= total exchange capacity, meq./gram sodium form (air
C Go C,
= copper concentration in solution, meq./l. = total cation concentration in solution, meq./l.
C*
= copper concentration in solution in equilibrium with solid a t concentration q, meq./l.
dried) = copper concentration in solution a t solid-liquid interface,
meq./l.
E = exchanger rate, grams/min. K D S = over-all mass transfer coefficient, meq./(min.)(gram) (mes./l. 1 ~ D = S individual mass transfer coefficient, meq./(min.)(gram) (mes./l.) = copper concentration in solid, meq./gram sodium form p (air dried) = copper concentration in solid a t solid-liquid interface, qt meq./gram sodium form (air dried)
Symposium Ser., No. 14, p. 17, 1954.
(4) Guthrie, J. D., IND.ENG.CHEM.,44, 2187 (1952). (5) Hiester, N. K., Phillips, R. C., Fields, E. F., Cohen, R. K., and Radding, S. B., Ibid., 45, 2402 (1953); Heister, N. K., Fields, E, F., Phillips, R. C., and Radding, S. B., Chem. Eng. Progr., 50, 139 (1954). (6) Higgins, I. R., and Roberts, J. T., Chem. Eng. Progr., Symposium Sw., No. 14, p. 87, 1954. (7) Jurpens. J. F., Reid, J. D., and Guthrie, J. D., Textile Research 18, 42 (1948). ( 8 ) Koenig, W. W., Babb, A. D., and McCarthy, J. L., Chem. Eng. Progr. Symposium Ser., No. 14, p. 103, 1954. (9) Little, R. W., “Flameproofing Textile Fabrics,” Reinhold, New Y o r k , 1947. (10) hIcCormack, R. H., and Howard, J. F., C h e m Eng. Progr., 49, 404 (1953). (11) Nordell, C. H., U. S. Patents 1,608,861 (November 1926); 1,722,938 (August 1929); 1,740,199 (December 1929). (12) Selke, W. A,, and Bliss, H., Chem. Eng. Prow., 47, 529 (1952). (13) Stanton, L. S., M.S. thesis, University of Washington, 1950. (14) Wilcox, A. I,.,U. 8. Patent 2,528,099 (October 1950).
x,
RECEIVED for review Scptemhpr 3, 1954.
ACCEPTED November 10, 1954.
Fluid Mechanics Studies
Transition Phenomena in Pipes Annular Cross Sections R. S. PRENGLE‘
AND
R. R. ROTHFUS
Carnegie lnsfifute of Technology, Piffsburgh, Pa.
B
REAKDOWN of viscous motion in fluids flowing in conduits of various shapes has been the subject of much speculation. The theoretical and experimental investigations of Meksyn ( 7 ) , Maurer (6),Schiller (I$’), Gibson ( 3 ) and others, however, have only partially clarified the physical picture of the phenomena that occur in the transition process. A recent study of velocity distribution and fluid friction in smooth tubes by Senecal and Rothfus ( I S ) has indicated that deviations from viscous behavior can be observed a t bulk Reynolds numbers as low as 1200 to 1300. This is in substantial agreement with the results of some preliminary dye filament experiments reported by Rothfus and Prengle (11). In the latter investigation, thin filaments of aniline green dye were injected a t various points in the cross sections of two plastic tubes through which water was flowing. It was found that the first observable departure from laminar behavior occurred a t the center line of the tube and a t a bulk Reynolds number of 932. As the Reynolds number was increased above this value, the region of sinuous motion was observed to spread toward the tube walls a t such a rate that the velocity of the fluid a t the edge of the still-laminar layer followed the simple relationship I
Present address, E. I. du Pont de Nemours &
March 1955
co., Buffalo, N. Y ,
At Reynolds numbers between 1500 and 2100, there appeared to be a strong tendency to set up a stable spiral motion in the sinuous core of the fluid. At a Reynolds number of about 2100, the spiral motion was observed t o be replaced occasionally by a large disturbance eddy. The frequency with which the eddy was cast off increased with increasing Reynolds number until, a t a Reynolds number of about 3000, the eddy form became the stable one. The authors did not attempt to eliminate the effect of injector diameter on the flow characteristics. Therefore, the value of the right-hand side of Equation 1 was not firmly established, although the form of the expression appeared to be satisfactory. Lindgren ( 6 )recently studied the flow of birefringent bentonite suspensions in polished Plexiglas tubes and concluded that the basic flow was essentially laminar a t Reynolds numbers below 2900. Rare turbulent flashes were observed a t 2900 and complete turbulence was attained a t about 3600 Reynolds number. The bulk Reynolds numbers at which Lindgren reported changes in the flow regimes were somewhat too high to be consistent with the velocitv distribution and Dressure dror, data of Senecal and Rothfus (is) and others, Ii is possible- that only large dis-
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