Julv. 1927
INDUSTRIAL A N D ENGINEERING CHEMISTRY
809
Rate of Growth of Crystals in Aqueous Solution'" By G . H. Montillon and W. L. Badger ~ K I V E R S I T YO F
MICHIGAN, AKN
ARBOR,
MICH.
There has been a considerable discussion as to whether or not RYSTALLIZATIOS in commercial practice is cona crystal nucleus could form spontaneously, and no definite ducted in two principal ways. The first is the older conclusion has yet been reached. method of allowing a batch of strong, hot solution to Some work has been done on the rate of crystal growth after crystallize by slow cooling. The second and newer method nuclei have been formed. Le Blanc8 studied the rate of crystalconsists of continuous cooling of a stream of hot solution lization of potassium dichromate in aqueous solution. The as calculated from the equation with agitation so that the crystals are held in suspension velocity of crystallization dx = KS(C2 - CI) until the magma leaves the apparatus. I n attempting to design crystallizers for this method it was found that very where d x i d t is the rate of increase of weight, S is the surface little was known about the actual rate of growth of crystals exposed, C2 is the concentration of the saturated solution, and C,is the average concentraand t h i s i n v e s t i g a t i o n t i o n of the supersaturated marked the beginning of an solution. attempt t o supply that inA considerable amount of A n e w a p p a r a t u s has been designed a n d a new1method work was done by formation. h a s been developed f o r the s t u d y of c o n t i n u o u s crystal-
C
Previous Work
There is considerable work described in the literature on the mechanism of the formation of crystal nuclei. A useful picture of the origin of such crystals has been given by Von Weimarn.s H e assumes t h a t molecules, moving in the solution under the influence of convection currents or artificial agitation, form at intervals larger collections of molecules whose existence in unsaturated and saturated solutions is only momentary. Link' thought he could detect such nuclei a t the moment of seDaration. Von Weimarn further states that, since very small particles of any substance are always more soluble than larger particles, one must assume that, even in solutions supersaturated t o a limited extent, the existence of collections of molecules is transitory. With increasing supersaturation of the solution the concentration would be such as to be in equilibrium with the largest of these aggregates. They become stabilized and a t intervals become larger by the addition of new molecules. Owing t o this growth' the solubility of the particles decreases rapidly and the surrounding solution becomes very strongly supersaturated by them. The formation of further crystal centers is hindered when the supersaturation has been depressed to a level corresponding t o the unstable solid phase. As soon as the particles reach microscopic size the difference in solubility is usually inconsequential and there will exist only a small supersaturation t o act as a driving force for further growth. The mechanical action of velocity is important here, because it hinders diffusion and, therefore, the rapid exchange of particles in the solution in the immediate neighborhood of the crystal. Jones and Partington' have given a mathematical discussion of the supersaturation theory which agrees in principle with the above. An idea of the necessary size of such particles is obtained from the observations of Ostwald6 that in a saturated solution of sodium chlorate 10-9 gram was capable of crystal formation. This corresponds to a radius of 10 microns. McIntosh' says t h a t the weight of particles which induce crystallization of supersaturated solutions of sodium sulfate were found to be to 10-'8 gram in one case and lo-'? to 10-1' in another. Received March 17, 1927. Presented before the Division of Industrial and Engineering Chemistry at the 73rd Meeting of the American Chemical Society, Richmond, Va.. April 11 t o 16, 1927. A thesis submitted in partial fulfilment of the requirrmeDts for t h r degree of doctor of philosophy a t the University of Michigan. "States of Matter," pp. 40, 150 (1914). P o g g . A n n . , 46, 258 (1839). Z . p h r s i k . Citem., 88, 291 (1914). "Lehrbuch der allgemeinen Chemie." Vol. 11, 2nd ed., p. 7 5 4 . 7 Trans. Roy. SOC.Cuin., 111, l S , 265 (1919).
'
He inoculated a supersaturated solution of potassium sulfate with very fine seed crystals, keeping the solution rapidly stirred. Lnder these circumstances the velocity of crystallization appeared to follow the laws of a reaction of the second order. He first used the equation given by LeBlanc above, and later modified it t o conform to a second order equation. Marc's work has been criticized by \Vagner,lO the discussion centering largely on the calculation of surface area. Jenkinsll carried on similar w o r k , which is mentioned later in this article. The principal d i f f i c u l t y with Marc's work is that his values for K vary over a considerable range. Campbell'* has shown that it is almost impossible for two crystals to grow a t the same rate even when they a r e symmetrically placed i n a solution. whereas Marc assumed that all the crystals grew a t the same rate. Kucharenko'J has investigated the crystallization of sucrose. H e experimented with large, individual, perfect crystals in solutions of known degree of supersaturation. He expressed his results in terms of increase in weight in milligrams per square meter per minute and found that this rate of growth varied with temperature, velocity, and degree of saturation. If these were all kept constant, a n equal rate of growth per unit of surface would mean that a large crystal would increase more in absolute weight but less in relative weight than a small one. Kucharenko's work, though very extensive, is not strictly comparable with the problem in hand, because supersaturated sucrose solutions are easily prepared and their degree of supersaturation may be measured; whereas this is not true of ordinary inorganic solutions,
l i z a t i o n of a q u e o u s solutions. The a c t i o n of s o d i u m s u l f a t e a n d m a g n e s i u m s u l f a t e in t h e c o n t i n u o u s crystallizer has been s t u d i e d q u a n t i tatively in the t e m p e r a t u r e r a n g e of 27" to 31' C. I t has been s h o w n that t h e r e i s a definite r e l a t i o n bet w e e n the weight of m a t e r i a l crystaIlized a n d t h e n e w s u r f a c e generated d u r i n g that crystallization u n d e r definite c o n d i t i o n s of c o n c e n t r a t i o n changes. T h e probable effects of variation of this r e l a t i o n d u e to c h a n g e s i n t e m p e r a t u r e a n d viscosity have been indicated. A m e t h o d f o r t h e application of the d a t a on t h e variat i o n of weight a n d s u r f a c e of crystals u n d e r given cond i t i o n s t o the prediction of the a p p r o x i m a t e size of p r o d u c t has been devised.
EXPERIMENTAL
It would therefore seem desirable t o determine the rate at which a crystal of some common inorganic substance would grow when kept in suspension in a moving solution which was a t the same time being cooled regularly. Because it would be difficult to accomplish this with a single crystal of Considerable size, it was decided to work with a large number of crystals of known size and t o determine the factors affecting their rate of growth. Z. pi7ysik. Chem., 77, 614 (1911). I b i d . , 61, 355 (1907); 67, 470, 640 (1908); 68, 104 (1908); 73, 685 (1909). I b i d . . 71, 401 (1910); Z. Eleklrochcm., 17, 989 (1911). 11 J . A m . Chem. S o r . , 47, 903 (1925). J . Chem. SOC.(London), 107T, 476 (1915). Louisiana Planter, 71, 211, 231 (1923).
810
1NDUSTRIAL AND ENGINEERING CHEMISTRY Description of Apparatus
The apparatus, all stationary parts of which are of glass, is shown in Figures 1 and 2. It consists of a saturator, A , nearly filled with crystals, through which heated, undersaturated liquid passes downward to make as long a path as possible to the outlet of the vessel, which is surrounded by a 40-mesh monel metal screen, U . The temperature of the liquid in A is maintained by the hot-point immersion heater, HI, of 500 watts capacity, which is controlled by
DIAGRAM
Vol. 19, No. 7
The temperature of the crystallizer is maintained by blowing compressed air of suitable temperature between the outer wall of the tube and the air jacket F, as it is necessary to cool the solution slowly and uniformly and to avoid local cooling. The spiral stirrer, which was revolved by a motor, M , acting through a speed reducer, G, was turned a t 9.5 to 12 r. p. m., and not only agitated the solution but also slowly conveyed the growing crystals to the discharge pipe a t 0. A salt leg was provided at 0 by means of large-size glass and rubber tubing. The clamps KI and Kz allowed the easy removal of the crystalline material. The impoverished solution flowed from the top of the tube to the outlet pipe, Y , which was provided with a resistance heater of 150 watts capacity, H4. The temperature of the heater was regulated by the lamp-bank resistance RI in parallel with the slide-wire resistance RI. This method of heating immediately after the solution had left the crystallizer prevented any stoppage in the return line and insured smooth operation of the Pyrex pump P, This pump was a
OF A P P A R A T U S
Figure 1
the thermostat TI in the mixing vessel B. The temperature of the saturated solution leaving A and being siphoned into B is kept about as high as desired in C. The mixing vessel B provides a supply of slightly supersaturated solution to the vessel C. The temperature of the liquid in B is held constant by the 60-watt heater H2 in circuit with the thermostat TI. The liquid in B is agitated by the stirrer L. The liquid from B passes through a fine-mesh cloth filter a t J to prevent any chance introduction of nuclei. The vessel C is heated by the 60-watt heater Hs controlled by the thermostat T z . The liquid is agitated by the stirrer L, and the temperature is held a t such a point that crystallization barely starts before the nuclei enter the crystallizer proper, D. A weighed number of sized seed crystals are added to C every 5 minutes. The crystallizer D is a 3-inch (76-mm.) Pyrex tube about 5.5 feet (1.7 meters) long, set with a slope of 1 inch (25 mm.) throughout its length. The ends of the tube are closed by brass plates held in place by four steel tension rods 3/16 inch (4 mm.) in diameter. The nuclei are kept suspended in the solution by the agitation produced by a spiral stirrer of copper and brass. This stirrer is smaller in diameter than the tube, and is finished with a 0.5-inch (13-mm.) rubber ribbon which on turning maintains continuous contact with the Pyrex tube. The ribbon itself makes two turns in 5 feet (1.7 meters). Attrition is almost entirely prevented by the use of the flexible rubber ribbon while a t the same time effective agitation is produced. The shaft of the stirrer is supported by bearings in each of the brass plates a t the ends of the tube and by a specially constructed central bearing held in place by brass spring clips.
single-cylinder reciprocating pump, operated by an adjustable eccentric, E, rotated by a moto-, M . A cone pulley on a n intermediate shaft driven by the motor allowed a speed variation in individual runs such as to produce a pump discharge of from 128 to over 200 cc. oc solution a minute. The piston consisted of a rubber cylinder held in place on the piston rod by brass rings. The valve seats were rubber cylinders with openings controlled by glass ball valves. It was found after adjustments had been made that very uniform flow of solution could be maintained with this pump. Comparison of Batch Method with Continuous Method
A continuous method of procedure was chosen because in this method constant terminal conditions may be maintained, whereas in the batch method all conditions would vary. A series of ,preliminary experiments in a small batch apparatus showed that this theoretical reasoning was correct. For example, results with the batch method, using 3 liters of sodium sulfate solution saturated a t 30" C., stirred with a propeller-type stirrer a t 160 r. p. m. in the presence of 10 grams of 35-mesh seed crystals and cooled at the rate of 0.5" C. per hour, gave results which varied from the mean by -8.8 per cent to f5.9 per cent. That the batch method is subject to variations in rate which are difficult to control has been shown by Jenkins,14 who studied the effect of initial supersaturation upon the velocity of crystallization. His calculation of the average 14
J . A m Chkm S o c , 47, 903 (1926).
1NL)I;STRIAL S N D ENGINEERING CI€EMlSTRY
July, 1027
vclucity of crystallisution of ammonium nitrate sliows that with an initial supersaturation of 1.00 gram per 100 cc. of solution, a bath temperature of 0.10" C., a stirring rate of 1000 r. p. m., and aii amount of seed crystals of 1.0 gram per 100 cc., the following constants, calculated over a total period of about 2 minutes, were obtained: 162, 161, 168, 176, 166, 163, 162, 152, 160. The average is 164; the maximum deviation, i 7 . 9 per cent. WdteridlS Sodium sulfate and magnesium sulfate were prepared for use by dissolving the commercial sslts in water, aerating a t the boiling temperature to oxidize any iron present, and filtering with Filter-eel to remove any suspended solid material. From the clear solutions thus obtained the material was recrystallized for use. PKOPERTIES OF Na2S04-l'he solubility of soditmi sulfate in the range oi 20" to 32" C. wm taken from the recently determined values of Richards.'b The Following equation expressed the solubility relation very closely:
811
+
X = 1.2210 0.003471, whew t is the trrnperature (3) The solubility and specific gravity curve6 are given iii Figure 4. Preparation of Seed Crystals Seed crystals were prepared by using the material which gassed through a. 28-mesh and was retained on a 35-mesh Tyler standard screen. In these screens the successive 1.414 4: openings have a ratio of -= -, so that each successivf: 1 1
Let X = grams KazSOI per 100 grams of solution, and t = tetnperature in degrees Centigrade. Then = 10.102 - 0.a7145t t 0.0336t' (1)
x
The density values oi sodium sulfate solutions were taken from those of the Earl oi Rerkclcy" and Dawson and Williams." The solubility and specific gravity curves are given in Figure 3. PROPERTIES OF M@04 -Tim solubility of magnesium sulfate in the raiigc 0" to 10* C. >
