INDUSTRIAL A N D ENGIiYEERI,VG CHEMISTRY
670
quired for cubical packing tends to flow into the track made by the stirrer, more or less of the remaining paste assuming a condition of tetrahedral packing. Inverted plasticity might appear under such circumstances when the shearing stress was great enough to cause relative movement of the particles in the regions where they are packed more closely than those in cubical piling. This critical shearing stress might also be expected to increase with decrease in concentration of the dispersed phase. As a matter of fact, curve I, Figure 2, obtained with a purely viscous liquid (60 per cent sucrose), bends slightly convex to the stress axis, so that the unique portion of the inverted plasticity curves is that part where the rate of stirring remains essentially constant, independent of the shearing stress. One of the writers has attempted to account for this in the following manner: It is known that the particles in starch-water suspensions are well dispersed and closely assembled. It would not seem improbable that initial motion of the paddles would cause most of the particles in its immediate vicinity to arrange themselves in more or less concentric shells, with most of the shear taking place in the liquid between “shells.” It is difficult t o conceive of any appreciable rate of shear in a closely packed dispersion of particles, separated from each other by less than one-tenth of their diameter, unless some orderly arrangement of particles is obtained. As the rate of shear is increased, the shearing stress between shells would also increase, until finally it might be expected to reach a value capable of pulling particles from the adjoining layer. This would disrupt the orderly flow. The innermost “shells” would lose their identity and seize to the stirrer. The zone of shearing would then spread to outer shells of increased diameter and require an increase in total shearing stress to maintain the same rate of shear between shells.
Vol. 23, No. 6
The postulate of a critical disrupting force between ‘‘shells,” together with the laws of viscous flow, would demand a linear relationship between the critical rate of stirring and the average distance between particles. This is what was actually found by experiment. Furthermore, this mechanism may account for the failure to observe the property of inverted plasticity with the Murray-Bingham plastometer. It is a well-established fact that laminar flow takes place when liquids are passed through small capillaries. Both the manner in which shearing stress is applied and the shape of the container conspire t o preserve this orderly, laminar type of flow. Under these conditions “seizure” of adjoining layers would probably only occur a t much higher rates of shearbeyond the range of these experiments. A method for testing this mechanism has been planned but as yet has not been carried out. Recently a somewhat different type of flow has been observed which deserves a little description. When needleshaped CaSO4.2H20 was stirred into a small amount of water, a dispersion was obtained which alternately “seized” and then “released” a spatula which was stirred through the mass. It appears quite certain that this modified form of inverted plasticity is definitely connected with the needle shape of the particles. The phenomenon was only observed in certain cases where the needle-shaped characteristics were very marked (a sample of Baker’s precipitated CaS04.2H20). More finely divided calcium sulfate did not show the phenomenon. Literature Cited (1) Mead, W, J., J . Geol., 33, No. 7 (1925). (2) Reynolds, Osborne, “Scientific Papers, Vol. 11, p. 217 (1901); Phil. M a g . , Dec., 1885; Proc. Roy. I n s ! . , Feb., 1886; Nature, 33, 30 (1901). (3) Williamson, R . V , I N D . E N D . CHEM., 21, 1108 (1929).
Speed of Crystallization of Lactose, Galactose, Glucose, and Sucrose from Pure Solution’ E. 0. Whittier and S. P. Gould RESEARCH LABORATORIES, BUREAUOF DAIRYINDUSTRY,
N T H E course of work on the manufacture of lactose it became necessary to know the effect of differences of temperature on the s p e e d of its crystallization. Galactose and glucose were included in the investigation because of their constituent relationship t o lactose; sucrose, because it is not a mutarotating sugar, was included for purposes of cornprison.
I
20”
c.
The most striking conclusions drawn from previous work on speed of crystallization of sucrose are: (1) that it is imPossible to correlate velocity and viscosity (3); (2) that the Velocity Of CryStalliZatiOn increases with speed Of agitation UP to 400 r. p. m., above which it is no longer iduenced by December 6, 1930.
D. C.
change in this factor (8); and (3) that the velocity of cryp t a l l i z a t i o n v a r i e s as the s q u a r e of the a m o u n t of supersaturation (4). These conclusions are based on observations on the growth of individual crystals. No work appears to have been published on the crystallization rates of galactose and glucose. The course of crystallization of lactose from a 60 per cent s o l u t i o n a t s e v e r a l temperatures has been calculated and plotted by Sharp (7) for the later stages on the assumption that the rate of p + change is the sole determining factor at this time. If the amount of ,plactose initially representing supersaturation to the alpha form crystallized instantaneously a t the time plotted by Sharp as 0 hours, his calculated values should agree with experimentally determined values, provided that viscosity and rate of stirring could be disregarded
The courses of crystallization Of lactose, galactose, glucose, and sucrose from pure solution have been followed by refractometric methods at temperatures from 0’ to 30’ C. and the velocity constants calculated. In the earlier stages Of CrYStallization of lactose, galactose, and glucose the rate of crystallization of the form separating is the principal contro!ling factor. Subsequently the rate is diminished considerably as the rate of attainment of equilibrium among the isomeric forms becomes the major determinant. The most rapid crystallization of lactose takes Place if the solution is maintained at or slightly above 30” C. for 3 hours and is then allowed to cool to approximately
Previous Work
1 Received
WASHINGTON,
IiVDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1931
d 9
\
4 v,
671
Crystui//zatron of Lactose , a f Various Temperatures
T/me
- Minutes
Figure 1
\9 c
*@
c-ysrul/ization of Glucose Yottaus Temperatures
J t
Erne -Minutes
Time
- Minures
0
Figure 3
Figure 4
or correction made for them. It is not to be expected, however, that lactose would crystallize a t room temperature with the suddenness characteristic of its supersaturated solutions near the boiling point. Furthermore, the change from a crystallization actuated solely by the tendency of excess a-lactose to crystallize to one controlled entirely by /3 --+ a change is not an abrupt one. The course of the process is further complicated by the fact that, as long as the degree of supersaturation t o a-lactose is varying, so long is there a varying amount of a + p change opposing the /3 .--) a change. Sharp's calculations are therefore more of theoretical than of practical interest. Hudson ( 1 ) somewhat earlier obtained data on the rate of crystallization of lactose a t 0" C. Since he was interested primarily in the determination of the value of the rate constant for the /3 --+ a change, he allowed crystallization to take place for about 20 minutes before beginning his measurements in order t o eliminate as far as possible the effect of the initial precipitation. He obtained values for the constant in satisfactory agreement with those which he obtained from measurement of maximum rate of solution. He states that the small difference observed was probably due to the fact that the rate of the physical precipitation was not great enough to keep the solution from becoming somewhat supersaturated. Several measurements of the velocity constant of crystallization of lactose a t 30" C. have been made by Jenkins (2), both from pure solution and from solutions made alkaline with ammonium hydroxide. As might be expected from the effect of hydroxyl ions on the rate of attainment of a+ equilibrium, the presence of ammonium hydroxide accelerated the crystallization.
The course of crystallization was followed by means of successive refractometer readings on the solutions from which the sugars were crystallizing. The method was essentially that employed by Jenkins (6). An Abbe type refractometer, recently calibrated by the Bureau of Standards, was used. Water a t 30" C. was circulated through the jacket and all readings were taken a t that temperature. Charts for conversion of refractometer readings to percentage sugar were prepared on the basis of readings made on sugar solutions of known concentrations. The crystallizations were carried out in a 250-cc. widemouthed Erlenmeyer flask, the stopper of which was fitted with a glass stirrer. The flask was immersed in a thermostat kept a t the desired temperature * 0.02" C. The rate of stirring during crystallization was always above 400 r. p. m. The solutions were prepared a t approximately the boiling point and were then allowed to cool t o the temperature of the thermostat. The initial concentration of each was determined by making a refractometer reading on a few drops of the solution. Five grams of fine seed crystals were then added for each 100 grams of solution and the stirring was started simultaneously. The time of adding the crystals and the time of taking each subsequent sample were noted. A pipet attached to the laboratory vacuum line and fitted a t the lower end with a short section of rubber tubing containing a wad of cotton was used to filter and draw off the few drops required for each determination. I n only a few cases did crystals pass the filter or form in the sample after removal. These cases were easily detected by the appearance of spectrum colors when the sample was being examined in the refractometer. Readings were not taken on such samples. Samples were taken every few minutes a t first, while the crystallization was proceeding a t a rapid rate, but less often as the rate became slower. At the lower temperatures solutions of less degree of initial supersaturation were used
Method
Sugars of high degree of purity were used. The d-lactose was the a-monohydrate, the d-galactose was the a-anhydride; the &glucose was the a-anhydride.
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
672
because of difficulty of sampling due to high viscosities. This was particularly bothersome in the solutions of glucose and aucrose. Only a few readings were possible on lactose solutions a t -5" C., because after a short time ice began to separate. Saturation values were obtained a t each temperature by allowing solutions to remain in the thermostat until several constant readings were found. For lactose a t -5" C. it was necessary to extrapolate from saturation values a t higher temperatures. Rote
4 C&all~zlzoflofl of Lactose a t Various Temperafures I
I
would require months below 0" C. to ciystallize as much lactose as could be obtained in a few hours a t 25" or 30" C. It appears from the results of Parisi (6) that addition of alkali would not greatly increase the efficiency of crystallization a t the lower temperature unless added in extremely large quantities. Calculation of Velocity Constants
In order to evaluate crystallization velocities relative to degree of supersaturation possible with the different sugars and a t the different temperatures, velocity constants of all the runs were calculated and mean values plotted against temperature (Figure 6). Values for the early and late portions of each run were discarded, since they invariably showed extreme variations from the means. Calculations were based on the integrated form of the Noyes and Whitney equation for velocity of solution (6))
K =
Time -Minutes Figure 5
r:,,The H-ion concentrations of the solutions were not stable owing to lack of buffer. Potentiometric measurements indicated that the pH value in no case exceeded 7.0 and in only a few cases fell below p H 6.0.
1 CI 0.4343 S(t2 - t l ) log
c,
in which K is the velocity constant, S is the mean surface area of the crystal or crystals, C1is taken as the concentration of the solution a t time tl, CZ as the concentration a t time t2, and C, the concentration a t saturation or time t m . Jenkins ( 2 ) introduces into this equation an expression for correcting for the change in surface area during time tz - tl. The present writers calculated values of K from their data both by use of Jenkins' corrected formula and by use of the form given above in which S was assumed to be constant and equal to unity. Much better agreement of the successive values in any run
Course of Crystallization
Determinations were carried out on the four sugars a t 30", 25", 20°, 15", IO", and 0" C. and on lactose a t -5" C. The courses of the crystallizations may be followed in Figures 1 to 4. At least two runs were made for each sugar a t each temperature, representative runs being selected to furnish data for the curves. Perhaps the most striking fact from the practical standpoint is that, in the temperature range covered, the higher the temperature the greater is the quantity of lactose crystallized in 1 to 5 hours, in spite of the fact that its solubility decreases with the temperature. A similar situation is brought out for galactose in a less striking degree. The relationship of amount of crystallization t o temperature is the reverse for glucose. It is reasonable to suppose that the extreme and variable viscosities of the glucose and sucrose solutions have a considerable effect on the course of crystallization of these sugars. Rate of Crystallization
The rate of crystallization of lactose is plotted against time in Figure 5. A study of this figure, along with Figure 1, shows how effectively lowering of temperature retards the later stages of crystallization. At first, when the crystallization of the a-lactose in excess of that required for saturation is the major factor, differences in temperature appear to be of minor importance. Thereafter, as the rate of p-+ a! change becomes the major factor, temperature becomes of considerable importance. Without considering any higher temperatures, it appears that the most efficient crystallization would be obtained by holding the solution a t 30" C. for approximately 3 hours, then cooling it gradually to near 20" C., and holding it a t that temperature for as long as is otherwise practical before filtering off the lactose. There is an evident disadvantage in cooling the solution below 20" C.in the first 12 hours of crystallization. The advantage of lessened solubility a t lower temperatures is more than offset by the decrease in the rate of the p + a! change. It
I/elociti. Cons font of Crystu/hzQlm~ = Sucrose f = Galarfose x = Glucose
TeTDerature + "C
Figure 6
was obtained when the uncorrected formula was used. One explanation for this is that, with agitation sufficiently rapid to maintain the layer of solution in contact with the crystals a t practically the concentration of the rest of the solution, the variation in actual area becomes of negligible importance in comparison with other factors. It should also be noted that the method of applying corrections for varying surface area presupposes that the crystallization process is a growth of crystals already present. It is common experience that, in seeding a highly supersaturated solution, large numbers of new crystal nuclei form. Inasmuch as for the mutarotating sugars the crystallization curve is the resultant of merging two distinct overlapping curves, one of the crystallization of the form actually separating and the other the curve of equilibration of the isomeric forms, it is perhaps surprising that the values of K should be a t all constant. The first one or two constants for these sugars were high in every run and probably express roughly the velocity of the simple crystallization. These high values
June, 1931
INDUSTRIAL A N D ENGINEERING CHEMISTRY
were not included in the calculation of the mean values plotted in Figure 6. Presumably the velocity-constant curve for crystallization of sucrose is typical of what may be expected for sugars when isomeric changes are not involved. The curves for lactose and galactose appear to involve mainly the effects of isomerism. In the case of glucose, some additional influence evidently comes into play, as manifested by the difference in slope of the curve above and below 20' C. It should be mentioned that additional runs on glucose a t 20" C. were made in an effort to discover possible errors in the earlier runs. The earlier results were confirmed.
673
Literature Cited (1) Hudson, J . A m . Chem. Soc., 26, 1065 (1994). (2) Jenkins, Ibid., 47, 903 (1925). (3) Kucharenko and Kartashev, Nauch. Zapiski Sakharnoi Prom., 5, 177 (1927); C. A . , 22, 1490 (1928). (4) Kucharenko and Nachmanowitsch, Nnuch. Zapiski Sakharnoi Prom., 2, 173 (1924); Cenlr. Zuckerind., 33, 1609 (1925). (5) Noyes and Whitney, Z . p h y s i k . Chem., 83, 689 (1897). (6) Parisi, Giorn. chim. ind. a p p l i c a f a , 12, 225 (193G). (7) Rahn and Sharp, "Physik der hlilkwirtschaft," pp. 151-4, Paul Parey, Berlin, 1928. ( 8 ) Savinov, Nauch. Zapiski Sakharnoi Prom., 7, 416 (1929); C. A . , 23, 3825 (1929).
Viscosity-Tempera ture Relationship of Lubricating Oils' R. G. Sloane and Carl Winning STANDARD 0x1.DEVELOPMENT COMPANY, ELIZABETII, N. J.
T IS standard practice in this country to determine viscosities of lubricating oils a t temperatures of loo", 130", and 210' F. (37.8",51.4",and 98.9" C.) However, the viscosity at some other temperature is often required. Pumping effort and fluid-film friction are functions of the viscosity a t the temperature in question, and this temperature may be such as to make viscosity determination inconvenient or impossible with the usual Saybolt viscometer. I n such cases it is very helpful to be able to obtain the viscosities mathematically or graphically by extrapolation from known values. Most of the graphical methods devised comprise plotting viscosity versus temperature on such a system of coordinates that a straight line is obtained. Since no mathematical expression has yet been given to these coordinate systems, they are not easily reproduced and a market has consequently developed for such ready printed forms as those of MacCoull ( I O ) and Herschel ( 7 ) ,which permit the desired linear plotting. Naturally the forms have not always covered the desired range and they have on occasion been extended, as by Larson
I
(9)
Extrapolation on such charts over wide temperature ranges based on viscosities a t 100" and 210" F. (37.8' and 98.9" C.) may give viscosity data greatly in error and figures so obtained can be considered approximations of only a low order. This misfortune cannot be avoided. The charts are more valuable for coordinating viscosity data secured over a wide range of temperatures by special instruments, and it is in this service that most of the published accounts have appeared
plot could be obtained. If such a relation could be found it would free the worker from printed forms, which are often either not available or not adapted to the particular problem. Many equations have been written to express the variation of viscosity with temperature, such as:
++ +
log q = A log (t B) C (5, 6 ) log log 9 = At B (14)
(1) (2)
but they are generally applicable only t o a limited temperature range. The relation (3)
has been shown by Bingham ( 2 ) to possess a high degree of accuracy, but it is too involved for graphical representation. The writers finally turned to a modification of the Vogel equation (7, I S ) : (log q k - A ) ( t
-
B)
=
c
(4)
(3, Q l 15).
where q k is the kinematic viscosity. \Then tested on a number of oils over a wide temperature range, calculated values in good accord with the experimental data were obtained. Unfortunately, the equation contains three constants, and since a method of linear plotting was desired, only two constants, which vary from oil to oil, could be tolerated. A , B , and C were therefore calculated for ten oils on which very accurate viscosity data were available, in the hope that one of them might be common to all oils.
Since to set up a chart based on this information requires accurate viscosity-temperature data on a number of oils besides considerable time and patience, an attempt was made t o find a simple mathematical expression by which a linear
ivote-Three different types of viscometers were used in obtaining the above data, the choice being based on convenience in handling. At moderate temperatures a Saybolt Universal viscometer was used. For viscosities at high temperatures a capillary viscometer as described by Upton (12) was used. This instrument permits of easy and rapid determinations with increasing temperatures. The specific gravities required to compute the viscosities were calculated from the gravities at 60" F. using the Bureau of Standards formula ( I ) . For the high viscosities obtained at low temperatures it was necessary to employ greater pressures than could he applied to the Upton viscometer; a special instrument was therefore designed for this work. This viscometer, resembling somewhat a Saybolt instrument, was closed at the top to permit the application of pressure and was provided with a long glass capillary at the bottom through which the oil was forced. The viscosities were calculated from constants of the capillary together with the amount of oil discharged in a given time.
1 Received March 17, 1931 Presented before the Division of Petroleum Chemistry at the 81st Meeting of the American Chemical Society, Indianapolis, Ind March 30 to April 3 1931.
The least variation was found in B, but, as Table I shows, even this leaves much to be desired. However, the average
The coordinate systems in common use are apparently based on the observations of Porter (11) that if the temperatures a t which two oils have identical viscosities are plotted against each other a straight line will result. From this relation it follows that if the coordinates are so adjusted that one oil appears as a straight line all others will also give linear relationships. Proposed Method
