1290
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
freezing properties alone the following rough classification could be made: Good: benzene, toluene, xylene, carbon tetrachloride, amyl acetate, ethyl acetate, na htha, butyl alcohol. Intermediate: methyy alcohol, ethyl alcohol, isopropyl alcohol, water. Bad: chloroform, acetone, methyl ethyl ketone, ethyl ether, cyclopentanone, cyclohexanone, ethylene glycol, glycerol. (The last two are viscous.) Another method involves t,he addition of a hot solution to a diluent slorvly and with stirring. Solvents are best when the solubility of the solute in the boiling solvent is of the order of 2 t o 10% w/v. I n any method to make fine sizes, an optimum size for any set of conditions will be found empirically. This size may be altered somewhat by a change in the scale of operations but not radically. A determining factor in the choice may be thc cost of solvents. Solvent, loss is low in the dry ice process, hut with solvent mixtures, solvent recovery may be necessary.
gree of elongation of crystals, but the extent and direction of this effect depend on the nature of the solvent. The effect of slow stirring in slow cooling is complex. A slowly stirred solution t,ends to give flatter crystals than either a quickly stirred or an unstirred solution. There may be an optimum condition of centrifugal motion for this effect, as indicated by the centrifuge experiments for nitroguanidine shown in Table VIII. With pebble milling neither the shape nor the range of shapes can be controlled or predicted. The effect of heat transfer am1 stirring on shape is shown i n Tables I V to XII. R E P K O I ~ C C I R I L I T YO F RESULTS
Some indication of the reproducibility of results is shown i n Table XIII. Range sizes 011 the basis of 95 and 997, corificicmcr limits are shown, calculated froin the t distribution ( I ), These results may bc considered t:ipical for materials made by similar processes. LITERATURE CITED (1) Snedecor, G. W., “ S t a t i s t i c a l
\IODIFICATIOh OF CRYST&L SHAPE
The shape of crystals is in most cases affected by the mode of cooling. Generally the rate of heat excharige will govern the de-
Vol. 41, No. 6
State
Methods,” pp. 62-5,
Arrics. Iowa
College Press, 1946.
RECEIVED April 2 8 , 1948. Prevented before t h e Division of Indu3criaI and Engineering Chemistry a t the 113th Meeting of the AMXRICANC I I X ~ I I C A I ~ SOCIETY,Chicago, Ill. I-’ublished by permisvion of the Directiw, L7, S . Bureau of Mines.
Temperat re Gradients an iffusivities in Turbulent Flui ROBERT J. MCCARTER, LEROY F. STUTZMAN, AND HOW-4RD A. KOCH, JR. ATorthwestern Technological I n s t i t u l e , Ezunston, I l l .
An outline of turbulent flow theory is presented and its relation to problems of diffusivit? discussed. Elementary equations for the process of diffusion are derived and applied in the correlation of data. The equipment and e x perimental procedure are described for two methods of determining the dimensional value of eddy diflusivit> in turbulent gas flow by studies of thermal energy transfer. Experiments were conducted in a vertical %inch diameter steel duct with flow velocities ranging from 2 to 7 feet per second. Preliminary results obtained indicate ranges of diffusivitj for certain conditions of turbulence from which qualitative deductions may be made regarding the factors influencing diffusion and mixing. These methods olYer a possibility for a simple and useful tool in the investigation of turbulent fl6w and transfer problems.
E
DDY diffusivit,y or the tendency of a fluid in turbulent flow to disperse material, energy, momentum, or other intensive property is a fundamental factor in several unit operations such as heat transfer, mixing, extraction, and absorption. Diffusivities are particularly basic t o gas absorption, and a more exact knowledge of the nature and magnitude of eddy diffusivity might be utilized to reduce the uncertainties in the application of gas absorption theory t o cases where transfer rates are dependent on both molccular and eddy diff usivities, Therefore, the objective of this investigation was to examine possible methods for measuring eddy diffusivities, t o determine these diffusivities under measured flow conditions, and t o at,tempt to evaluate the factors that influence eddy diffusivity.
G E N E R A L THEORY
11any investigators have explored the analogies between material, moment,uni, and thermal energy t’ransfers Tvithin flowing fluids. Ton-le and Sherwood (12, I S ) , and Sherwooci and TIToertz ( 6 ) have studied diffusion in gas streams and have shown that eddy diffusion is analogous t o molecular diffusion although the eddy diffusivity coefficient is considerably larger. They hypothesized that, an eddy diffusivit,y, De, could be defined for t u r h u l m t Hon- by the equation:
~ v h e Qi ~= rate of transfer of any transferable property per unit area, and dcidy = concent,ration gradient of the property in t h r diffusion direction. Kaliriske and eo-n-orlters (2, 3) found that the distribution of concentrations of injected ~naterialperpendicular to the flow of water in a n opcn channel followed the normal error Ian which is the Fi‘tme type of distribut’ion predicted by diffusion theory. Stutzman ( 7 ) derived a more rigorous equation based on the assumptions fundamental to niolecular diffusion for a p,rocc:ss in which a dye was introduced into the cent,er of a circular pipe in which n-ater was flowing under turbulent conditions. Hi-i experimental data were in agreement Kith the equation and indicated the analogy between molecular and eddy diffusion. Prandt,l (j), Taylor (8-11), arid von Karman ( d ) , have macle fundamental contributions to turbulent flow theory and have advanced the concept. of dividing eddy diffusivity (longth squared per time) into two parameters, intensity of turt)ul(,nce (length per time) and miring length (length).
Intensity of turbulence is defined as the mean square value of the instantaneous secondary velocities perpendicular to the mean flow. Mixing length is a statistical average length that has been described as the average distance through which any transferable property of fluid flows transverse to the mean flow until that property assumes, the characteristics of the surrounding fluid. An elementary description of this theory would be to postulate that a fluid in turbulent flow behaves as if i t were composed of small temporarily distinguishable masses of fluid that proceeded in a sequence of random jumps, with the velocity of t h e jumps representative of intensity of turbulence, and the length of the jumps representative of the mixing length. Then, the dispersing tendency or eddy diffusivity would be equal to the product of the velocity of the jumps and the length of the jumps. Thus Prandtl ( 1 , 6) proposed the alteration of Equation 1 to:
where Q = rate of transfer of any transferable property per unit area; = root mean square of the secondaryvelocity transient to the main flow; 1, = Prandtl’s mixing length; and dc/dy = conrentration gradient of the property in the diffusion direction. Taylor (8-11) proposed a correlation derived by statistical methods which is analogous to Prandtl’s mixing length. For his correlation Taylor proposed the term, scale of turbulence, which was defined as:
472
12
=
/
Rudy
J O
zaab/dzd2;
where li = scale of turbulence; R, = u, and uh = vectorial velocjties a t points a and b which are y distance apart; and k’ = distance of y where R, = 0. METHOD I.
1291
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune 1949
DIFFUSION OF THERMAL ENERGY BETWEEN GAS STREAMS
The first method was analogous to previous material diffusion methods where diffusible matter is introduced into the center of a turbulently flowing fluid in a circular duct. A stream of hot air was introduced through an insulated pipe to the center of a flow of turbulent air, and the thermal energy dispersion determined by means of temperature measurements. This method offered simplicity, adaptability, and ease of gradient determinations. Calculations indicated that transfer by thermal conductivity in air was negligible in comparison to t h a t by eddy diffusion in the range of turbulence studied. APPARATUS. The schematic arrangement and the significant dimensions of the apparatus as used with the first method are presented in Figure 1. Calibrated orifices were employed t o measure and globe valves to adjust the air s t r e a m t o the same linear velocity of flow at the introduction into the mixing section. The tube introducing the hot air stream was fabricated from 19and 25-mm. outside diameter glass tubing to form a vacuuni jacket. The walls were silvered and the exit end smoothed and tapered to a sharp edge. A self-centering probe with thermocouples affixed at set radial distances and adjustable t o any height in the mixing section of the column was used t o determine the space-temperature relation of the mixing process. Standard fine-wire copper-constantan thermocouples and Type K Leeds and Northrup potentiometer were employed to allow comparative temperature measurement to a n accuracy of 0.1 * F. AMLYSIS OF METHOD. Based on the postulated mechanism of a property being transferred in small masses making numerous small jumps in random directions, it is logical to predict the distribution of the property after any period of time with the normal
THERMOCOUPLE HOLDER a PROBE
... I.......
..........
’ t SCREEN
TUBE
4 FT. GENERALIZING SECTION
L
HOT AIR AIIR REGULATORY
/
I H.i? BLOWER BLOWER DISCHARGE DIFFERENTIAL MANOMETERS
Figure 1. Schematic Diagram of Apparatus
(Method I)
error curve. This would be comparable in mechanism and correlation to Galton’s quincunx where shot pours down a pattern of deflectors and collects in a series of bins in an approximation to the normal error curve. Thus, if the property were released from a plane in space and were diffusing unidirectionally, it would be predicted that : u2
fo = -=e
1
d2TU
- -2c2
(4)
where fc = fraction of total property per unit length; u = standard deviation or the square root of the mean square value of distance traversed from the origin plane by individual masses of property; and y = distance from plane of origin. Since the total integrated value of the normal error curve over its linear range is unity, it follows from a property balance that :
(5) where c = concentration per unit length; co = a constant equal to the integrated value of concentration over its linear range in y a t any time. From the application of the original definition of diffusivity to an infinitesimal cube within a space of unidirectional diffusion, it may be derived by a property balance that:
where c = concentration of a property, e = time, and y = distance from the plane of origin. Then if the assumption is made that u2 equals the product of some constant and time, it will be found by differentiation of Equation 5 that the simultaneous solution with Equation 6 yields ~2 = 2 DO. This is in agreement with Einstein’s derivation for molecular diffusion that:
1292
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY (7)
where Y z = mean square of particle travel, molecular diffusivity. Therefore, the equation:
e
= time, and
D
ETould be applicahle to the case of diffusion in a turbulent stream where the property diffusing is uniformly introduced in a line across the flow, and the velocity of flov is such that diffusion effects in the flow direction are negligible. If this system of analysis is then extended to two-dimensional diffusion from a line in space, and x and y designate distance from the origin line a t right angles to each other, it follows that:
and _ _Y2 l
e
2u;
~
d2&,
Thus, the equstion: ,. 2
=
112
fob) =
Vol. 41, No. 6
(10)
where the terms have their previous definitions as applied to the respective linear directions. Since the 1: and y ordinates are a t right angles, the random nature of the dispersion leaves the distributions in these two directions statistically independent and by the rules of conditional probabilitiej, the fraction probability density for any infinitesimal area in the zy plane vi11 he the product of the respective probabilities f ? ~ and ~ ) .fccILI) so that:
where,fc(,,,) = fraction of total property per unit area. If T represents the distance from the origin line, then r2 = z* y% and because of the complete randomness of the assumed motion, uz = u v = u7,then
+
is applicable to the analysis of the temperature-space data obtained by method I, where the velocity of flow is such t,hat the effects uf temperahre gradients in the direction of flow are negligible, and where diffusion has proceeded for a time sufficient for the normal error law to apply. For distances close t o t,he source, the equation is altered toward a linear correlation of logarithm concentration to radius. The concentration considered is heat units per unit volume and is evaluated hy degrees Fahrenheit of t,em p era t u r e a b o ve datum taken a t the temperature of t,he 0 I 2 main air stream a t the R' (IN?) introduction point to Figure 2. Typical Plot of mixing Radial Temperature Profile The origin of diffusion (Method I) is the axis of the duct; D is considered a constant' over the range of calculation; and 8 is the elapsed time of diffusion or the distance of flow from the introduction point divided by the average velocit,y of flow. Equation 15 cont,aining. the variables temperature c, time 8, and radius r may most simply be employed to evaluate the constant, D by analyzing the relation nhen any one of the variables is held constant hy selection. Thus, a radial temperature profile a t a specified height in the mixing sect'ion where e is a constant' allows a determination of D through a plot of logloc against T ' ~as in Figure 2. If the experimenta,] determinat,ions conform to theory, a linear relat,ion should be obtained with a slope equal to and an intercept of log
7 2
wheref,(,) = fraction of total property per unit area. Since the total integrated value of the normal error surface over its area range is unity, it follo~mfrom a property balance that:
where c = concentration per unit area, c1 = a constant equal to the integrated value of concentration over its area range in r a t any time. If a circular ring of unit length and differential thickness is taken concentric in a space of radial diffusion, the application of the definition of diffusivity results in the relations that:
If the assumption is again made that u2 equals the product of some constant and time, it will be found by differentiation of Equation 13 that the simultaneous solution with Equation 14 again yields ~2 = 208.
Similarly, with T a constant such as zero by selection, the equation indicates a linear relation. The diffusivity, D , may be evaluated by a plot of c against l / B where the indicated slope equals [ 4%]
and c1 equals the product of the cross-sectional area
of the hot air stream and the degrees Fahrenheit above datum of the stream at introduction. Table I gives the calculation of diffusivities by these correlations within the range of flow conditions permitted by the apparatus. The ranges of the better correlations are presented in Table I1 to summarize the effects of screens and flow velocity. METHOD 11.
DIFFUSION O F THERiMAL ENERGY FROM A SOLID INTO A GAS STREAM
APPARATVS.The same apparatus was employed as for method I with the elimination of the hot air stream and the subst'itution of a spiral Xichrome wire heating element centered in the axis of the mixing section of the column. Thermocouples on slip-tuhe mountings permitted temperature determinat,ions a t any radius a t four heights within the difFusion space. A schematic diagram of the apparatus is presented in Figure 3. ANALYSIS OF METHOD. The objective of this arrangement was the formation of ostensibly constant temperature gradient,s by means of a constant heat source parallel to the &earn flow. The
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
TABLE I. CALCULATION OF DIFFGSIVITIES-METHOD I screen. Mesh
Run No. 10 I1
None
93
10 I11
None
95
I
None
83
13
None
90
15
None
102
11
17 rI
None
108
18
None
101
19
None
98
I
40
96
22 I1
40
97
22
40
90
23
8
98
24
8
93
25
8
94
21
Initial Difference Flow between Velocity, Mixing Diffusivity, Streams, li (In./ Distance, D (Sq. F t . / x (In.) Hr.) O F. Sec.) 6 51.8 60.7 86 8 93 12 73.5 56.5 6 64.0 86 8 110 65 0 12 86 6 50.3 142 59.5 8 6 45.8 84 8 50.5 112 61.7 10 44.5 6 8 135 86 50.7 10 47.5 6 26.0 97 30.0 48 8 12 35.0 34 24 6 20.3 24.4 8 ’ 12.8 8 48 12 21.7 89 24.4 16 24 8 43 9.5 12 9.7 24.3 8 10 29.5 87 12 178 31.2 16 34.5 20 40.0 23.3 6 146 86 12 30.0 16 33.5 6 34.5 145 42.7 87 8 10 43.5 12 54.0 6 14.5 24 38 8 17.8 12 23.5 6 21.0 99 49 8 27.2 12 37.0
Datum Temp., F.
TABLE 11. METHOD Ia
uniformity in the pattern of these gradients permitted the direct evaluation of the terms of Equation 14. The radial temperature profiles plotted on semilog coordinates as in Figure 4 gave correlations of relatively small curvature and permitted a relatively accurate determination of point differentials of temperature to radius by evaluation of tangencies t o the curve. The magnitude of the first differentials a t intermediate points then in turn were plotted on semilog coordinates as in Figure 5. From these curves the second differentials of temperature t o radius were determined graphically. The temperature t o time differR U N 41 ential was evaluated 40 from the flow velocity f 20 and vertical temperatures gradients. * 10 Flow velocities were m s8 sufficient to render in.r6 c significant the diffuL 4 sion effects in the flow 0’ p 2 direction. D was calculated directly from \I I the evaluation of the I 0.8 I I three differential terms
P
givesthe calculation of diffusivities by this method. The ranges of the better correlations are presented in Table IV to summarize the effects of screens and flow velocity. Figure 4. Typical Plot of Radial Temperature Profile (Method 11)
Diffusivity Ranee, Ss. Ft./Hr. No screen 8-mesh screen 40-mesh screen
FlowLVelooity, Ft./Sec. 2
20-30 28-35 50-60
4
7
15-18 20-30 35-43
10-11 15-22 30-35
a Circular duct, 8-inch internal diameter, screens positioned 6 inches below introduction point.
MOUNTED / SLIP-TUBE THERMOCOUPLES
4 FT. MIXING SECTION IROME HEATING ELEMENT --SCREEN
I
) 4 FT. GENERALIZING SECTION
II
CONCLUSIONS
Tables I and I1 show that the diffusivities determined by each method decrease with induced turbulence from screen insertion and increase with increased flow velocities. The decrease in the determined diffusivities with finer screen size emphasizes the differences between mixing and eddy diffusivity and the difficulty of defining or measuring turbulence without the mixing length concept. With the turbulence induced by the screens, the homogeneity of the mixed stream a t any point was increased but the thermal energy transfer by eddy diffusion was decreased. This apparent contradiction is resolved by separating the effects of scale and intensity of turbulence.
400
200 100
80 60 40
20
a
BLEED DIFFERENTIAL MANOMETER -
Schematic Diagram of
Apparatus (Method 11)
I
I
I
I
6
4
Figure 3.
I\
10
CALIBRATED
-
1293
..... . I
\
I
I
0.5
1.0
I
I 1.5
I 2.0
R (IN.)
Figure 5. Typical Plot of Magnitude of Slope of Radial TemperatureProfile (Method 11)
1294
INDUSTRIAL AND ENGINEERING CHEMISTRY TABLE111.
Run
D a t 11ni Temp ,
E.1I.F. on Heating Element, Volts
Flow Velocity, I n /Sec.
Mixing Distance, z (In.)
NO.
Screen, Mesh
31 I1
40
87
50
84
34
32
40
83
50
48
34
O F
3'
I1
40
86
30
48
34
33
I
Sone
88
30
81
34
33 11
Xone
87
30
26
34
34
None
77
40
84
31
35
None
82
An
24
34
36
Sone
84
40
48
34
37
8
83
4n
84
34
38
8
81
40
24
34
39
8
82
40
48
34
40
40
87
40
84
OF
ClLCULATION
3L
DIFFT'SIVITIES
Radial Distance, r (In ) 0.5 0.7,; 1 1 i 2 0.5 0.75 1 1 .5 2 0.5 0.7,j 1 0 5 0.75 1 0.5 0.75 1
0.5 0.75 0 , 2.5 0 , .j 0.75 1 0.5 0 7,; 1 0.5-
n
1 0.3 0.75 0.25
0.5 0.75 0 5 0.73 1
1,a
Radial Temp. Gradient, dt/dr io F.iIn.1 - 86 - 39 - 20 - 6.7 - 2.6 - 87 - 41 - 22 - 8.0 - 3.2 - 43 18 - 9.5 - 15 - 7.3 - 4.3 - 43 - 20 - 11.8 - 21 - 10.6
-
14.7 34
-
12.0
-
89
40
48
34
42
40
88
10
24
31
0 .3 0.75 1
Thus, the screens decreased the scale of turbulence (or m ~ a n length of individual eddies) and increased the intensity of turbulence (side velocities of the stream). Both of these effects increased the homogeneity or mixed condition of the stream a t any point. However, the decrease in scale exceeded the increase in intensity of turbulence so that the product of the tn.0, eddy diffusivity, was decreased. The diffusivities appeared t o increase in a roughly linear correlation with increase in flow velocities and constant duct conditions. From this it niight be induced that for similar duct conditions, t,he scale of t.urbulence tends t o remain constant, and that the intensity of turbulencc or side velocities of the stream tcnd to he proportional t>othe flow velocit,y. S o computable measurements were obtained of these i d w ences since the cxaotitude of the methods and spatial variations did not allow a separation of the det'ermined diffusivties into scale and intensity of turbulence. Refinement of the methods or the use of hot wire anemometry would permit this. However, qualitative recognition of the changes of scale and inlensii.y could be made in both methods by observation ol the balancing galvanometer for the potent'iometcr during temperature determinations. Each temperature determined was a visual average taken of a fluctuating value, and the frequencies of the fluctuations were representative of the int'ensity of turbulenue and the range of the fluctuations were representa,tive of the scale of turbulence. The accuracy of the calculated diffusivities is soineivhat difficult to evaluate. The physica.1 meaaurenients of method I deviated from ideality in that: 1. The turbulence was altcred to some extent by the hot air introduction tube, although the tube was parallel t o the floadirection and smoothed t.0 a knife edge a t the extremity.
1.6 85 24
Torvp. t o Tirne Gradient, dt/,do (" F./Sec.) 87 47 30 11.9 4.4 42 23 1.? .1 , 7 2.J 22 12.4 8.2 18 11.4 7.9 13.8 10.5 4.1
23 15.8 40 15.4 10.3 8 . .5 1.5.8 10.2 8.8 27 20 12.6 14.2 10.9 38 14.8 10.6 40 20
,. u
- 94
34
- 15.2 - 43 - 19.0
- 10.1 - 3 8 - 24 - 12 3 - 4.4
14.8 4.0 31 16.8 9,1
2,7 10.9 5.2 2 2
49 - 19
-
Gradient t o Radius, 1/r X d t / d r (" F./Sq. In.) - 171 - 52
-
50 - 26.8
-
Ratio
of Radiai
-
.17
- 17 e - 9.1 - 26
-
40
6
isn
- 1?6 - 08 - 26
1.5
PI
R a t e Change in Radiai Gradient, d2t/dr2 ( " F./8q. I n . ) 274 122
-
- 34
0.5 0.73 1
-METHOD I1
Vol. 41, No. 6
9.8
Diffunivity. D e (Sq. I t./Hr.) 21.0 16.8 24.5
3G.0 32.0 6.8 9.8 13.5 14.3 14.5 6.0 9.5 17.7 38.2 29.5 44.5 4.5
11.1 I ,*I
19.3 38.5 9 ,0 3.8 7.2 18.0 8.5 11.0 22.0 28.8 32.0 38.2 9 . .? 12.7 14.2
7
fj
14.2 17.8 16.2 24.' 21.2 8.8 11.5 12.0 13.0 3.8 'I . 0 4.0
2 . Thr! diffusivity varied to some extent arid the correlrttion indicxtcs a11 average diffusivity, rat,her than diffusivity TI: it position. 3 . The heat source was a stream of finite diameter rather than :I point, although the dimensional discrepancy was not large. -1. The diffusional process was confined by the duct walls. This axid the previous factor could be included in a more rigorously derived but cunibersome equation involving Hessel funct ions. 5 . Some heat leak occurred from the hot air imtroductioii tube. 6. Some minor radiation effects were obtained, hut these were essentially uniform and self-canceling. The physical measurements of method I1 deviated fro111 idcslit9 in that: 1. The spiral wire heating element altered the turbulence in the central portion of the column. This effect was more appreciable with t,he lower turbulence of the runs with no screen in the duct. 2 . The temperature gradieiits most useful for correlation were obtained a t 4.5 duct diameters above the screen position. The f u~hulenceinduced by the screens tends to decline t o the level
l'iow \ e l o o i t y , Pt./dec.
2
?!
Diffusivity Range. Pq P'L./llr. .... No screen 8-mesh >oreen 40-mesh screen 5-8 ... 3 7-4 13-22 8 -15 8-12 15-22 33-45 28-37
.~
a Circular duct,, 8-inch internal diameter 0.2,;-inch diameter r p i r a l l\jichrome ivire heating element in t h e axis of'mixing section, 34 inches in length, screen positioned 2 inches below lower extremity of heating element.
June 1949
TABLEV.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1295
V, t o values calculated for turbulent flow in straight ducts by the COMPARISON OF CALCULATED AND EXPERIMENTAL semithooretical equation : DIFFUSIVITIES
Diffusivity (Sq.Ft./Hr.) for Flow Open D u c t by Method Velocity, Equation Method I Ft./Sec. 16 I1 2 18 20-30 5-8 13-22 4 33 28-35 50-60 33-45 7 55
D = 0.08 U d & Reynolds
Number 7,300 14,100 25,900
Friction
Factor 0,0088
0.0074 0.0064
of turbulence natural t o the duct. Hence the point diffusivities calculated are for positions where the screen effects have been partially dissipated. 3. The diffusional process was confined by the duct walls, although the points of correlation were such as not to be appreciably affected. 4. Some radiation effects were obtained, although these were minor to the best t h a t could be measured. No experimental determinations were made of velocity gradients in t h e duct since instruments of sufficient sensitivity were not available. However, the maximum variation in flow velocity between correlation points with the open duct at the lowest flow velocity was calculated t o be 6% by the von Karman equation. Higher velocities and screen insertion would serve to reduce the velocity gradient. The hot air introduction tube of method I and the heating element of method I1 would affect the velocity traverse, but would act t o reverse the ducts natural velocity gradient. The range of the diffusivities shown in Tables I and I1 for each condition is not indicative of a n order of error, but only represents a variation range of the pattern of diffusivities within the selected d a t a at any set of conditions. This pattern of the variation of diffusivity with spatial position was reproducible within runs, and comparable between runs within each method. This variation may be attributed principally t o the above first listed deviations of each method. Neither is the difference in the magnitudes of the diffusivities determined by each method indicative in itself of experimental error. This difference may be resolved principally by consideration of the first two deviations of each method. The results for flow without screens are compared, in Table
(16)
where D = eddy diffusivity; U = average velocity, A = distance from wall to center of duct, andf = friction factor. This equation was derived and utilized by Sherwood and Woertz (6) t o calculate diffusivities agreeing almost within experimental precision with experimental values. Although the generalizing duct section of the apparatus was only 6 duct diameters long, the agreement between values in Table V is reasonable. The agreement is best a t the highest flow velocity where the effects of the listed deviations should be lessened. The determined diffusivities appeared t o be independent of temperature and of heating rates with either method within the utilizable range of the apparatus. It would be of interest t o investigate these hypotheses into more extreme conditions of temperature, flow velocity, and turbulence. Several factors of mixing and diffusion might be profitably investigated with methods of this type and equipment of larger range and capacity. LITERATURE CITED
Goldstein, S., “hlodern Developments in Fluid Dynamics,” Val. I, New York, Oxford University Press, 1938. Kalinske, A. A., and Pien, C. L., IND.ENG.CHEM.,36, 2 2 0 (1944).
Kalinske, A. A., and Robertson, J. M., Eng. News Record, 126, 539 (1941).
Karman, T. v., Gottinger Nochrichter, ;Math-Phys. Klasse, p, 58 (1930).
Prandtl, L. A., 2. angew. Math. u . Mech., 5 , 136 (1925). Sherwood, T. K., and Woertz, €3. B., Trans. Am. Inst. Chem. Engrs., 35, 517 (1939). Stutzman, L. F., abstract of doctor’s thesis, Univ. Pittsburgh (1946).
Taylor, G. I., Natl. Advisory Comm. Aeronaut., Rept. 272, No. 23 (1916).
Taylor, G. I., Proc. London X u t h . Soc., 20, 196 (1921). Taylor, G. I., Proc. Roy. SOC.(London),151A,421 (1935). Ibid., 159A,496 (1937). Towle, W. L., and Sherwood, T. K., Proc. 6th Intern. Congrese Applied Mech., p. 146, Cambridge (1938). Towle, W. L., Sherwood, T. K., and Seder, L. A., IKD.ENG. CHEM.,31, 457 (1939). RECEIVED June 11, 1948.
Distribution of Anabasine between Certain Organic Solvents and Water C. V. BOWEN Bureau of E n t o m o l o g y a n d Plant Quarantine, U . S . D e p a r t m e n t of Agriculture, BeZtsuilZe, M d .
Because the distribution of the alkaloid anabasine between organic solvents and water is important in its isolation the distribution coefficients of anabasine between certain organic solvents and water have been determined. Of the solvents tested for the extraction of the alkaloid anabasine from aqueous solution, ethylene dichloride is the most practical because of its efficiency and low cost.
S
EVERAL organic solvents have been used t o remove anabasine from aqueous solutions. Campbell et al. (Z), Orekhov and Menshikov ( 7 ) , and Khmura (4) used ethyl ether for this purpose. Shvaikova (8) used chloroform, and Khmura (6) found t h a t chloroform was 100% better than petroleum ether.
Sokolov and Trupp (IO) used ethylene dichloride. According t o Sokolov and Demonterik (Q),kerosene has been employed most commonly in Russia. As the distribution of the alkaloid anabasine between organic solvents and water is important in its isolation for use in oil emulsion sprays and in analytical determinations, the distribution coefficients of anabasine between certain organic solvents and water have been determined. EXPERIMENTAL
The anabasine used in this investigation was obtained from Nicotiana glauca, tree tobacco, a plant t h a t grow’s wild in the southwestern United States. An aqueous extract of the ground.
