50?
V O L U M E 25, NO. 3, M A R C H 1 9 5 3 Table 111. Lactic Acid Content of Heavy Steep Liquor as Determined by Ether Extraction for 58 Hours % Lactic Acid (Dry Basis) Conditions 22.8 Acidified and evaporatedbefore extraction 24.0 Acidified but not evaporated before extraction 12.4 S e i t h e r acidified nor evaporatedbefore extraction
traction time. Similar extractions have been conducted on steep liquor which was acidified but not evaporated, and also on samples which were neither acidified nor evaporated (Figure 1, Table 111). CONCLUSIONS
Lactic acid present in heavy steep liquor must exist partially as a salt which may or may not be extracted with ether; in either caqe it would not be included in the final alkali titration. Direct extraction of heavy steep liquor after acidification with sulfuric acid yields results which agree well with values obtained by the oxidation-distillation technique on pretreated samples. On the other hand, values obtained by the standard extraction twhnique were about 1% lower. It does not seem likely that thii. is due to loss of volatile acids during evaporation, as heavy stwp liquor is produced by a concentration operation which should rcmove such volatiles. Friedemann and Kendall(4) have shown that determination of lactic acid in urine by ether extraction alv ays results in a loss of lactic acid due to oxidation by organic
peroxides formed during evaporation and extraction. There also exists the possibility of lactic acid condensation during evaporation, which would result in lowering the apparent lactic acid content determined by extraction. Although the extended ether extraction of acidified heavy steep liquor (not evaporated) yields reliable results which are in agreement with the values obtained by the modified Friedemann technique, the oxidation-distillation procedure is recommended because of the short time required for analysis. LITERATURE CITED
(1)
Elgart, S., and Harris, J. S I IND. ENG.CHEV.,ANAL. ED., 12” 758 (1940).
Friedemann, T. E., J . Biol. Chem., 76,75 (1928). Friedemann, T. E., and Graeser, J. B., Ibid., 100, 291 (1933). Frjedemann, T. E., and Kendall, A. I., Ibid., 82, 23 (1929). Fries, H., Biochem. Z., 35,368 (1911). Kerr, R. W., “Chemistry and Industry of Ptarch,” 2nd ed., Chap. 11,New York, Academic Press, 1960. ( 7 ) Kondo, K., Biochem. Z., 45,88 (1912). (8) Leach, A. E., and Winton, A. L., “Food Inspection and Analysis,’’4th ed., New York, John Wiley & Sons, 1936. (9) Mendel, B., and Goldscheider, I., Biochem. Z., 164, 163 (1926). (10) Pigman, 11’. Ti’., and Wolfrom, M. L., Advances in Carbohydrate (2) 13) (4) (5) (6)
Chem., 1, 257 (1944). (11) Somogyi, M., J . B i d . Chem., 90,725 (1931). 112) Trov. H. C.. and Sharp. P. F., Cornell Cnic., Agr. Ezpt. Sta.. iGemoirs, 179 (1935): (13) Van Slyke, D. D., J . B i d . Chem., 32, 455 (1917). (14) Wolf, C. G. L.,J . Physiol., 48, 341 (1914).
RECEIVED for review
Accepted October
January 17, 1952.
27, 1952.
Calibration of the Rolling Ball Viscometer H. W. LEWIS Bell Telephone Laboratories, Murray Hill, N. J . N 1943, Hubbard and
Brown ( 1 ) carried out a systematic
1 experimental calibration and dimensional analysis of a rolling
ball viscometer. They determined a dimensionless calibration curve, which enables one to design a viscometer of this type to measure any given range of viscosities. It is the purpose of this note to show that one can, to good approximation, derive this calibration curve from a simple approximate treatment of the problem in terms of the hydrodynamics of viscous fluids ( 2 ) . IVe consider a cylindrical tube of diameter D, inclined a t an angle 29 to the horizontal, and filled with a fluid of viscosity L,A, and density p,. SVe suppose to be rolling down the tube with velocity V, a spherical ball of diameter d, and density pa. We will use a cylindrical coordinate system, with Z-axis parallel to the axis of the tube, with polar angles referred to a vertical plane through the 2-auk, and with the origin a t the center of the sphere. We Tvill also make the approximation that the gap between the sphere and the tube is small compared to the diameter of either one, so that the sphere nearly fills the tube-this is the usual, practical situation, and makes the calculation possible. We will systematically neglect higher powers of ( D - d ) / D . Now, if we call the distance betn-een the sphere and the wall of the tube u (79, Z ) , a little consideration of the geometry will show that
a narron- channel of this sort gives rise to a parabolic velocity profile a t any given point. In particular, if L is the mean velocity of the fluid in the gap, then d 2 i l b r 2 = 12; /u2, where r is our radial cylindrical coordinate. But the longitudinal gradient of pressure is given by p LPu/dr* = 12 p u/u2, so that our problem may now be stated as follows: rye have to determine the distribution of G as a function of 9 and 2, so that the total difference of pressure is enough to balance the reight of the sphere, and the total flow across any plane Z = constant is equal to D2V. This will determine p as a function of V , n.hich is the problem we have set ourselves. K e will use the f o l l o ~ ~ i nprocedure: g for each value of 2, we will distribute the flow velocity, as a function of 9, in such a way that the longitudinal pi essure gradient is independent of $-this implieb that we x-ill neglect all components of velocity perpendicular to the axis of the tube. Thus, we write
3
u (79,
a
(2)
The total flux through any plane perpendicular to the axis of the tube \vi11 then he flux =
=
So we have to consider the flow of a viscous fluid through a narrow channel of width given by ( 1 ) . The total flow through this channel will be D2V, since we will, everyn-here except in the expression ( D - d ) , neglect the differencebetu-een D and d. Now, it is well known that the flow of a viscous liquid through
Z) = B ( 2 ) uy9, Z )
a fT
L(79, Z )
flux
x Fz
fx
D ( D - d ) 3B ( Z ) 16
u(8,
Z ) X D d9 (3)
;B(2)
Substituting the expression for ing the integral, we find
x
u3(9,
u
Z ) d8
from Equation 1, and perform-
[5
+ 18a + 24aa + 1 6 4
(4)
A N ALY TICAL CHEMISTRY
508 where
(Y
=
[D
-
4 D 2 - 422]/2(D
- d)
1 .o
But this must be independent of Z, and must be equal to so that we find
B(Z) =
-
T H E O R E T I C A L . NO
10
4 DT.’
(D
- d)3[5 + 18a + 24a2 + 16a3]
(5)
1 CY‘
48 p DT’
(D
TI0 D
Consequently, the longitudinal pressure gradient is grad p =
0 - E X P E R I M E N T A L , LIQUIDS 0 -EXPERIMENTAL, A IR
DV,
- d ) 3 [ 5 + 18a + 24a2 + 1601~1
(6)
and the total pressure drop along the tube, due to the ball, is AP =
grad p dZ = Jr m n
r
[&d]6’2x dE 5
(7)
where, if we call the integral 8 r I / 3 , thereby defining a number I , we have
I =
1 [.\/a 1/2 - + 21’’’ 45
0.398
(7’)
In passing from Equation 6 to 7, we have defined a quantity by the equation $2 = a,and have again neglected terms which contribute only in higher orders of ( D - d ) / D . Thus, for example, the limits on the integrals are not really infinite, but depend upon D/(D - d). This pressure drop must now support the sphere, so that ? r ~ a
(i
-
p l ) g sin 8 =
7r
- ~
4
a 10
2
~
3
u IC
I
.
I
lo5
10-6
I04
10-3
Figure 1. Plot of Theoretical Equation 9’with Experimental Points with the calibration constant K of Hubbard and Brown, in terms of which Equation 9 is
K = -2o 7
[ DT ]- d
512
D-d 7 = 0.0891 [ ] (9’) ‘ “
I n Figure 1 has been plotted the expression for K given by Equation 9’, the points measured by Hubbard and Brown, and the points calculated by them from other experimental data. The fit, considering the simplifications in the calculation, is satisfactory. I t can serve for the design of rolling ball viscometers, although, for precision work, the usual calibration in terms of fluids of known viscosity should be carried out. Equation 9 should, of course, be used directly, without going through the definition of K .
p
LITERATURE CITED
and
(1) Hubbard, R. M., and Brown, G. G., IND.ENG.CHEM.,ANAL. ED.,15, 212 (1943). (2) Lamb, H., “Hydrodynamics,” New York, Dover Publications, 1945.
which is our final result.
It will be convenient to compare this
RECEIVED for review
July 7, 1952.
Accepted October 15, 1952.
Identification of Flavonoid Compounds by Filter Paper Chromatography Additional Rf Values and Color Tests HELEN WARREN CASTEEL AND SIMON H. WENDER University of Oklahoma, Norman, Okla. APER chromatographic techniques applicable to flavonoid Pcompounds have been developed by Bate-Smith and Westall (1, 9) and by Gage, Douglass, and Wender ( 3 ) . Because of the interest indicated by many research workers in these paper chromatographic studies of flavonoids, the present investigation was undertaken to extend the usefulness of this technique by the determination of R f values for a number of flavonoid compounds not yet reported in the seven solvent systems listed. The colors produced by chromogenic sprays when considered in conjunction with the R, value often aid in the tentative classification of an unidentified flavonoid pigment into one of the major subdivisions of flavonoid compounds. Therefore, the colors produced on paper by chromogenic sprays and certain of the newly studied flavonoids were also determined.
EXPERIMENTAL
Experimental apparatus, materials. and procedures used correspond BB nearly as possible to those of Gage et al. (3). A newer
model “Chromatocab” chamber (Chromatography Division, University Apparatus Co., Berkeley, Calif.) was used in the present study, however. This chamber was much better sealed and better insulated than the previous model used. Thus, uniform saturation, indicated by movement of solvent fronts through equal distances for all strips within the chamber, was obtained if sufficient time (usually 24 hours) was allowed for saturation. Also, rate of movement on the paper was usually much more rapid in the newer chamber. A 250-ml., all-glass spraying flask (University Apparatus Co.) operated by compressed air a t 5 pounds pressure delivered an even mist of chromogenic reagent. The spray was controlled by an air hole covered by the thumb during delivery. RESULTS AND DISCUSSION
Table I lists the R / values obtained for twenty-one flavonoid compounds in seven different solvent systems. These listed values represent average R f values for each compound. Some variation in Rt of a pigment occurred from time to time, but the variation was usually less than 1 0 . 0 4 Rf value and, in most cases, was less than 50.02 Rr value. Some of the flavonoid samples used in this study were found by
