175
Ind. Eng. Chem. Fundam. 1982, 27, 175-181 i 420
'
l
'
i
'
l
'
N- TETRADECANE
It should be added that samples that decompose at the critical temperature should be heated for a limited time only. As the decomposition progresses gaseous products are formed and pressure builds up which may cause the tube to burst. The prevent this, an insert may be used consisting of a thin-wall metal tube with viewing windows cut to match the windows of the furnace. In our work, the bursting pressures of seven tubes were determined in a separate experiment and were found to range between 4136 and 7584 kPa, with an average of 5612 kPa. Acknowledgment
Grateful acknowledgement is made to the College of Engineering, Ohio State University, for financial aid and to the Phillips Petroleum Company for samples of pure hydrocarbons. TIME
MINUTES
Figure 3. Repeatability testa using three samples of n-tetradecane.
The performance of the apparatus was, in general, satisfactory. Due to the low heat capacity of the furnace it was possible to heat the sample rapidly and by locating the thermocouple in the well surrounded by the sample, the control and measurement of the temperature were superior to that achieved by others.
Literature Cited Ambrose, D. Trans. Faraday Soc.1983, 59, 1988. Ambrose, D. "Vapour-LiquM Critical Propertles"; National Physical Laboratory, Teddington, England, Report Chem. 197, Feb lW0. Ambrose, D.; Cox, J. D.; Townsend, R. Trans. Faraday SOC. 1980, 5 6 , 1452. Ambrose, D.; Grant, D. G. Trans. Faraday SOC. 1857, 5 3 , 771 Cheng, D. C.; McCoubrey, J. C.; Phillips, D. G. Trans. Faraday SOC. 1982, 58, 224.
Received for review June 22, 1981 Accepted December 9, 1981
A Simple Capacitance Sensor for Void Fraction Measurement in Two-Phase Flow Mlng 1. Shu, Charles B. Welnberger,' and Young H. Lee Department of Chemical Englneering, Drexel University, Philadelphia, Pennsylvania 19 104
An inexpensive and simple capacitance sensor has been developed for void fraction measurement of two-phase flow of gases and liquids in cylindrical channels. The sensor causes no flow disturbances and the output is independent of channel diameter. The sensor is especially suitable in terms of sensitivity for void fraction measurement in annular flow. The governing electromagnetic equations are solved to give predictive relationships between void fraction and sensor signal, and the predictions agree wlth the experimental results.
Introduction
For two-phase flow of gases and liquids the gas volume fraction, or void fraction, is one of the primary design parameters. Much effort, therefore, has been devoted to developing techniques for the measurement of void fraction. The available techniques include quick-closingvalves (Hewitt et al., 1961), radioactive attenuation (Isbin et al., 1959; Schrock, 1969), hot wire anemometry (Hsu et al., 1963); Delhaye, 1969), and electrical impedance methods (Gregory and Mattar, 1973; Merilo et al., 1977). The electrical impedance methods, in particular, are attractive and suitable for most investigators since they are simpler to use and are relatively inexpensive compared to the other techniques. Also, the resulting void fraction measurement is time dependent and is averaged over a much shorter distance than that needed for quick-closing valves. These time traces of void fraction are especially useful for flow pattern identification. The electrical impedance of a two-phase mixture depends on void fraction if there exists a difference in dielectric constant or electrical conductivity of each phase. Depending on the electrical characteristics of the two 0196-4313/82/1021-0175$01.25/0
phases and the configuration of the sensing element, impedance can be governed by conductance or by capacitance or by both. Measurements based on capacitance generally provide better reproducibility than those based on conductance because the latter depend on ion concentration and kind, and these can be difficult to control. Besides reproducibility, there are other design considerations for impedance sensors, including flow channel geometry, sensor-induced flow disturbances, flow pattern, and sensitivity. To avoid sensor-induced flow disturbances, the electrode surfaces must either be part of the channel boundary or external to it. For example, in annular channels, Sachs and Long (1961) and Cimorelli and Evangelisti (1967) used the inner and outer walls of the annulus as the two sensor electrodes. For the most common geometry, cylindrical pipes, Gregory and Mattar (1973) tried several types of capacitance sensor geometries, including parallel plates, curved plates, and continuous helices. A major difficulty of impedance sensors concerns the effect of flow pattern on the relationship between sensor signal and void fraction. Cimorelli and Evangelisti (1967) 0 1982 American Chemical Society
170
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982
C'
Front View
Side View
-e=o
Top View
Figure 1. Dimensions of sensor (A, terminal; B, shield; C, electrode; D, tube).
Figure 3. Geometric arrangement for annular flow within the sensor.
i
n
Frequency Generator, VS,f
Figure 2. Circuit for measurement,
and Bouman et al. (1974) showed theoretically that such an interaction was to be expected. They also showed that, for the annular flow pattern, the sensitivity of impedance sensors is low at high void fractions; since annular flow normally occurs at relatively high void fractions, this leads to intolerably low sensitivities for this particular flow pattern. The objective of the present work was to develop, for cylindrical channels, a capacitance sensor which introduces no flow disturbance and which retains a high sensitivity for the annular flow pattern. To check the experimental measurements, the governing electromagnetic equations are solved, where possible. These solutions, which depend on flow pattern as well as sensor geometry and electrical characteristics of the fluids, provide independent predictions of the relationship between void fraction and sensor signal. Capacitance Sensor Design A sketch of the sensor is given in Figure 1. The electrodes consist of two identical half-cylinders of 0.2 mm thick aluminum foil. The electrodes are positioned exactly opposite each other on the outside of the nonconducting tube. The closest spacing between the electrodes corresponds to an angular separation of roughly 5 O ; thus, the electrodes are not quite half cylinders. The electrode length is approximately ten times the tube diameter. Note that the conductance component of the impedance is eliminated by the nonconductive tube wall; the sensor is therefore almost purely capacitive. The entire sensing volume is shielded to minimize external interference. All connecting cables are coaxial and short in order to minimize internal capacitance and resistance. The sensor is placed in series with a frequency generator (variable) and a variable resistor as shown in the circuit diagram, Figure 2. The additional capacitors, resistor, and diode provide a filtering action for the sensor signal. The voltage drop V across the resistor R can be expressed as
tween the sensor electrodes, and Ciand Riare the internal capacitance and resistance, respectively, within the circuit. The frequency and resistor values are chosen to develop optimum sensitivity of VR to changes in void fraction; this signal sensitivity is independent of tube diameter for constant ratio of tube wall thickness to diameter and constant dielectric properties of the fluids.
Theory Annular Flow. Figure 3 shows the geometric arrangement for annular flow within the sensor. The gas core possesses a dielectric constant EG,the annular liquid q,and the tube eT. The length of the electrodes is L. Q and V are the charge and potential on the electrodes, respectively, and the capacitance CT is thus Q/2V. Q is evaluated from the charge density on the surface of the electrodes. Therefore, the first step is to solve the distribution of the potential q ( r , 6) in the vicinity of the electrodes. The potential distribution is obtained from the solution of the Laplace equation
This equation has been solved by Cronin et al. (1967) for the simpler case of identical electrode geometry and uniform dielectric constant within the electrodes. We extend their solution to include the present w e of multiple materials within the sensor. This solution is restricted to the case of axial symmetry within the sensor (such as exists in annular flow). We first postulate the following solutions, each corresponding to a particular material within the sensor. m
p,,(r,0) =
c A,(a/r)"
cos (me); a Ir
(3)
m=O
ur(r,0) = m
C [B,(r/a)" + c,(b/r)"] cos (me); b
Ir Ia (4)
m=O
' P L ( ~ . , O )= m
m=O
[D,(r/bP + E , ( C / ~ )cos ~ ] (me); c 5 r Ib (5) m
F m ( r / c ) mcos (me); r 5 c
pG(r,B) =
(6)
m=O
By symmetry where Vs is the input voltage tuned in from the frequency generator at the frequency selected, f is the frequency selected for the measurement, CT is the capacitance be-
v(r,e) = v(r,-0) (7) and the boundary condition that, on either electrode, the
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 177
potential is +V or -V enable us to evaluate the constants A,. Multiplying each side of eq 3 by cos (ne) and integrating over 0 from zero to 27r at r = a yields A0
=0
becomes
;)[
Rex'(
-]
1 - iyeie - 1 +1iyec8 dy
(25)
(8)
and
Therefore, after completing the integration
A , = ( 4 V / n a ) sin ( n a / 2 ) ; n = 1, 2, 3,
...
(9)
The remaining constants B,, C,, D,, E,, and F, can then be solved as a function of A , simply by algebraic manipulation of the following boundary conditions dae) =
(10)
*(b,e) = a ( b , e )
(11)
a ( c , e ) = m(c,e)
(12)
m
E (-1)n-l-
n=l
x2n-1
2n - 1
1 cos [(2n - l)0] = -1m log 2 = -1 tan-' 2
(-)
2x cos 0 1 - x2
and
tan-l A
Our interest resides in the solution *(r,e) since this region
0 1 + ixeie 1 - ixeie
(
2ar cos 0 a2 - r2
)
(28)
The surface charge density on the electrodes is q. aw/arla and is obtained by differentiating (15)
is adjacent to the inside surface of the electrodes.
(29)
$(92n-1]) (15)
where
This surface charge density can be integrated over 6 from -[(s/2)- ( 6 / 2 ) ] t o [(7r/2) - ( 6 / 2 ) ] to yield the charge per axial length of the electrodes, q. This quantity, along with the relationship C = Q / 2 V , yields the total capacitance, CT
+
= e l n ( 1 cos ( 6 / 2 ) A 1 - cos ( 6 / 2 ) 6eTL
m
)-
(-I)"-'
-EA .=12n - l where
The first series expansion in eq 15 can be expressed as
which, after using the expansion m
In order to illustrate the dependence of the sensor readings on tube geometry and the various dielectric constants, the preceding equation was solved for the physical cases of water/air and glycerin/air in annular flow in glass tubes of various thicknesses. The results, given as normalized overall capacitance vs. void fraction, are shown in Figure 4. We note that the relationship becomes more linear as dimensionless tube thickness decreases and as we move from a fluid pair (water/air) with a high ratio of dielectric
178
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982
a d8 * dC, = CTL(a- b ) sin 8'
80
(32)
I 8 I X-80
a d8 8, 50 Ix - 80 2b sin 6'
dC, = E,&-.
(34)
Rearranging eq 31 and integrating over 8 from Bo to K 8,, we have
02
0
0 4
0.6
0 4
10
VOID FRACTION,(I
Figure 4. Theoretical prediction of normalized capacitance for annular flow as a function of void fraction.
=n
Bo can be related to ( b / a ) by
(36)
8, = c o d ( b / a )
and 8, is a function of the void fraction, cy, according to 8, - cos 0, sin 8, a = l (37) x
e=o
Since 8, = 60 when have
cy
= 1 and 8, = x - 0, when
cy
= 0, we
Figure 5. Geometric arrangement for stratified flow within the sensor.
constants to one (glycerin/air) with a low ratio. For annular flow the gas volume fraction is normally above 0.6 so that, according to Figure 4, the sensitivity of the sensor appears to be higher for the thicker tube wall. This observation is not exactly accurate, however, since the ordinate is a normalized quantity and the maximum range of the capacitance decreases as tube wall thickness increases. Toward the bottom of the plot are predictions for the hypothetical case of liquid core and gas annulus; this physically unrealistic case illustrates clearly that, in addition to void fraction, the flow pattern strongly affects the sensor signal. Stratified Flow. For stratified flow, the lack of axial symmetry of the two phases within the sensor precludes analytic solution of the Laplace equation. Instead, we shall adopt a simple electrical viewpoint corresponding to parallel lines of the electrical force field between the two electrodes. This simple model cannot be exactly correct but it does permit estimation of the form of the resulting void fraction calibration. The task now becomes one of summing the differential capacitances corresponding to horizontal slices of Figure 5. Note that the two electrodes are placed side by side rather than top and bottom; because of the geometry of stratified flow, the former configuration provides much better sensitivity over a range of void fraction than does the latter. Of course, in annular flow the positioning of the electrodes is much less important. Moreover, since our interest is in the overall capacitance change due to change in void fraction, only the section between 80 and x - 60 has to be considered. The total differential capacitance, dCT, is related to that of the tube, dCt, and that of the fluid within the slice de,, by 1-+-2 1 -= dCT dCt de,, where
and
(39) The normalized signal CN then becomes
c,
=
C,(cy) - C&=l) CT((Y=o) -
CT(a=1)
ln (tan
-
:)
- In (tan
2 1n (tan
:)
:)
(40) Figure 6 shows the normalized capacitance signal as a function of void fraction for stratified flow, as predicted by eq 40. As with annular flow, the relationship becomes more linear as tube wall thickness increases; however, the absolute sensitivity should be greater for the thinner tube wall, as expected. Experimental Calibration Annular Flow. This flow pattern was simulated in static tests by holding the glass tube with the sensor vertically and inserting tubes of smaller diameter into the center of the first tube. Symmetric annular flow with a gas core was simulated by adding liquid to the annular region, whereas the hypothetical case of a liquid core was simulated by adding liquid to the center tube. The dielectric constant of the glass in the smaller tube was 4.0, which is close in absolute terms to that of air, 1.0; in
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 1.0 L
h
I
I
I
I
1
z
~
0.8
o,8
1
.’
\
:
-04 24 0.6
179
Static Simulation
\
0
n W
A Dynamic
Measurement Using Quick Closing Valves
0.4
P
4
2 P
u:= 0.2
0.2
1
14.4-54.0 m / s
&‘k1
us = 0.002-0.023m l s
0
0 0
0.2
0.4
0.6
0.8
VOID FRACTION,a
Figure 6. Theoretical prediction of normalized capacitance for stratified flow as a function of void fraction. 1.o
0 0
1 .o
0.2
0.4
0.6 VOID FRACTION a
1.0
0.8
Figure 8. Comparison between static and dynamic calibrations of annular flow of glycerine/air mixture (tube i.d. = 10.21 mm, T = 0.173, f = 1 Mhz, R = 350 Q ) . 1 .o
> : 0.8 w
a d I-
9
Static Simuiation of Stratified Flow
0.6
0,
Static Simulation of Annular Flow Dynamic Measurement of Annulara Flow Using Qulck Closing Valves
U: = 9.1-38.1 mls
U: = 0.025-0.68 m/s 0
0.2
0.4
0.6
0.8
ll
\4
“I
\I
1.0
VOID FRACTION,^
Figure 7. Results of static simulation of annular flow (f = 1 Mhz, R = 350 Q ) .
comparison, the dielectric constants of the liquids was 78.5 and 42.5 for water and glycerin, respectively. A correction factor, corresponding to the difference between the sensor signal for an empty tube and that when the smaller tube is inserted (with no liquid added) is substracted from the measured capacitances to account for the glass material in the core geometry. The results, obtained with two different outer tubes, six inner tubes, and two different liquids, are shown in Figure 7. Note the similarity between the experimental calibration and the theoretical calculations illustrated in Figure 4, especially with regard to the effects of tube diameters, dielectric constants, and gas vs. liquid core. The slight quantitative differences can be attributed to internal resistances and capacitance within the entire measuring circuit. Moreover, the effect of shielding which is not included in the theoretical derivation should also contribute some of the deviation. Dynamic calibrations for annular flow were also performed by using a quick-closing valve technique. These dynamic calibrations are important when one considers the possible effects of mist in the core and nonaxial symmetry (introduced by a horizontal layout of the tube). The question here then is whether the static calibrations would suffice or whether dynamic testing would also be required for each new sensor. The experimental apparatus is typical of that for two-phase flow studies: air and water flow rates were measured by rotameter, quick-closing valves are ball valves with a 10.3 mm opening and linked mechanically 1.49 m apart; the pipe is 10.2-mm copper pipe except for
the sensor section located midway between the ball valves; the sensor is the same as that used in the static tests with a 10.2 mm i.d. glass tube; the LID ratio for the pipe between the mixing tee and the first ball valve is roughly 350; and, finally, a Plexiglas window for visual observation of the flow is located 100 mm upstream of the first valve. Reproducibility checks assured us that the time required to close the valves manually did not affect the resulting void fraction measurement. The flow pattern maps of Choe et al. (1976) and Barnea et al. (1980)were used,along with the visual observations, to assure us that the flow pattern was indeed annular. The results, shown in Figures 8 and 9, show excellent agreement between the static and dynamic calibrations. In Figure 8, the slight departure from the curve for the dynamic measurements for glycerin/air corresponds to the very edge of the flow pattern transition from annular to intermittent flow and is probably not significant. Thus, static calibrations should provide sufficient accuracy for these sensors. Stratified Flow. This flow pattern was simulated simply by holding the sensor horizontally and by adding a measured volume of liquid. The fluid velocities do not affect the sensor reading so that there is no need for dynamic testing for this flow pattern; moreover, a 10.2 mm i.d. tube is too small to permit stratified flow for the air/water system. The results of the calibration, shown
180
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 10 WaterIAir
n W CI
2
I
04-
U
e L
0.2
VA
P
---_-------__-_--__-___
LIE= 2 7 1 mlssc
vw/hi-o-3---
p I
-_
~
Annular Flow
- - - - - - - -.-----
VOID FRACTION,a
Figure 10. Resulta of static simulation of stratified flow (f = 1 Mhz). in Figure 10, approximately match the predicted behavior illustrated in Figure 6. The effect of the resistance chosen for the measuring circuit illustrates the possible optimization in sensitivity that can be achieved for this flow pattern.
Flow P a t t e r n Identification The stratified flow data were replotted in Figure 9 in order to illustrate the effect of flow pattern on the signal/void fraction relationship. What this means is that the flow pattern must be known in order to determine the void fraction from the signal. If one does not have a flow pattern map for the particular fluid pair involved, this influence of flow pattern could be a severe disadvantage. In terms of detecting flow pattern transitions, however, this disadvantage could be turned into an advantage since it could provide a more quantitative criterion for the location of the transition. The form of the signal itself, as a function of time, can reveal the flow pattern. Figure 11 illustrates some typical traces of voltage signal vs. time; for this figure the superficial liquid velocity is maintained constant at 54 mm/s and the superficial gas velocity ranges from 0.17 to 38.1 m/s. As gas velocity increases, the flow pattern changes from intermittent (withelongated bubbles and liquid slugs) to annular flow (with wave frequency increasing with increasing gas velocity). Summary
A capacitance sensor capable of detecting void fraction in two-phase flow of gases and liquids has been designed and tested. A theoretical analysis of the performance of the sensor for an annular flow pattern has been substantiated by experiment and approximate substantiation was also obtained for stratified flow. The capacitance sensor described above possesses a number of highly desirable characteristics. In particular, the sensor: (1)introduces no flow disturbances, (2) is effective for both large and small diameter tubes, (3) can be calibrated for annular and stratified flow patterns by static tests, (4) provides high sensitivity in annular flow at high void fraction, and (5) can be used to detect flow pattern transition. The chief disadvantage of the sensor is perhaps the requirement that the pipe within the sensor must be made of a material with a low dielectric constant-this of course rules out metallic pipes, but there do exist many suitable materials with low dielectric constant.
TIME (9)
Figure 11. Typical traces of void fraction fluctuation for different flow patterns (tube i.d. = 9.53 mm, VLn= 0.054 m/s, V, range is 60 mV from a = 0 to a = 1).
Nomenclature a = outside radius of the tube b = inside radius of the tube c = radius of the gas core in annular flow f = frequency selected for capacitance measurement q = surface charge per unit length of electrodes (= Q / L ) r = radical coordinate CN = normalized capacitance defined by eq 40 CT = overall capacitance pertained between the sensor electrodes Im = the imaginary part L = length of the sensor electrodes Q = electrical charge pertained on the surface of the sensor electrodes R = resistance in series with the sensor and the frequency generator Re = the real part T = ratio of the tube thickness to tube outside diameter defined by eq 20 UGs= superficial gas velocity ULs= superficial liquid velocity V = electrical potential on the surface of the sensor V, = normalized voltage = [ VT(a) - VT(a = I)]/ [ VT(a = 0) - vT(a = I)] V, = voltage drop across the resistor R Vs = output voltage from the frequency generator VT = output voltage from the measuring circuit
Greek Letters a = void fraction of the two-phase mixture PT = dielectric constant ratio of tube to gas PL = dielectric constant ratio of liquid to gas 6 = angular separation between the two sensor electrodes tC = dielectric constant of the gas tL = dielectric constant of the liquid tT = dielectric constant of the tube 0 = angular coordinate
electrical potential function electrical potential function for a 5 r cpr = electrical potential function for b 5 r 5 a (PL = electrical potential function for c 5 r 5 b cpG = electrical potential function for r 5 c Literature Cited cp =
po =
Barnea, D.; Shotern, 0.;Taitel, Y.; Dukler, A. E. I n t . J . Muniphase Flow 1980, 6, 217. human, H.;Van Koppen, C. W. J.; Raas, L. J. European Two-Phase Flow Group Meeting, Harwoll, June 1974. Paper A2. Choe, W. G.; Weinberg, L.; Weisman, J. "Proceedings of Symposium in TwoPhase Flow and Heat Transfer"; Universlty of Miami, 1976. Cimorelli, L.; Evangelisti, R. I n t . J . Heat Mass Transfer 1987, IO, 277.
181
Ind. Eng. Chem. Fundam. 1982, 21, 181-183 Cronln. J. A.; Greenberg, D. F.; Telegdl. V. L. “University of Chicago Graduate Problems In Physics with Solutions”; Addlson-Wesley: Reading, MA, 1987. Deihaye, J. M. Eleventh Nat. ASMElAIChE lit. Transfer Conference, Minneapoiis, Aug 1969, p 58. Gregoty, 0. A.; Mattar, L. J . Can. Pet. Techno/.Aprii-June, 1973, 48. Hewkt, 0. F.; King, 1.; Lovegrove, P. C. Br. Chem. Eng. 1963, 8 , 311. Hsu. Y. Y.; Simon, F. F.; Graham, R. W. Mulfiphase Flow Symp. ASME, 1963, 26. Isbin. H. S.;Rodriguez, H. A.; Larson, H. C.; Pattie, B. D. AIChE J . 1959, 5 ,
427.
Merllo, M.; Dechene, R. L.; Clchowlas, W. M. J . Heat Transfer 1977, 99, 330. Schrock, V. E. Eleventh National ASMlAIChE lit. Transfer Conference, Minneapolis, Aug 1969, p 24. Sachs, P.; Long, R. A. K. Int. J . Heat Transfer 1961, 2 , 220.
Receiued for reuiew July 17, 1981 Accepted January 26, 1982
COMMUNICATIONS Preferential Crystallization of Ionizable Racemic Mixtures I n the separation of mixtures of optical Isomers by fractional crystallization it is essential to control the degree of supersaturation of the isomer remaining in solution. This can be accomplished for racemic mixtures of amino acids by adding acid or base to the solution. With such additions a purer crystalline product of one isomer can be obtained. An explanation of this effect is given based on ionic equilibrium in the solution.
Introduction Of the several methods of resolution or separation of mixtures of optical isomers, only conversion to diastereoisomers and resolution by enzymatic methods have been regarded as generally useful. However, in resolving racemic amino acids, mechanical resolution of the isomers has been successfully used in industry. In this method, a supersaturated solution of a racemic mixture is inoculated with a pure crystal of one of the isomers, the crystal grows, and thus one active form is separated from the racemic mixture. The other isomer remains supersaturated in the solution. This system is unstable, however, and the optical antipode which remains supersaturated in the solution tends to precipitate, resulting in poor resolution of the racemic mixture. Several devices for stabilizing the solution supersaturated with the antipode have been developed. In the case of resolution of ionizable racemic mixtures, addition of acid or base to the solution has been found to stabilize the system and the yield of the desired crystal form becomes higher than that obtained without adding acid or base (Akashi, 1962; Mizoguchi, 1967a,b). The reason for this has remained obscure. Here we describe the theoretical basis for the stabilizing effect of acid or base on solutions supersaturated with amino acids, using thermodynamical considerations. When one acid isomer of an optical pair to be crystallized selectively by seeding coexists with the corresponding salt forms, the salts are more soluble than the acids and do not change the essential separability. The acid form that is not seeded will transfer part of its acidity to the acid form that is seeded, increasing the yield of desired product and decreasing the supersaturations of the unseeded acid form. Stabilizing Effect of NaOH on Supersaturation of Racemic Glutamic Acid L-Glutamic acid imparts meat flavor to foods and resolution of racemic glutamic acid has been of practical importance in industry. We will consider in the following the resolution of racemic glutamic acid in the presence of NaOH. 0196-4313/82/1021-0181$01.25/0
In the aqueous solution containing DL-glUtamiC acid and NaOH, the following reaction occurs L-A + D-S e L-S+ D-A
(1)
where LA, L-S,D-A, and DS are the free form of Lglutamic acid, sodium salt of L-glutamic acid, free form of Dglutamic acid, and sodium salt of Dglutamic acid, respectively. This reaction is an exchange of sodium ion between L-A and D-A. D-A differs from L-A only in optical rotatory power, but they are almost identical in any other properties such as activity coefficients. Therefore, for reaction I
where CLA,,,C CDA,and C m are the molar concentration of L-A,that of LS,that of DA and that of DS, respectively. I t is evident, therefore, that the direction of reaction I depends only on changes in entropy. By determining the solubilities of L-A (or D-A) in the solutions that contain various amounts of DA (or L-A) and that have been added a given amount of DL-S(racemic sodium glutamate), the mutual solubilities curves of L-A vs. D-A can be plotted and are shown in Figure 1. This figure demonstrates that, although the solubility of DL-A (free form of racemic glutamic acid) is almost independent of the concentration of DL-S(CDLS), the larger CD, is, the larger the solubility of D-A (or L-A) in the absence of its antipode becomes (Mizoguchi, 1967a). This result suggests that the transfer of the acidity of one isomer to the other occurs according to reaction I and the apparent solubility of D-A (or L-A) increases. On the other hand, the properties of these solutions are considered to be determined when three parameters, CLA, CD-A, and the concentration of NaOH (CNaoH),are given a t constant temperature. Therefore the mutual solubilities of L-AS (L-A plus L-S) vs. BAS (DA plus DS) are plotted and are shown in Figure 2. This figure can be considered to show the mutual solubilities of L-A vs. D-A in the NaOH-containing solutions. The sum of CD.s and CL-S equals CNaOH in the solutions. 0
1982 American Chemical Society
