1323
Ind. Eng Chem. Res. 1991,30,1323-1329 300 rpm 0.4
-
0
250 Temp., "C
300
Figure 9. Relationships between mean particle size and hydrothermal temperature for two levels of alkali molar ratio.
creases, the term in which both nucleation and particle growth overlap each other becomes shorter, and as a result the number of host nuclei is reduced. The mean size of particles decreases with increasing stirring speed. This experimental evidence may be ascribed from the fact that the nucleation rate rises in the early stage of the reaction and hence numerous host nuclei are generated. To prepare crystal barium ferrite, the hydrothermal temperature must go up to about 300 "C. As the alkali molar ratio increases, the mean size of particles decreases. Ultrafine particles of less than 0.1 pm can be synthesized by the hydrothermal treatment under the conditions of an alkali molar ratio of 6, temperature of 300 "C, and stirring speed of 300 rpm.
Nomenclature
d = mean size of hexagonal platelike particles, pm R.3
n = stirring speed, rpm R = alkali molar ratio defined by [OH-]/[NO,-] t = thickness of hexagonal platelike particles Registry No. Barium ferrite, 12047-11-9;iron nitrate, 10421-48-4; barium nitrate, 10022-31-8.
Literature Cited Time, h
Figure 10. Variation of mean particle size with time for two levels of alkali molar ratio.
Conclusion Barium ferrite ultrafine particles were synthesized hydrothermally from aqueous mixed solutions of femc nitrate and barium nitrate. The following findings were yielded After 1-2 h of hydrothermal treatment, the particle growth driven by Ostwald ripening dominated. At higher temperatures, that is, higher pressures, particles grow larger, because the particle growth rate in-
Barb, D.; Diamandescue, L.; Ruci, A.; Mihaila, D. T.; Moraeiu, M.; Teodorescu, V. Preparation of Barium Hexaferrite by a Hydrothermal Method: Structure and Magnetic Properties. J . Mater. Sci. 1986,21, 1118. Kiyama, M.Conditions for the Formation of Compounds Consisting of BaO and FezOafrom Aqueous Suspension. Bull. Chem. SOC. Jpn. 1976,49, 1855. van der Gissen, A. A. The Structure of Iron(II1) Oxide-Hydrate Gels. J . Inorg. Nucl. Chem. 1966,28, 2155. Yoshimura, M.; Kubodera, N.; Noma, T.; Somiya, S. Synthesis of Ba-Ferrite Fine Particles by Hydrothermal Attrition Mixing. J . Ceram. SOC.Jpn. 1989, 97,16.
Received for review July 3, 1990 Accepted January 14,1991
Measurements of Binary Diffusion Coefficients of C16-C24Unsaturated Fatty Acid Methyl Esters in Supercritical Carbon Dioxide Toshitaka Funazukuri, Sumito Hachisu, and Noriaki Wakao* Department of Chemical Engineering, Yokohama National University, Yokohama 240, Japan
Binary diffusion coefficients were measured for Cls-Czr unsaturated fatty acid methyl esters in supercritical carbon dioxide (at 313 K and 16.0 MPa) and linoleic acid methyl ester in supercritical carbon dioxide (at 308-328 K and 14.0-33.6m a ) . We propose an empirical equation that correlates the diffusion coefficients in terms of Schmidt numbers, (Sc - Sc*)/Sc*, with molar volumes, (u2 ( U ~ ) ~ > / ( L Jwhere ~ ) ~ , Sc and Sc* are Schmidt numbers at the prescribed pressure and a t atmospheric pressure, respectively, and where u2 and ( u ~are ) ~molar volumes a t the prescribed pressure and a t which viscous flow ceases, respectively. Also, it was found that C02self-diffusion coefficient values recommended by Chen (1983) were well correlated by this equation.
1324 Ind. Eng. Chem. Res., Vol. 30, No. 6,1991
cienta of solute molecules in SC C02 is required. Many diffusion coefficient measurements have been made for some common organic chemicals in SC C02 (Swaid and Schneider, 1979; Feist and Schneider, 1982; Lauer et al., 1983; Sassiat et al., 1987). However, as far as we know, few such measurements have been made for unsaturated fatty acids and their derivatives in SC C02, namely, Funazukuri et al. (1989; oleic, linoleic and y-linolenic acid methyl esters in SC C02 at 313 K and 16 MPa). In our study binary diffusion coefficients of C16-C24 unsaturated fatty acid methyl esters in SC C02 were measured by the Taylor-Aris tracer response technique. In addition, we propose an equation to correlate the diffusion coefficients of the solute molecules in SC C02with their molar volumes.
Theoretical Background Consider a tracer species injected, as a shot, into a stream of carbon dioxide flowing a t a laminar flow rate u in a tubing of length L and radius r. According to Taylor (1953,1954a,b)and Aris (1956),the concentration of the tracer species C at the column exit is
in which A is a constant, 0 the dimensionless time t/., in which 7 is the mean residence time L / u , and Den the effective axial dispersion coefficient, which is given by
where D '12 is the apparent molecular diffusion coefficient. Equation 1 can be written in the normalized form as
In experiment C+,denoted by C+exptl,is obtained from a readout curve, Cexptl:
Using the tracer response technique, Swaid and Schneider (1979),Feist and Schneider (1982),Lauer et al. (1983), and Sassiat et al. (1987) determined values of diffusion coefficient from the variances in the exit concentration signals. In this study, the PexpU-t curve experimentally obtained through eq 2a is compared in the time domain with C+*-t curves calculated from eq 2 with assumed values of D 12. The determined value of D'12 is that value that brings agreement between these two curves, i.e., when the following rms error is at the minimum value:
In this work, D'12values were determined with t less than 0.03.
Experimental Apparatus and Procedures The experimental setup is shown schematically in Figure 1. Zero-dead volume fittings were used to couple the components. A diffusion column consisted of a coiled (coil diameter 275 mm) stainless steel tubing of 0.80 f 0.03 mm i.d. X 30.86 m. Carbon dioxide, pressurized by a liquid
Ribbon heater
Capillary column
Figure 1. Schematic of the experimental apparatus. Table I. Unsaturated Fatty Acid Methyl Esters Used no. of mol mol double wt bonds compound formula Cle,.-AME, cis-9-hexadecenoic C17H32O2 268.4 1 (palmitoleic) CIB:.-AME, cis-9-octadecenoic CisHMO, 296.5 1 (oleic) trans-ClB.-AME, trans-9CisHMO2 296.5 1 octadecenoic (elaidic) Ci&z-AME,cis-9,la-octaC1BHsO2 294.5 2 decadienoic (linoleic) Ci,,-AME, ~i~-6,9,12-0~ta- C1,H3202 292.5 3 decatrienoic (-plinolenic) Cm.-AME, ~i~-5,8,11,14,17- CZ1H32O2 316.5 5 eicosapentaenoic Cas-AME, cis-4,7,10,13,16,19- Ca3H,02 342.5 6 docosahexaenoic 1 Cwl-AME, cis-15-tetracosenoic C,HU02 380.7 (nervonic)
chromatographic pump (Consta Metric Pump 111, Milton Roy) whose cylinder head was cooled at about 268 K, was introduced into the diffusion column. An injector (Model 7125, Rheodyne) equipped with a 5-pL sample loop was used to inject a small amount of methyl ester (either neat or dissolved in n-hexane a t about 5 wt %), as a shot, into the COPstream at the column inlet. Note that it has been confirmed (Funazukuri et al., 1989) that the same D'12 values are obtained with or without dissolution in n-hexane. The diffusion column together with the injector and a back-pressure valve (Model 26-3220, Tescom) were immersed in a water bath maintained at a designated temperature (with fluctuations less than f O . l K). Pressure in the apparatus was regulated by the back-pressure valve. The pressures, at the entrance and the exit points of the diffusion column, were measured by a pressure gauge and a pressure sensor, respectively. The pressure difference between these two points was within 0.1 MPa. In each run no pressure pulsation was observed. A W detector (Multi 320, JASCO, Japan) located at the column exit gave the response signals, UV absorbance at 205 nm. We noted that response signals in the absorbance range 200-220 nm were almost the same. The n-hexane used in this study was of spectroscopic grade. Unsaturated fatty acid methyl esters listed in Table I were purchased from Sigma Chemical Co. The purities of these methyl esters were confirmed to be 99+% by GC-MS. No further purification of these methyl esters was made. These materials were periodically examined for denaturation by the GC-MS during the course of this study.
Results and Discussion Diffusion CoefficientsMeasured. Figure 2 shows a response curve experimentally obtained for Cle,2-AME
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1325 Table 11. Measured Data of Binary Diffusion Coefficients of Linoleic Acid Methyl Ester in Supercritical COz
calculated w i t h
"
0
n tu v) 0
n 4
68
70
74
12
76
Time, min
Figure 2. Response curves measured and calculated, for Cla2-AME at 313.2 K and 16.0 MPa.
*-I
v 3
press., MPa 14.0 16.0 16.0 16.0 19.0 19.0 19.0 19.0 19.0 21.5 24.0 25.0 25.0 25.0 25.0 30.0 30.0 33.6 33.6
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
density viscosity diffusivity of COz, of Cop: D12,blo4 no. of K 1@kgm-9 10dPas m2%l meaata 308.2 0.803 7.23 6.30 (h0.06) 6 308.2 0.827 7.66 6.20 (h0.08) 6 313.2 0.793 7.06 6.52 (h0.07) 14 318.2 0.760 6.55 7.17 (iO.11) 7 308.2 0.858 8.27 5.78 (hO.09) 6 0.830 7.72 6.17 (h0.07) 6 313.2 318.2 0.802 7.22 6.68 (10.15) 10 323.2 0.771 6.72 7.13 (h0.18) 7 328.2 0.739 6.26 7.86 (hO.ll) 7 323.2 0.802 7.22 6.92 (10.13) 18 328.2 0.802 7.22 7.14 (h0.16) 16 313.2 0.880 8.74 5.76 (hO.06) 9 318.2 0.858 8.27 6.05 (iO.09) 6 323.2 0.835 7.81 6.30 (h0.14) 7 328.2 0.812 7.40 6.66 (i0.08) 11 313.2 0.910 9.44 5.42 (h0.06) 15 328.2 0.851 8.13 6.16 (hO.ll) 7 313.2 0.929 9.93 5.10 (h0.08) 5 318.2 0.912 9.49 5.41 (hO.09) 4
temp,
,
OEstimated by the method of Chung et al. (1988). bThe values in parentheses show 95% confidence limita.
I
0.6
0.7
0.8
,
,
0.9
.
1
Table 111. Measured Data of Binary Diffusion Coefficients of Unsaturated Fatty Acid Methyl Esters in Supercritical Cot at 313.2 K and 16.0 MPa molar vo1,O Vbl 104m mol-' 3.88 4.33 4.33 4.25 4.18 4.47 4.84 5.66
u t 10-2"S-l
Figure 3. Apparent diffusion coefficients Dflavs Cop velocity at 313.2 K and 16.0 MPa: (a) CIa2-AME;(b) Cms-AME.
injected, as a shot into the capillary column, at 313.2 K and 16.0 MPa as well as those calculated from eq 2 with various assumed values of D tl. The response curve calculated with Dsdlof 2.63 X 108m2 s-' or D\2 of 6.50 X lo4 m2 s-l agrees well with the experimentally obtained curve. Parts a and b of Figure 3, respectively, show D'12 for Clg2-AME and Cm.-AME plotted against linear velocity of carbon dioxide, u. The secondary flow resulting from column being coiled can be ignored when u is sufficiently small (Feist and Schneider, 1982). In fact, inspection of Figure 3 suggests that there is negligible secondary flow m s-l for Clk2-AME effect when u is lower than 0.8 X m s-l for Cm5-AME. Thus, the and lower than 0.7 X asymptotic values at D'12 are considered to be the values of intrinsic diffusion coefficient, D12. The measured values of the diffusion coefficients for Clg2-AME in the temperature range 308-328 K and pressure range 14.0-33.6 MPa are listed in Table 11;those of Cle- to C2,-AME at 313.2 K and 16.0 MPa are shown in Table 111. In these tables the figures in parentheses indicate 95% confidence limits. In Table I11 the solute molar volumes Vb1 at normal boiling points are estimated by the method of Le Bas (Reid et al., 1987). The densities of carbon dioxide are taken from the IUPAC data (Angus et al., 19761, and the viscosities are estimated from the method of Chung et al. (1988). Correlation of D12for Clg2-AME. Various correlation formulas tested are listed in Table IV together with the average absolute deviation (AAD) defined aa follows:
Balenovic et al. (19701, and Springston and Novotny (1984) stated that the product of solvent density, p2, and binary diffusion coefficient, Ol2,was roughly constant for
no. 1 2 3 4' 5 6 7 8
comvound CiaI-AME CiB:,-AME
trans-Cla.-AME
CiaZ-AME ClaS-AME CmS-AME
Ca.-AME
C=:l-AME
diffusivity Dip) IO* no. of ma& measts 6.83 1fo.07) 2 4 6.59 (h0.05) 30 6.24 (h0.08) 12 6.52 (f0.07) 14 6.64 (h0.09) 12 6.36 (h0.04) 21 6.04 (10.04) 32 5.57 (hO.09) 10
OEstimated by the method of Le Bas (Reid et al., 1987). bThe values in parentheses show 95% confidence limits. Also listed in Table 11. 7.4,
6 1
46
48
50
I
52
1
54
56
I
58
1
60
v2, 1 0 - ~ m ~ 1 1 1 0 1 - l
Figure 4. Plot of T/d),, vs up for Cla2-AME: (A)308.2 K; ( 0 )313.2 K; (0)318.2 K; (A)323.2 K; (m) 328.2 K.
each solvent. However, Dawson et al. (1970) found that plDll/(plDll)* for self-diffusivity of methane was a function of the reduced density, where (plDll)* was that at atmospheric pressure. Our data are also well correlated by eq A-1 (with 1.3% AAD, in Table IV). Equation A-2 of Wilke-Chang (1955) shows that T/ (ccDI2)depends on Vbl and 9M2but not on solvent molar volume u p Sassiat et al. (1987) pointed out that the Wilke-Chang equation was good for predicting diffusion
1326 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991
Table IV. Various Correlations Tested for Binary Diffusion Coefficients in Suwrcritical COS correlation formula ea no.
const in MKS and mol formula A B ClB2-AMEat 14.0-33.6 MPa and 308-328 K (Refer to Table 11) In ( ~ P ~ 2 / ( ~=9A~In2PZ ) *+)B -0.614 3.97
ref
A- 1
A-3 A-4
1 VbF6 T/pD,z = - A (4M2)'/' In ( T / ( @ d )= A In u2 + B D1z/dT = A ( u -~ B )
A-5
In Sc = A In
A-2
Wilke-Chang, 1955
UD,
no. of data
2.2 x 10-18
%
19
1.3
19
3.7
0.430 1.10 X lo*
38.3 2.08 X lo6
19 19
1.3 1.5
+B
-1.21
2.38
19
2.4
+B
0.748
-18.7
19
2.3
-26.0 -18.5
8 8
0.97 1.4
B-3
26
2.0
B-4
26
2.7
51
8.2
51
3.7
- (U2)o)
GJZ
( 4 0
A-6
In D12= A In
(u2
- (U2)O) ( 4 0
B-1 B-2
Cls- to C,-AME at 16.0 MPa and 313 K (Refer to Table 111) In D12/dT= A In Vbl + B -0.551 In D12/v'T= A In Ml + B -0.567
Cls- to C,-AME at 14.0-33.6 MPa and 308-328 K (Refer to Tables I1 and 111)
Cls- to C,-AME at 14.0-33.6 MPa and 308-328 K and C02 Self-Diffusion of Chen (1983) B-5" B-6
In
(F) = A In
(u2
(uzlo)
+B
-1.40
1.48
(U2)O
"Derived by Sun and Chen for binary diffusion coefficients, not for self-diffusion.
coefficients in SC C02 if the SC C02 density was higher than about 600 kg m-3. However, Figure 4 for our data shows that T / ( p D12)depends upon C02 molar volume up even at density higher than 600 kg m-3 (or u2 lower than 7.3 X m3 mol-'). Therefore, eq A-3 is obtained (with AAD of 1.3% for our data) by modifying Wilke-Chang eq A-2 (AAD of 3.7% for our data). Dymond (1974) obtained the following correlation formulas, respectively, for self-diffusivity and viscosity:
F
45
50
v2,
where ( u ~ =) 1.384(0Jo, ~ in which (iiJ0, the hard-sphere close-packed volume, is equal to N63/d2 (N = Avogadro's number; 6 = effective hard-sphere diameter). Note dimensions in eqs 5 and 6; u1 and (61)oare in cm3mol-', Dl1 is in cm2 s-l and p is in g cm-ls-l. For our system of CIB2-AMEeq 5 reduces to eq A-4. As shown in Figure 5, this equation correlates D12with u2 quite well (with 1.5% AAD). Equations 5 and 6 indicate that p/Dll is a function of (ul - (ul)o)/(ul)o but not of temperature. Therefore, p / ( ~ & ~or~the ) Schmidt number is expected to be correlated with (u2 - ( U ~ ) ~ ) / ( UIn~ )our ~ temperature range (308-328 K) 6 for C02 is found from a graph of Van Loef (1977) to be 3.58 X 10-lom. With this value, ( u ~is) estimated ~ to be 2.7 X 10" m3 mol-', and consequently eq A-5 is obtained. This equation correlates Sc with u2, which for our Cle:.-AME data AAD is 2.4%.
55
60
m3 mol-'
Figure 5. Plot of D12/dTvs u2 for ClB2-AME (same data and legend as in Figure 4).
Ertl and Dullien (1973) proposed the following equation for self-diffusion coefficients of aromatic compounds over normal liquid range: In Dll = A In
u1 -
(Udo
(UJO
+B
(7)
When this equation is applied to our C18,2-AMEdata (by replacing Dll, ul, and ( u ' ) ~ respectively, , by D12,u2, and ( u ~ ) ~eq) ,A-6 is obtained (with 2.3% AAD). Correlation of Ol2for Cle- to C2,-AME. Matthews and Akgerman (1987) employed eq A-4 to correlate D12 between alkanes with u2 at pressures up to 3.5 MPa and found that A was proportional to Figure 6 in-
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1327
vl N
0 lo,
-
t i %
3 I
I
I
I
ztu 350
400
450
550 600 t
500
9 -1-1
vbl.
Figure 7. Plot of Sc, Sc*, and Sc/Sc* vs V,, for Cls- to C,-AME at 313.2 K: (0)sc; (A)Sc*; ( 0 )Sc/Sc*.
t
0.01
>
0.4
4
1
- -v2
A correlation of our to CN-AMEdata by eq 8, Le., eq B-3, gives AAD of 2.0%. Note that the critical volumes of the unsaturated fatty acid methyl esters are estimated by the modified method of Lydersen (Reid et al., 1987). A New Correlation Proposed. Equations A-4 and B-1 indicate, respectively, that D12/dT is a function of u2 and vb1, However, for high molecular weight or thermally unstable material v b 1 value is uncertain or unmeasurable. To overcome this difficulty Sassiat et al. used solute molar volume at room temperature for v b 1 in eq A-2 of WilkeChang (1955) and then modified the value of coefficient A. Various correlations proposed by Sun and Chen (1985a-c, 1986, 1987) need molar volumes of solute and solvent at their critical points and/or at close packing of spherical particles. It is preferable to predict D12only by using common physical properties that are easily estimated or measured. In Figure 7 Sc a t 313.2 K and 16.0 MPa, Sc* at 313.2 K and atmospheric pressure, and their ratio Sc/Sc* for c16to C,-AME are plotted vs solute molar volume at normal boiling point, vb1. Note that values of D*12at atmospheric pressure are obtained by the method of Fuller et al. (1966). It is found that the straight lines for Sc and Sc* are almost parallel to each other, and then Sc/Sc* becomes independent of vble Since the ratio of Sc/sc* approaches unity aa u2 becomes sufficiently large, (Sc - Sc*)/Sc* is expected to be correlated with (up - ( U ~ ) ~ ) / ( UWe ~ ) then ~ propose the following empirical equation:
(v2)o
(u2 - (uz)o)/(uz)ofor bin? diffusion coefficients (0)of Cls- to C2,-AME determined in this study; self-diffusion coefficients (A)of COz collected by Chen (1983).
Figure 8. Plot of (Sc - Sc*)/Sc* vs
data (26 points) measured in this work. It also includes the self-diffusion coefficients of C02 (25 points) collected by Chen (1983) in the ranges of temperature from 308 to 373 K and C02density from 124 to 830 kg m-3. These data are well represented by a single straight line. The constants of eq 9 are then determined to be A = -1.4 and B = 1.48 with AAD of 3.7% (eq B-6). If eq 8 is employed for these data, AAD becomes as large as 8.2% (eq B-5). Also, note that our binary diffusion coefficient data are correlated by eq 9 with AAD of 2.7% (eq B-4). Equation B-6 is expected to be applicable not only to the higher fatty acid methyl esters but also to common organic chemicals as well. An examination of the many data reported in the literature seems to indicate this.
Conclusions Binary diffusion coefficients for cle-c, unsaturated fatty acid methyl esters in SC C02were measured by using the Taylor-Aris tracer response technique. For each of to ClB2-AME(at 308-328 K and 14.0-33.6 MPa) and C,-AME (at 313 K and 16.0 MPa) various existing correlation formulas were tested. A new empirical correlation was then proposed: In
Figure 8 shows the logarithmic plot of (Sc - Sc*)/Sc* vs (u2 - ( U ~ ) ~ ) / ( Ufor~ )all ~ the binary diffusion coefficient
10
(v2Io
(s c ~ c ~ c *=)-1.4 In ("'i2Yo) + 1.48
(B-6)
For all of the binary diffusion coefficient data measured in this work eq B-6 brought about a good correlation. Also,
1328 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991
it was found that the C02 self-diffusion coefficient values recommended by Chen (1983)were well represented by eq B-6. Nomenclature
C = tracer response concentration, mol m-3 C+ = normalized tracer response concentration D,, = self-diffusion coefficient, m2 s-' D12= binary molecular diffusion coefficient, m2 s-l D'12 = apparent diffusion coefficient, m2 s-' Den = effective axial dispersion coefficient, m2 s-' L = column length, m M = molecular weight r = tubing radius, m Sc = Schmidt number = cc/(pzDlz)or p/(plDll) T = temperature, K t = time, s u = flow rate of supercritical carbon dioxide, m s-' u = molar volume, m3 mol-' (u& = solvent molar volume at which viscous flow stops, m3 mol-' Do = hard-sphere close-packed volume, m3 mol-' V,, = molar volume of solute at its normal boiling point, m3 mol-' Greek Symbols t
p
= error defined by eq 3 = viscosity of SC C02, Pa s
e = tiT
p = density of SC T
C02, kg m-3
= L / u , mean residence time, s = association factor of solvent in eq A-2
Superscript
* = atmospheric pressure Subscripts
c = critical 1 = solute 2 = solvent Registry No. Clk1-AME, 1120-25-8; Cla..-AME, 112-62-9; trans-Cle,,-AME, 1937-62-8; Cla.2-AME, 112-63-0; Cla..-AME, 16326-32-2; &-AME, 2734-47-6; CZS-AME, 2566-90-7; C24.AME, 2733-88-2; COZ, 124-38-9.
Literature Cited Angus, S.; Armstrong, B.; de b u c k , K. M.; ZUPAC, International Thermodynamic Tables of the Fluid State, Carbon Dioxide; Pergamon Press: Oxford, 1976. Aris, R. On the Dispersion of a Solute in a Fluid Flowing through London, Ser. A 1956,235,67-77. a Tube. Roc. R. SOC. Balenovic, 2.;Myers, M. N.; Giddings, J. C. Binary Diffusion in Dense Gases to 1360 atm by the Chromatographic Peak-Broadening Method. J . Chem. Phys. 1970,52,91&922. Chen, S. H. A Rough-Hard-Sphere Theory for Diffusion in Supercritical Carbon Dioxide. Chem. Eng. Sci. 1983, 38,655-660. Chung, T. H.; Ajlan, M.; Lee, L. L.; Starling, K. E. Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties. Znd. Eng. Chem. Res. 1988,27,671-679. D a m n , R.; Khoury, F.; Kobayashi, R. Self-Diffusion Measurements in Methane by Pulsed Nuclear Magnetic Resonance. AZChE J . 1970, 16, 725-729. Dymond, J. H. Corrected Enskog Theory and the Transport Coefficients of Liquids. J. Chem. Phys. 1974,60,969-973. Ertl, H.; Dullien, F. A. L. Self-Diffusion and Viscosity of Some Liquids as a Function of Temperature. AZChE J . 1973, 19, 1215-1223. Feist, R.; Schneider, G. M. Determination of Binary Diffusion coefficients of Benzene, Phenol, Naphthalene, and Caffeine in Supercritical C02 between 308 and 333 K in the Pressure Range 80 to 160 Bar with Supercritical Fluid Chromatography (SFC). Sep. Sci. Technol. 1982, 17, 261-270.
Fuller, E. N.; Schettler, P. D.; Giddings, J. C. A New Method for Prediction of Binary Gas-Phase Diffusion Coefficients. Ind. Eng. Chem. 1966,58 (5), 19-27. Funazukuri, T.; Hachisu, S.; Wakao, N. Measurement of Diffusion Coefficients of CIS Unsaturated Fatty Acid Methyl Esters, Naphthalene and Benzene in Supercritical Carbon Dioxide by a Tracer Response Technique. Anal. Chem. 1989, 61, 118-122. Ikushima, Y.; Saito, N.; Hatakeda, K.; Ito, S.; Asano, T.; Goto, T. A Supercritical Carbon Dioxide Extraction from Mackerel (Scomber Japonicus) Powder: Experiment and Modeling. Bull. Chem. SOC. Jpn. 1986,59,3709-3713. Ikushima, Y.;Hatakeda, K.; Ito, S.; Saito, N.; Asano, T.; Goto, T. A Supercritical Carbon Dioxide Extraction from Mixtures of Triglycerides and Higher Fatty Acid Methyl Esters Using a GasEffusion-Type System. Znd. Eng. Chem. Res. 1988a, 27,818-823. Ikushima, Y.; Arai, M.; Hatakeda, K.; Ito, S.; Saito, N.; Goto, T. Selective Extraction of a Mixture of Stearic, Oleic, Linoleic and Linolenic Acid Methyl Esters with Supercritical Carbon Dioxide Using a Gas-Flow Method. J. Chem. Eng. Jpn. 1988b, 21, 439-441. Ikusima, Y.; Saito,N.; Goto,T. SelectiveExtraction of Oleic, Linoleic and Linolenic Acid Methyl Esters from Their Mixture with Supercritical Carbon Dioxide-Entrainer Systems and a Correction of the Extraction Efficiency with a Solubility Parameter. Ind. Eng. Chem. Res. 1989,28, 1364-1369. Lauer, H. H.; McMauigill, D.; Board, R. D. Mobile-Phase Transport Properties of Liquefied Gases in Near-Critical and Supercritical Fluid Chromatography. Anal. Chem. 1983,55, 1370-1375. Le Bas, In The Properties of Gases and Liquids, 4th ed.; Reid, R. C.; Prausnitz, J. M.; Poling, B. E.; McGraw-Hill: New York, 1987; p 53. Lydersen, A. L. In The Properties of Gases and Liquids, 4th ed.; Reid, R. C.; Prausnitz, J. M.; Poling, B. E.; McGraw-Hill: New York, 1987; p 12. Matthews, M.A.; Akgerman, A. Diffusion Coefficients for Binary Alkane Mixtures to 573 K and 3.5 MPa. AIChE J . 1987, 33, 881-885. Nomura, A.; Yamada, J.; Tsunoda, K.; Sasaki, K.; Yokochi, T. Supercritical Fluid Chromatographic Determination of Fatty Acids and Their Esters on an ODs-Silica Gel Column. Anal. Chem. 1989,61, 2076-2078. Sako, T.; Yokochi, T.; Sugeta, T.; Nakazawa, N.; Hakuta, T.; Suzuki, 0.; Sato, S.; Yoshitome, H. Studies on Production of Lipids in Fungi. XV. Extraction of Neutral Lipids in Mortierella Genus Fungi by Using Supercritical Carbon Dioxide. J . Jpn. Oil Chem. SOC. 1986,35,463-466. Sassiat, P. R.; Mourier, P.; Caude, M. H.; Rosset, R. H. Measurement of Diffusion coefficients in Supercritical Carbon Dioxide and Correlation with the Equation of Wilke and Chang. Anal. Chem. 1987,59, 1164-1170. Springston, S. R.; Novotny, M. Mobile-Phase Solute Mass Transfer in Supercritical Fluid Chromatography. Anal. Chem. 1984, 56, 1762-1766. Sun, C. K. J.; Chen, S. H. Tracer Diffusion of Aromatic Hydrocarbons in Liquid Cyclohexane up to its Critical Temperature. AZChE J . 1985a, 31, 1510-1515. Sun, C. K. J.; Chen, S. H. Diffusion of Benzene, Toluene, Naphthalene, and Phenanthrene in Supercritical Dense 2,3-Dimethylbutane. AZChE J . 1985b, 31, 1904-1910. Sun, C. K. J.; Chen, S. H. Tracer Diffusion of Aromatic Hydrocarbons in n-Hexane up to the Supercritical Region. Chem. Eng. Sci. 1985c, 40, 2217-2224. Sun, C. K. J.; Chen, S. H. Tracer Diffusion in Dense Ethanol: A Generalized Correlation for Nonpolar and Hydrogen-Bonded Solvents. AIChE J . 1986,32, 1367-1371. Sun, C. K. J.; Chen, S. H. Tracer Diffusion in Dense Methanol and 2-Propanol up to Supercritical Region: Understanding of Solvent Molecular Association and Development of an Empirical Correlation. Ind. Eng. Chem. Res. 1987, 26, 815-819. Swaid, I.; Schneider, G. M. Determination of Binary Diffusion Coefficients of Benzene and Some Alkylbenzenes in Supercritical COz between 308 and 328 K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography (SFC). Ber. BunsenGes. Phys. Chem. 1979,83,969-974. Taylor, G. Dispersion of Soluble Matter in Solvent Flowing Slowly London, Ser. A 1953,219,186-203. through a Tube. Proc. R. SOC. Taylor, G. The Dispersion of Matter in Turbulent Flow through a Pipe. Proc. R. SOC.London, Ser. A 1954a, 223, 446-468.
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Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, I , 264-210.
Received for review August 13, 1990 Accepted December 11,1990
Diffusion Coefficients of Long-chain Esters in Supercritical Carbon Dioxide K. Keat Liong,
P.Anthony Wells, a n d Neil R.Foster*
School of Chemical Engineering and Indwtrial Chemistry, University of New South Wales, P.O.Box 1, Kensington 2033, Australia
Binary diffusion coefficients, Ol2,of CIBfi,Cm, and Cz. ethyl esters and Cm6 and C2M methyl esters were measured in supercritical carbon dioxide in the temperature range 308-318 K and a t pressures between 96.7 and 210.5 bar. Measurements were obtained using a capillary peak broadening technique. The experimentally determined diffusion coefficients were approximately 1 X lo4 cm2/s a t 313 K and 97 bar, decreasing to approximately 0.5 X lo4 cm2/s with an isothermal rise in pressure to 210 bar. The applicability of several correlations to the experimental diffusivity data was examined. In particular, the free-volume-type diffusion model was found to correlate the experimental data to within f3%. Introduction Supercritical fluid (SCF) extraction has received considerable attention in recent years as a technique for the separation of relatively nonvolatile materials. It is a novel separation technique that embodies several features of conventional solvent extraction and distillation in addition to several important, unique features such as liquidlike densities, gaslike viscosities, and diffusivities between typical gas and liquid values. The combination of liquidlike solvent power and gaslike transport properties is exploited in SCF extraction. Another feature of this type of extraction is that the overall properties of the fluid are very sensitive to changes in pressure and temperature in the vicinity of the critical point. This means that small changes in extraction conditions are often all that is required to effect complex separations. In addition, the relatively low operating temperatures often required to achieve criticality make the technique suitable for treating heat-sensitive substances that could not be extracted by conventional distillation. Despite the potential that SCFs can offer to extraction processes, the lack of fundamental thermodynamic data required for process design and scaleup has hindered development of the technology to a substantial commercial level. Hence, much research effort has been directed to obtaining procsas design parameters under SCF conditions. Diffusion is the dominant rate mechanism and is significant in equipment design for and process development of SCF extraction. There are currently very few sets of data for binary diffusivity in SCF systems (Groves and co-workers, 1984). Therefore the aim of this study was to obtain binary diffusion data for long-chain ethyl and methyl esters in supercritical carbon dioxide. These long-chain esters are typical of those found in esterified marine lipids. Clinical studies have shown that diets rich in these lipids can play an important role in regulating human metabolism. In particular, both cis-5,8,11,14,17eicosapentaenoic acid (EPA, C20:6w-3) and cis4,7,10,13,16,19-docosahexaenoicacid (DHA, C,#-3) have attracted considerable attention from researchers as having beneficial effects on human health (Dyerberg, 1986). As few binary diffusivity data for solutes in SCFs exist, there have been few attempts to model this property. With
the substantial data obtained in this study the merits of several currently available correlation models have been assessed. Experimental Section Binary diffusivities in supercritical carbon dioxide were measured by using the capillary peak broadening (CPB) technique. The principle of the CPB technique is based on the fundamental work of Taylor (1953, 1954), later extended by Aris (1956),which involved the dispersion of a solute in a laminar flow of mobile phase through a tube. The application of this technique to high temperature and pressure has been demonstrated by a number of researchers (Matthews and Akgerman (1987), Sassiat and co-workers (1987)). A comprehensive discussion of the basic theory has been given by Groves and co-workers (1984) and Alizadeh and co-workers (1980). Theory. Taylor (1953) showed that a narrow pulse of solute will broaden into a peak due to the combined action of convection along the axis of the tube and molecular diffusion in the radial direction. This concentration profile of the peak can be described mathematically by
or in terms of the theoretical plate height H
H = a2/L
(2)
where DI2 = diffusion coefficient, cm2/s; L = length of column, cm; U,, = linear velocity, cm/s; 2 = variance, cm2; H = theoretical plate height, cm; and ri = internal radius of tube, cm. For flow through a straight tube, the concentration profile becomes essentially Gaussian (Levenspiel and Smith, 1957) if D,/U& < 0.01 (3) where (4) DefI= D12+ r?Uo2/48Dl2 However, due to the lengths of the tubing required for diffusion experiments, the tubing generally has to be coiled
0888-5885/91/2630-1329$02.50/00 1991 American Chemical Society
