Diffusion Phenomena in Solvent Extraction of Pea,nut Oil Effect of Cellular Structure H. 6. FAN1.AND J. C. MORRIS Tulane University, New Orleans, La.
HELMUT WAKEHAM Southern Regional Research Laboratory, U. S . Department of Agriculture, New Orleans, La. T h e theory of diffusion extraction of oil from a porous solid is examined in the light of previous investigations on solvent extraction of oil seeds. Peanut kernels were prepared and extracted in such a manner as to meet the conditions required by the diffusion theory derived from Fick’s law. The diffusion coefficient under these conditions varies with solvent and with the moisture content of the oil seeds but is essentially independent of the thickness of the peanut sections extracted. It is shown that the results with peanut sections closely follow the theory when the broken cells at the surfaces of the sections and the void spaces due to moisture loss are taken into consideration.
of oil in the cell must be uniform; (d) the thickness of the slab must be small compared with the dimensions of the surface, and diffusion through the edge of the slab must be negligible; and (e) the thickness of the slab must be uniform and the same for all slabs extracted a t the same time. If these conditions are assumed, the mathematical problem is the same as that for a porous slab, which has been touched upon repeatedly in the literature (8, 3, 4, 8, 10, 14). Boucher and coworkers (4) gave the solution of the diffusion equation as
T
where q
quantity of.oi1 in a unit volume or weight of solid at t seconds after d8usion has started qo = initial quantity of oil in solid-that is, a t t = tp 21 = thickness of slab D = diffusion constant
H E solvent extraction of a vegetable oil from a crushed or flaked oil seed involves solution of the free oil from the broken cells and diffusion extraction of the oil in the undamaged cellular structure of the seed. Intelligent design of an efficient extraction procedure requires a thorough knowledge of all the factors which may influence the extraction process. The present paper reports a study of diffusion phenomena occurring during solvent extraction of peanut oil from specially prepared sections of peanut kernels. The techniques and conclusions presented may be of assistance in studying extraction from other oil seed systems.
=
The derivation of Equation 2 stems from a solution of the Fourier heat equation for the case where a slab, originally a t a uniform temperature 60,suffers a sudden change of surface temperature from eo to el. The origin is taken a t the center of the slab, and the equation for the temperature a t any point z a t time t is (16)
THEORY
When a porous solid containing a liquid solute is brought into contact with a solvent liquid, interdiffusion of the molecules of the two liquids follows. This diffusion may be defined by Fick’s law for the so-called nonstationary state of flow,
n=l
where c = concentration of solute a t point z distance from the origin; t = time; D = diffusion constant, amount of material which passes a plane of unit area in unit time when under unit concentration gradient Various solutions of Fick’s law may be obtained by applying suitable boundary conditions to the differential equation. The result of such a solution for the analogous problem of heat conduction has been used by March and Weaver (19) in the,case of a solid in contact with a stirred liquid. Similar solutions for a number of cases have been compiled by Barrer (1) and applied to various diffusion problems by other workers (4, 6, 6, 7 , 9 ,IS). To obtain diffusion accorditng to Fick’s law certain conditions must be met: (a) The diffusion coefficient, D , must be a constant independent of thickness; ( b ) the structure of the kernel must be reasonably homogeneous and isotropic; (c) the distribution
Figure 1. Preparation of Peanut Slices for extraction^ A and B , peanuts and kernels; C, pqanut kernels imbedded in paraffin wax; D, imbedded kernels mounted on metal base after a portion has been removed with the microtome; E , extraction thimble; F, slice. of peanut kernel after extraction.
1 Present addresa, China Fatty Oil Industries, Ltd., 50 Hankow Road, Shanghai, China.
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Converting the left-hand temperature function directly to the 3 by analogy, concentration gradient ratio ' CQ - c1 C - C ~
-CQ
- el
_ -eea- -e 1el
=
right-hand term of Equation 3
(4)
where c = concentration (might per unit volume) of oil at any point z in the slab ca = originaluniform conceritIation in the slab c1 = concentration of liquid solution into which slab 1s immersed At any time t the concentration gradient ratio varies with x but assumes a definite value for each value of t. I n the experimental procedure, however, an average value of the concentration gradient ratio is determined. This is found by integrating the ratio in Equation 4 between the limits of 0 and I as follows, keeping t a constant:
If the Concentration c1 of the oil in the liquid in contact with the slab is zero, the concentration ratio becomes C / C Q . This may easily be converted into the quantity ratio q/po of Equation 2, since concentration is the quantity of material per unit volume. The series of Equation 2 converges rapidly, so that a few terms are sufficient for most practical calculations. In fact, except for very small values of t all but the first term in the series may be neglected. Equation 2 then reduces to
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by a roller mill, and therefore did not meet the conditions specified in the theory. As pointed out by Osburn and Katz (IS), an average thickness cannot be used in this type of measurement. The material used, furthermore, 'cyas probably not homogeneous since the cellular structure of the oil seed was partially crushcd in the roller mill. In the experiments to be described an attempt as made to prepare, by means of a microtome. uniform sections of peanut kernels which would meet the conditions necessary to obtain diffusion according to Fick's law. EXPERIMENTAL PROCEDURE
Ordinary commercial peanuts (Virginia variety) were employed. The kernels n-ith skin attached Tvere first packed vertically into a paper boat. The 1%-holeboat of peanuts was kept, in a refrigerator for 1 hour and then filled with ordinary paraffin wax to imbed the peanut kernels. The refrigeration protected the peanuts against any heat, effect when in contact xvith the melted paraffin (melting point 56' C.). The resulting block (Figure 1) was mounted on a suitable metallic base for slicing with a microtome. A standard 14-inch Spencer sliding microtome was used to cut the peanuts imbedded in paraffin into cross-sectional slices of any desired thic1;nctss up to 0.04 em. The slices so prepared Tvere not britt,le and would withstand gentle shaking, flushing with solvents, and other manipulation required in the experiment tTithout excessive breakage. Only sections cut through the middle portion of the kernel were used for experimental purposes to give slabs with the maximum ratio of face area to edge, since the theory does not take into account extraction from the edges of the sections. This condition was, as a matter of fact, easily met, because the first layer of kernel cells just under the skin of the peanut was found greatly to retard extraction by petroleum solvents. Careful microscopic observation of the slice prepared by the microtome revealed that, in general, only those cells a t the surface of the slice were damaged by the microtome knife (Figures 2 and 3). The peanut slices prepared in this manner contained considerable quantities of the paraffin imbedding material. Fortunately this material is infinitelv soluble in the petroleum frac-
and logio p/po = -0.0911
D - 4.286 -i(21)
t
(10)
This is the equation for a straight line \Then loglo p/po is plotted against t. The slope of this line may be used to evaluate the diffusion constant. Boucher and co-workers (4)set up nearly ideal conditions for testing this theory in their extraction of soybean oil from impregnated slabs of porous clay plate. They obtained data which shoved that the extraction process obeys Fick's law. King, Xatz, and Brier, (9), on the other hand, carried out similar experiments using soybean flakes and reported that the simple diffusion theory for uniform porous solids does not correspond to the observed extraction data for soybean flakes. These flakes, however, were not of uniform thickness, having been prepared
Figure 2. Section Near Surface of Peanut Kernel Showing Epidermal Layer with Tough Cell Wall through Which Oil and Solvent Diffusion is Relatively Slow (Stained with Eosin;
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the calculations. Since this factor influencw the rate of extraction, however, the moisture content of the peanut slices was determined and noted for each extraction. The initial concentration of oil in the sample, qo, was determined from the weight lost during complete batch extraction of chopped peanuts selected a t random from the peanuts used throughout the experiment. It was found that QO = 0.82 gram per gram of oil-free dry solid peanut kernel. RESULTS
.
Eight series of experimental extractions were made to determine q/qo as functians of time. The curves for these are plotted in Figures 4, 5, and 6. A theoretical curve based on Equation 10 is included in Figure 4 for comparison. I n all cases the observed experimental curves were straight lines after t = 30 minutes. This similarity between the experimental curves and the theoretical curve indicates that, no matter what deviation may exist in the beginning of the process, after 30 minutes the diffusion in such cellular material obeys Fick's
Figure 3. Cross Section of Extracted Peanut Slice, Thickness 0.032 Cm., Showing Surface Cells Ruptured during Preparation of Slice and Whole Cells Near Center (250 X)
tions used as extracting solvents. A rapid flow of solvent a t the beginning of the extraction period washed away the paraffin in a few seconds, leaving the peanut sections free for extraction in the normal manner. As long as the,solvent flowed rapidly enough to keep the concentration of oil in the solvent essentially zero, the rate of solvent flow did not matter, since we need only determine 9/40 as a function of time in order to calculate the diffusion coefficient. Extraction was carried out in a small U-tube extractor, one side of which held a previously weighed 25 X 80 mm. paper extraction thimble containing the peanut sample. The solvent was run by gravity from an elevated storage flask into the side of the U-tube containing the thimble and drained out the adjoining side of the U into another flask. At the end of time t, the whole thimble with the extracted sample was removed, drained, and dried in a hood for 1 hour to remove any remaining solvent. It was then dried in an oven at 130' C. for 2.5 hours to remove any traces of moisture present. After weighing, the thimble with sample was placed in a large bottle containing fresh solvent for complete batch extraction for 24 hours. Two such extractions and a final wash were found sufficient to remove completely any remaining oil from the sample. The thimble and sample were then again air-dried in a hood, oven-dried, and weighed to obtain the weight of the oil-free, dry peanut slices. The difference in weight of the peanut sample before and after complete batch extraction was taken as the oil content of the sample a t time of removal from the extractor. Experiments were performed with Skellysolve F and Skellysolve B as solvents. The former consists essentially of n-pentane, the latter of hexanes (boiling points 30' to 60" and 60' to71 O C., respectively). Temperature influences the viscosity of the solvent and the oil and, consequently, the rate of diffusion. These experiments were carried out at room temperature (24-26 C.). The moisture content of the kernel does not enter directly into O
0*03R,*
0.02
I
0.0I 0 Figure 4.
20
40 TIME IN MINUTES
60
Extraction Curves for Experiments 1 and 2
The theoretioal aurve is for a diffruion coef€iaientapproximately equal to that obtained in experiment 1.
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0.05 1 0
1
I
I
300
200
100
J
TIME IN M I N U T E S .
Figure 5. Extraction Curves for Experim e n t s 3-6 Using Slices of Similar Moisture Values
law. I t is therefore valid to calculate by Equation 10 the diffusion coefficient from the straight-line portion of the semilogarithmic plots shown in the figures. The results of these calculations, along with other pertinent data on the experimental determinatiohs, are shown in Table I.
OF TABLE I. DIFFUSIOXCOEFFICIENT^ FOR EXTRACTION PEAXUT SLICES WITH PETROLEUM SOLVENTS
D Cor-
hf oisture, Wt. % of Oil-Free Expt.
No,
Solvent Skellysolve F Skellysolve B
Thickness, Cm. 0.012 0.032
o , ozo
0.026 0,032 0,040 0.032 0.032
Dry
Solid 12 20 13 14 13 17 10 22
reoted to 13% Moisture, D , Scl. Cm./Seo. 1 6 . 5 X 10-9 8 . 2 x 10-0 7 . 1 X 10-9 6 . 8 X 10-9 5 . 6 x 10-9 1.8 x 1 0 - 9 7 . 8 X 10-9 3 . 2 X 10-9
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4. Comparison of the experimental curves (Figures 4, 5 , and 6) with the theoretical curve indicates that in all cases some of the oil is extracted from the peanut slices much more rapidly than predicted by the theoretical relation, The thicker the slice, the less the initial drop in the curve and the more it resembles the theoretical curve. Osburn and Kat2 (13) explained this phenomenon in terms of two diffusion coefficients, the more rapid diffusion being that from ruptured cells. This agrees with the views of the present authors that the cell wall is the major obstacle t o diffusion extraction. From a microscopic study of the peanut slices it was found the cells have a diameter of approximately 0.007 em. A slice of 0.032em. thickness may, therefore, have about five layers of celk (Figures 2 and 3). Assume that the slice is cut so that the layers of undamaged cells lie in the middle of the slice. There are, then, two half layers on each face of the slice. The oil in the half layers on the surfaces of the slices will be washed off rapidly, leaving the remainder of the oil in the unruptured cells to diffuse out according to Fick's law. The actual oil content of the peanut slice which is involved in Fick's diffusion 1aiT is not PO, but PO reduced by a factor (21 - 0.007/21), where 21 is the thickness of the slice. For example, in experiments 7 and 8 the slices were 0.032 em. thick. If p; be the actual oil content and qo the apparent nil content which includes the oil in the ruptured surface cells, q; = 0.781 90. The experimental values used in plotting the curves for the peanut slices of 0.032-em. thickness should have been q / 0.781 40 This correction has been made in the curves of Figure 7 in which the solid lines A and B are the corrected curves for experiments 7 and 8, respectively. Curves A' and B' are theoretical lines calculated from the diffusion coefficient shown in Table I for the same experiments. The agreement is seen t o be good in the A curves for experiment 8 and demonstrates that Fick's law may be used to predict accurately diffusion extraction in cellular material when the conditions outlined by the theory are set up. 5. Comparison of the corrected experimental curve B (Figure 7) with the theoretical plot B' indicates that still another factor must be taken into consideration in an experimental test of the theory. Table I shows that the moisture values of experiments 7 and 8 differed appreciably. The authors bclievc that the disagreement between the B and B' curves mav be related t o the low moisture in the peanut slices
sq.
Cm./Seo.
...... ......
7 . 1 x 10-9 7 . 2 x 10-9 5 . 6 X 10-9 3 . 4 x 10-9 6 . 6 X 10-9 6 . 8 X 10-9
"Ot
I
DISCUSSION
Table I reveals a number of interesting generalizations. 1. The diffusion coefficient is more than twice as great for the lighter Skellysolve F than for the Skellysolve B. This effect, brought out by a comparison of experiments KO. 2 and 8 in which the peanut, slices had the same thickness and moisture values, is t o be expected, since the lighter solvent differs in viscosity, chemical affinity, molecular size, solvent power, and other factors. Boucher, Brier, and Osburn (4) showed that the diffusion coefficient was related t o the viscosity of the solvent for a given extraction. The viscosities of Skellysolve F and B are 0.28 and 0.35 cent'ipoise, respectively, at 25" C. 2. The greater the moisture in the seed material, the smaller was the diffusion coefficient and, consequently, the slower the diffusion. This is illustrated in experiments 5 , 7, and 8 run with peanut slices of the same thickness but with different moisture values. A comparison of KO.8 with 50.7, the experiments with the highest and lowest moistures, indicates that a difference of 1% in moisture content changes the diffusion coefficient approximately 0.4 X 10-9 square centimeter per second. This factor was used to correct all the diffusion coefficients obtained with Skellysolve B to a common moisture content of 13%. The corrected values appear in the last column of Table I. 3. The corrected data for experiments 3 t o 8, inclusive, show that the diffusion coefficient is essentially independent of the thickness of the peanut slices, as predicted by the diffusion theory outlined earlier. The most serious discrepancy, the case of experiment 6, may be due to experimental error in determining D. Figure 5 shows that the slope of the extraction curve, from which the diffusion coefficient is evaluated, approaches zero at higher thicknesses. The method of measuring D thus becomes less accurate as thickness increases.
0.1 1
0
Figure 6.
100 200 TIME IN MINUTES
300
Extraction Curves for Experiments 5, 7, and 8 Using Sliccs 0.032 C m . Thick
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199
where V , is the volume of the void space. I n the diffusion equation (Equation 9) co is not a conltant when void spaces exist in the kernel but changes with tim$ after the kernel is immersed in solvent to the saturation value CO. Let the variation of ~0 with time be represented by co+(t). C
Equation 9 may then be written -= f ( t ) or codJ(t)
c
’
- = 4/qo
CO
=
+(t)f(t)
(12)
and log q/oo = log +(t)
+ 1ogm
(13)
At any given time the term log + ( t ) is the difference between the experimentally determined value of log {q/qo) and the term log f ( t ) calculated from the diffusion coefficient. The curve of log +(t) against time represents the rate a t which the solution fills up the void spaces in the material and mixes with the oil. The values of +(t) shown in Figure 7 were obtained from the differences between the B and B’ curves a t various time intervals. The curve shows that at 1 = 1’ = 30 minutes, + ( t ) reaches a constant valueof 0.85. At this point +(t) = V,/(V, V,) = 0.85, from which we obtain V , = 0.176 VO. This evaluation of the void spaces in the dry peanut slices may be checked roughly by a consideration of their moisture contents. In experiment 8 the material was essentially saturated with moisture and should, therefore, have contained a minimum of void space. I n experiment 7 the material had been vacuumdried. The difference in moisture was 0.22 - 0.10 = 0.12 gram of water per gram of oil-free dry solid. This quantity of water would have occupied approximately 0.12 cc. of space. Since the density of the peanut oil, p, is about 0.92 (If), the total volume of oil per gram of oil-free dry solid was qo/p = 0.82/0.92 = 0.89 = VO. Hence, V,/VO= 0.12/0.89 = 0.135. This value is comparable with the ratio of 0.176 found experimentally from the curves in Figure 7. The agreement between the evaluation of +(t) and the volume condition obtained from the moisture considerations indicates that the presenwof the void spaces may be one explanation of why the experimental curve drops rapidly a t the beginning of the extraction process. Other equally satisfactory explanations could probably be made, but their experimental support must await further detailed investigation of the phenomenon of diffusion in oil-seed extraction.
+
0
100 200 TIME IN MINUTES
300
Figure 7. Extraction Curves for Experiments 7 ( B ) and 8 ( A ) Corrected for Ruptured Cells at Surfaces of Slices Curves B’ and A’ are theoretical curves based on the diffumion coefficients shown i n Table I. Curve + ( t )is t h e difference between the B and B’ curves and represents the rate at which the nolution fills up the void spaces in the material.
The explanation for this deviation from theory is based on the iaasumption that certain spaces exist in the material which are filled with moisture when the peanut is saturated with moisture and which become void when the material is dried out. Thus, not all the pore spaces in the cellular material are filled with oil. When the material is immersed in solvent these spaces are gradually filled with solvent which dissolves some of the oil. In the preceding discussion of the solution of Fick’s law, co (the original concentration of thg oil in the slab) was assumed to be constant at any time. Actually co varies with t, and during the time that the void spaces are filling with solvent, or solution, the concentration ~0 is decreasing. A rigorous mathematical consideration for such a system is beyond the scope of this paper. However, the factors involved may be indicated as follows: A unit volume of peanut kernel consists of (a) impermeable and insoluble material, ( b ) oil, and ( c ) void space which may be filled with gas. Before the material is placed in a solvent, co represents the initial weight of oil per unit volume occupied by the oil. For 1 = 0, co=p-
vo = vo
p
where V Ois the volume occupied by the oil and p is the density of the oil. After a certain time, t’, during which the material is immersed in the solvent, all the void space is saturated with solvent, or solution. Hence, when t = t’, ci is the weight of oil per unit volume when all void space is filled with solution. Then
ACKNOWLEDGMENT
The authors take pleasure in acknowledging the assistance of Mary L. Rollins and Anna T. Moore in preparing the photomicrographs of Figures 2 and 3, and the advice of E. F. Pollard at whose suggestion the present investigation was undertaken. LITERATURE CITED
Barrer, R. M., “Diffusion in and through Solids,” Cambridge University Press, 1941. Becker, J. A., Trans. Faraday SOC.,28,148(1932). Bosmouth, R. C. L., Proc. Roy. Soc. (London), 150A,58 (1935); 154A, 112 (1936). Bouoher, D. F., Brier, J. (I. and , Osburn, J. O., Trans. Am. Inst. Chem. Engrs., 38,967 (1942). Cady, L. C., and Williams, 3, W., J. Phys. Chem., 39,87 (1935). Friedman, L., J. Am. Chem. Soc., 52,1305 (1930). Friedman, L.,and Kraemer, E. O., Ibid., 52,1295 (1930). Hatta, 5. J., SOC.Chem. Ind. (Japan), 39,486B (1936). King, C. O.,Kats, D. L., m d Brier, J. C., Trans. Am. Inst. Chem. Engrs., 40,533 (1944). Langmuir, I., and Taylor, J. B., Phya. Rev., 40,463(1932). Magne, F. C., and Wakeham, H., Oil & Soap, 21,347(1944). March, H.W., and Weaver, W.,Phys. Rev., 31,1072 (1928). Osburn, J. O.,and Kats, D. L., Trans. Am. Inst. Chem. Engrs.. 40,511 (1944). ’ (14) William, J. W., and Cady, L. C., Chem. Revs., 14,171 (1934). (15) Williamson, E.D., and Adms, L. H., Phys. Res., 14,99 (1919). RECEIVED January 16, 1947.
