ANALYTICAL CHEMISTRY
388 The results show an increase in raffinose during storage in the pile, but the rate of increase is much less than in roots stored in the cellar. DISCUSSION
That the raffinose content of sugar beets increases during storage appears to be demonstrated without question, but it is too early to attempt an authoritative discussion of the factors which determine the absolute level of raffinose in the roots a t harvest time or the rate a t which the raffinose content increases during storage. Environmental factors during the growth of the beet may be of major importance. Heredity appears to be a factor. Much additional information is needed on the whole subject. The quantities of raffinose found in most beets tested during the past season were far above the expected value. However, it has been demonstrated that the quantities of certain other components may differ widely between beets grown on average commercial fields and beets grown on highly fertile experimental fields, and since only the results given in Table I11 were obtained on commercially grown beets, it is possible that the data presented herein may tend to create a false impression of the normal raffinose content of commercial beets. Most of the beets encountered in the present investigation were far above the normal for commercial beets of the Rocky Mountain area. As a check on the above observation, press juice was obtained from a large batch of pulp from the same group of beets considered in Table I (average, 1.33% raffinose on sugar). The press juice was given the standard lime defecation and carbonation treatments, and a pan was boiled from the juice in order to produce a green sirup in which the raffinose content would be sufficiently great to ensure accuracy of the raffinose determination by
invertase and melibiase hydrolysis. The green sirup showed 82.6% sucrose and 2.25% raffiose on dry substance, equivalent to 13y0 raffiose on impurities. On further crystallization of eugar, this raffinose would be found in the molasses a t the same per cent on molasses impurities. The average raffinose content of molasses from beets in the Great Western Sugar Co. area in 1950 was about 4.5% on impurities. While the mother beets that were tested averaged abnormally high in raffinose content, a few of relatively low rafFmose content were found, and possibly the plant breeders may develop a strain of low raffiose beets from those few. ACKNOWLEDGMENT
The writer is indebted to numerous persons for assistance in this investigation. First, he gives his thanks to H. C. S. deWhalley, director of the Tate and Lyle Research Laboratories, for information, in advance of publication, on his work on the determination of raffinose in raw beet sugars. Various members of the staffs of the Research Laboratory and the Experiment Station of the Great Western Sugar have given valuable assistance, especially Ralph Wood. LITERATURE CITED
(1) Albon, N., and Gross, D., Analyst, 75,454-7 (1950). (2) Bacon, J. S. D., and Edelman, J., Arch. B i o c h m . , 28,467 (1950). ( 3 ) Blanchard, P. H., and Albon, N., Ibid., 29,270 (1950). (4) deWhalley, H. C. S., Intern. Sugar J . , 52, 127-9, 151-2, 267 (1950). (5) Partridge, S. M., Biochem. J.,42, 258 (1948). RECEIVED April 27, 1951. Presented before the Division of Sugar Chemistry at the 119th Meeting of ANERICAN CHEMICAL SOCIETY, Boston, Maas.
Determination of Geometric Surface Area of Crushed Porous Solids Gas Flow Method SABRI ERGUN Coal Research Laboratory, Carnegie Institute of Technology, Pittsburgh, Pa.
D
ETERMINATION of specific surface area of solids has long been the subject of numerous investigations in connection with correlating the energy spent in crushing with new surface created. Although the establishment of such a relationship would be of great practical use to the process industries of crushing, the interest in surface determination has by no means been limited to crushing. Surface determinations are generally a means to an end-i.e., the knowledge of surface in itself is not so important as the application of such knowledge to estimation of reaction, heat and mass transfer rates, and pressure drop, and to numerous processes in industrial operations. Most solids possess, in addition to their external visible surface, an internal surface due to existence of empty spaces within their boundaries. If these internal spaces are considerably larger than molecular sizes, they are referred to as pores, and the material is spoken of as being porous. Differentiation between the external surface and the internal surface of porous particles is often important, but is difficult to make, as there exists no definite boundary between them. A geometric surface, as distinct from external surface, may be visualized as the surface of an impervious envelope surrounding
the body in an aerodynamic sense. Irregularities and striae on the surface would not be taken into account in a geometric surface in contrast to external surface. Whether the value of the internal, or the external, or the geometric surface area is desired will depend on the objective. Geometric surface areas are required in connection with sedimentation rates, resistance to the flow of fluids, bulk density and packing problems, and heat and mass transfer rates in flow processes. If rates of solution and reaction, and hygroscopic or total adsorptive properties are in question, the total accessible area is the relevant area. Diversified interests in surface area measurements have led t o the development of various methods, and in recent years the literature on the subject has grown rapidly. Dissolution methods developed by Wolff (83), and Martin and coworkers (YO),and later extended by Schelte (76) and Gross and Zimmerley (38), have been used to measure surface areas of glass beads, crushed quartz, etc. These methods, however, are limited t o materials for which a suitable solvent exists; even then critics have regarded the method as doubtful (S, 7 4 ) . The proportionality of heat of wetting for a given solid-liquid pair to the surface area of the solid has been utilized by various
V O L U M E 24, N O . 2, F E B R U A R Y 1 9 5 2
Particles of crushed porous solids possess a geometric surface-the surface of an impervious envelope surrounding the particles in an aerodynamic sense. Knowledge of geometric surface areas is essential to solving problems arising from gas flow through beds of solids, and no satisfactory method has existed for crushed porous solids. A gas flow method is described that permits determination of the geometric surface areas of crushed porous solids from the measurements of pressure drop as a function of gas flow rates and bulk densities. The method, which is based on a fundamental flow equation, automatically determines the particle density of the porous solids and offers two alternative methods of mathematical analyses. The equation employed in one of
woikers (8, 13, 14, 37, 39, 57) to determine the surface area of powders. Gregg (37) regarded heat of wetting methods as free from uncertainties if the specific heat of wetting for the solidliquid pair in question is known. The area measured, however, is necessarily t h a t of the surface accessible to the molecules of the wetting liquid. Adsorption of dyes (69, 73, 76), radioactive substances (73), and various other solutes from solution (34, 37, 49), has been perhaps the most widely used method on account of of its relative experimental ease. The method, hoT\ever, cannot be u5ed for the absolute determination of the total surface area of porous poi\ den. Uncertainties regarding the relative adsorption of solvent arid solute, and also the orientation of the solute molecules on the adsorbent surface, render the method doubtful. The area measured, as in the case of heat of wetting method, is that o f the surface accessible to the molecules of adsorbate. If a knonledge of external area is desired, the molecules of the adsorbate should be large enough so that they do not penetrate the pores. Recent advances in gas adsorption theories, with the development of the Brunauer, Emmett, and Teller (17) and Harkins and Jura (39-41,53,54) methods, have attracted wide interest; and gas adsorption methods have been used widely for determination of total surface area of solids (d,7,9-12, 15,16, 18,94-28,36,37,44, 50,51,57,59,67,7f,84-86). Adsorption methodsin general depend on the evaluation of the monolayer capacity of the solids. For solids having extremely h e pores, however, capillary condensation greatly affects the course of the isothermal adsorption curves and, in many instances, may account for nearly all of the adsorption. Ilistler, Fischer, and Freeman (58) have utilized the Boltzniann equation relating the capillary condensation to relative pressure and surface tension to develop an equation that permits evaluation of the total surface area from an adsorption isotherm. Other treatments base their origin on the Kelvin equation relating the capillary radii to vapor pressure of the liquid condensed. Early attempts are due to Lowry and Hulett (69),Foster (39), and Lowry (68). Based on the same principle, Harvey (42) outlined a method for obtaining the surface area of a large volume of pores distributed over a wide range of radii with the use of adsorption isotherms. Surface estimation methods based on size analysis by sieving, elutriation, sedimentation, centrifugal sedimentation, etc. (3, 43, 45-47, 74),aim to establish a shape factor or volume and surface factors which would enable calculation of specific surface when the characteristic dimension is determined by the particular method of size analysis. These methods are based on statistical processes by which size segregation is effected. Size analyses by ordinary or electron microscope measurements ( 2 , 33, 43,
389
the methods is entirely new in this field. Results are reported for numerous cokes of different origin as well as mesh sizes. Geometric surface areas are essential in the estimation of rates of sedimentation, resistance to flow of fluids, bulk density and packing problems, and rates of heat and mass transfer in flow processes. For example, in the passage of appreciable quantities of gas through beds made up of porous solids, the Row, in effect, surrounds the particles, the gas almost entirely passing through the void space, and the pressure loss, heat, and mass transfer rates accompanying the flow are a function of both the surface surrounded and the void space. The method also determines void space as a result of the measurement of particle density.
55,62,81,82) differ from those mentioned above in that the particles are measured individually instead of being grouped statistically by some process of classification. There remains the problem of obtaining a representative sample which may involve a large number of particles if there is a great variation in size. The position in which the particles rest when distributed on a slide introduces uncertainties in that the particles will not rest in all random positions, but only in stable positions. Photometric or light-extinction methods (33,45, 52, 77, 78) are baEed on the absorption of light by solid particles dispersed uniformly in a fluid medium. These methods, like the microscopic one, measure the projected area of the particles, but unlike the microscopic methods, they yield the projection area in :dl random positions. Calculation of the surface area is based on a relationship set forth by Cauchy (22), who has shoan that for irregular solids randomly oriented in all positions, the geometric surface area is four times the average projection area. Size analyses and photometric methods necessarily measure the geometric surface area unless corrected empirically by factors accounting for surface roughness. Permeability or fluid flow methods are used extensively for determination of specific surface of powders on account of the simple apparatus required. The principle of the methods is the use of a flow equation to determine the specific surface from measurements of flow rate and pressure drop. Permeability methods ox-e their widespread use to the development of the Kozeny equation (19, 60, 63,64), The Kozeny equation is based on the Poiseuille flow and has been found to be satisfactory a t low rates of gas flow through beds of particles having specific surfaces less than 2000 sq. em. per cc. (1, 12, I S , 36, 61, 76, 79, 80). Through extremely fine material whose dimensions ale comparable to the mean free path of the gas, diffusion or molecular flow must be taken into account. Rigden (75), Keyes (56), Arne11 (4,5 ) , Lea and Kurse (63), Carman ( $ I ) , and others have modified the Kozeny equation t o include terms that account for the molecular flow, while Holmes (48)and later Deryagin et al. (23) have developed flow equations based on Knudsen’s law for gas diffusion through a fine channel. While these modifications stemmed from the investigation of the validity of the Kozeny equation a t extremely low rates of gas flow through fine powders, studies on coarser material a t the higher rates (20, S i , 65, 66, 72) have shown great departure from the Kozeny equation. The validity of the results of the specific surface determinations by the use of flow methods depends upon the validity of the flow equation used. Accepting, for the moment, the validity of any one of the flow equations, an additional problem presents itselfi.e., determination of the fractional void volume, one of the im-
ANALYTICAL CHEMISTRY
390 portant variables in the flow equations, offers difficult)- in the case of crushed porous Politis. The fractional void volume is calculated from the bulk tlensity of the packing and the particle density of the solids, the latter of \\-liich is not usually k n o w and Yhich is not a characteristic property because it changrs with particle size. Therefore, deterniinration of the specific surface of porous solids by gas flow niethods hinges upon a determination of the particle demity of the material, as well as the validity of the flow equation used. For this reason the presenl paper was preceded by two articles-one on the development of a flow equation in the flow of fluids through m n u l a r beds (30), the other on the determination of the particle density of crushed porous solids ($9). Consequently, it has been possible to develop methods whereby the specific surface of crushed porous solids can be determined by gas flow methods. The flow equation drveloped is for hpds having specific surfares less than 2000 sq. cni.
400
clcq, ,mtl the gas almost entirel~pasac$ through the vold 'pac't'. As the pressure loss aec~~niparij lug the flow is a function of both
the surface surrounded and the void epace, its measureinetit should lead to the determination of the surface and the void volume The theoretical coIisiderations anti the experimental d.ita Ird to the development of the follo\iIng linear expression tor p i wsure drop through granular bedfi (50)
AP/I,b,,,
= 0
' 1)
4- bG
ulieie AP is the plrqsure drop, I, is the height of the bed, CTm the average linear gas velocity h s e d on the cross section of the m p t y column, G is the m:tv f l o ~rate per unit area of the ('rncs wetion, and a and b are rocfficientL;which are represented h \ ic
wherc fi represents t,he a h o l u t r visccsity of the gas, 8, the specific: surface area of the part'iclefi, e the fractional void voluine of the bed, and kl and k, are numerical constants. When the ratios of pressure gradient) to average velocity are plotted agairlst ni:~ss flax ra.te according to Equation 1, a straight line is obtained (Figure I) having the intercept a and the slope 6 . .To determine t,he specific surface from either the slope or the intercept, it is neceesary to know the fractional void volume. The fractional void volume can he obtained from a knowledge of the bulk density of the solids in t,he bed and the particle density of ttir solids by t,he UPR of the follo~ririgrelationship:
3 00
200
\\liere p B is the bulk density and p i h th? particle density. Sui)stitution of Equation 4 into Equatioiia 2 and 3 and solviiig for S , will yield
and I
0 0
001
002
003
004
005
006
Figure 1. Typical Plots of Equation 1 for a System Packed to Different Fractional Void Volumes Nitrogen flow throu h 40- to 60-mesh hi h temperature oven coke (sample 8). A s - s e c t i o n a l area of tube 7.24 sq. om. P/Lllmisindyneseec./cm.4oringrarns/sec.oc.and G i s i n grams! iec. 99. om. Lines drawn according to method of least fiqurires
per cc. This roughly correspoiids to particles larger than 0.1 i i i n i . iii size or 140-mesh. Therefore, the method to be developd niu5t necessarily be limited to particles larger than 0.1 nun. (for fine powders cf. 4 , 5 , 2 1 , 5 6 , 6 5 ,75).
+
~-
__ __-
G 'Table I.
Specific Surface Determinations for High Temperature Coke Slierifir Suriac,r. CLn. --I -. I'srtirle I ~ P - I I s I ~ ~____..~ , G .'c'c . Eq. 7 Eq, 8
Sieve Size
u. 9. Standard
0.92 1.07 1.16 1.23 1.30 1.47 1,5
