Ind. Eng. Chem. Fundam. 1982, 21, 447-451 Weisz, P. B. Z . Phys. Chem. (Frankfurt am Main) 1957, 1 7 , 1. Weisz, P. B.; Prater, C. D. Ab.. Cafal. Relat. Sub/. 1954, 6, 143. Welsz, P. B.: Hicks, J. S. Chem. Eng. Sci. 1962, 77, 265. Whyte, T. E. Catal. Rev. 1973, 8 , 117.
Segal, E.; Madon, R. J.; Boudart, M. J . Catai. 1976, 52, 45. Sinfelt, J. H. C9fel. Rev. 1989, 3 , 175. Smith, H. A.; Fuzek, J. F. J . Am. & e m . Soc.1946, 68, 229. Stewart, W. E.; Vllladsen, J. V. AIChEJ. 1969, 75, 28. TaJbl, D. (3.: Simons, J. B.; Carbeny, J. J. Ind. Eng. Chem. Fundam. 1966, c
447
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3. I 1 I .
Receiued for reuiew September 28, 1981 Accepted May 7, 1982
Temkin, M. I . Klnet. Kafal. 1962, 3 , 509. Wanke, S. E.: Dougharty, N. A. J . Cafai. 1972, 24. 367.
Mechanism of Stickiness in Hygroscopic, Amorphous Powders Galen E. Downton,' Jos6 L. Flores-Luna,2and C. Judson King' Department of Chemical Engineering, University of Callfornia, Berkeiey, California 94720
Sticking, caking, and agglomeration tendencies of hygroscopic, amorphous powders are interpreted in terms of a mechanism of viscous flow driven by surface energy during particle contact. The mechanism predicts that stickiness should occur for combinations of temperature and moisture content corresponding to viscosities of the amorphous material below some relatively constant value, which for short-time contact should be within the range loe to 10' Pas. The viscosity is affected by both moisture content and temperature, thereby explaining the inverse relationship between sticky-point temperature and moisture content for such powders. Both bulk-solution and powdered specimens of a 7:l w/w mixture of sucrose and fructose were prepared, with moisture contents in the range of 2 to 7% w/w. Viscosity measurements of the bulk-solution specimens were made with both a falirg-baii method and a rheogoniometer. Viscosities correspondingto experimentally measured sticky-point temperatures fell consistently within the range 0.3 X lo7 to 4.0 X lo7 Paos, thereby lending support to the proposed mechanism and quantitative model.
Introduction Dehydration of liquid materials is widely used to produce stable, easily handled and stored products in an economical fashion. Several techniques, such as spray drying, freeze drying, and drum drying, are available for producing dried powders from a wide range of raw materials including liquid foods, plastics, detergents, fertilizers, and pharmaceuticals. One phenomenon frequently encountered during production and storage of these dried powders is stickiness. A familiar example of stickiness is caking during storage. Hygroscopic dried foods such as instant coffee or drink mixes tend to form hard cakes when subjected to high temperatures and/or humidities. The powder is no longer free-flowing and, because the cakes are less porous, they reconstitute less readily. Another example of stickiness, which can be turned into an attribute, is agglomeration, a process commonly used with dehydrated powders to obtain larger, porous particles with better rehydration and handling characteristics and/or more pleasing and consistent color, shape, and appearance. This operation is redly one of controlled stickiness; particles are deliberately subjected to steam, moist air, or a fine mist of water, as well as repeated contact, so that surfaces become sticky and clusters form via particle collisions and adherence. In spray drying, stickiness can be a major problem, which occurs when particles which are insufficiently dry collide with one another or with the walls of the drying apparatus and become stuck. This can lead to lower product yields,
operating problems, and powder-handling difficulties. For heat-sensitive products this can also lead to overheating, resulting in unpleasant sensory characteristics and/or degradation. These problems are preventing some materials-notably fruit juices which contain large amounts of hygroscopic, amorphous sugars-from being successfully dehydrated. Coping with stickiness in spray dryers and in powdered products and achievement of successful agglomeration have largely been matters of trial-and-error experimentation to find conditions which avoid or control the sticky characteristics of a given material. Cooling the dryer walls and flushing them with cool air have been employed to avoid stickiness in spray dryers (Lazar et al., 1956; Gupta, 1978a,b). Various additives, often of high molecular weight, have also been used to combat stickiness in spray drying (Brennan et al., 1971; Gupta, 1978a,b) and in powders (Peleg and Mannheim, 1969,1973,1977). There is as yet no quantitative model which describes the mechanism of stickiness in dried powders and explains the success of failure of past approaches to the problem. Previous mechanistic speculations are nearly all qualitative and incomplete. White and Cakebread (1966) recognized dried liquid foods as amorphous glasses, i.e., metastable, supercooled liquids below their glass-transition temperature, Tg.At temperatures below Tg, the viscosity is extremely high, of the order of 10l2Pa.s (Jones, 1956). A t higher temperatures and/or humidities, the glass assumes more of a liquid nature, with a lower viscosity. Stickiness defects, such as lumpiness and caking, were attributed to this incipient liquid state. Peleg and Mannheim (1977) attributed caking of onion powder to moisture absorption and proposed a humidity-based caking mechanism. In their model, water absorbs on particle surfaces, forming a saturated solution and thereby making the particles sticky and capable of forming
Procter and Gamble Company, Coffee Division, The Winton Hill Technical Center, 6210 Center Hill Road, Cincinnati, OH 45224. 'Mezquital de Oro, Apdo. Postal 138, Hermosillo, Sonora, Mexico. 0196-4313/82/1021-0447$01.25/0
0
1982 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982 FREE PARTICLES
ST I C K I N G PA AT I C L E S
Figure 1. Stages of stickiness.
liquid bridges. Shrinkage, which often accompanies caking, was attributed to the interparticle forces due to surface tension and/or capillary pressure becoming sufficiently great. Lazar et al. (1956) noted that stickiness in powders causes the force required to turn a stirrer embedded in the powder to increase sharply. This situation amounts to the formation of a hard cake and is the basis for a test commonly used to determine the sticky conditions of a material. Rumpf (1974) and Schubert (1973) present a quantitative analysis of different types of forces which may hold agglomerates together, once they are formed. However, their analyses do not deal with the tendency for stickiness to occur, or for agglomerates to form in the first place. The purpose of the present work was to propose and test a mechanistic model which can describe quantitatively the tendencies for particles to stick to one another or to a wall.
Mechanistic Model Figure 1shows schematically the stages presumed to be involved when two initially dry amorphous particles become moist and then stick to one another. Moistening the particle surface layers (shaded areas) reduces the viscosity. If two particles then come in contact they may or may not stick together, depending upon whether sufficient liquid flow can occur to build a bridge between the particles that is strong enough to resist subsequent mechanical deformations. The driving force for flow during contact is surface tension. Resistance to flow is measured through the viscosity. Either dimensional analysis or a simplistic energy balance relating the reduction in surface energy due to flow to viscous energy dissipation, similar to that given by Bellows (1972), leads to an equation of the form where k is a dimensionless proportionality constant of order unity. Greater surface-tension driving force (y) or longer contact times (7)increase the tendency toward sticking, while greater viscosity ( p ) or greater distances (KD)over which flow must occur decrease the sticking tendency. Typical values can be inserted into eq 1to predict the order of magnitude of particle viscosity critical for stickiness during contact times of a few seconds between powder particles: k = 1 (assumed); y = 70 mN/min for interstitial concentrate; T = 1-10 s for the method of Lazar et al. (1956) for determining stickiness; D = 7 Km (actual particle sizes in the present work were 1-10 pm); K = 0.01-0.001. Rumpf (1974) and Schubert (1973) showed
that a small contact area is sufficient to form strong liquid bridges between particles. These values predict a critical viscosity range of lo6-lo8 Pa-s. Since the viscosity of amorphous concentrates is usually extremely sensitive to temperature and concentration changes, such an orderof-magnitude analysis should be sufficient for most purposes. This model for stickiness is very similar to the analysis put forward by Bellows and King (1972, 1973) to describe the phenomenon of collapse (loss of structure) during freeze drying. In that case collapse, or apparent melting, was related to viscous flow of webs of the porous matrix left behind after ice sublimation, under the impetus of surface tension. Tsouroflis et al. (1976) noted that the inverse temperature-moisture content relationship found experimentally for stickiness is similar to that found for collapse during freeze drying. They also measured temperatures at which collapse occurred in freeze-dried powder samples of orange juice and carbohydrates with different moisture contents. Here collapse was defined as transition to a fused state, with loss of the powdery appearance. Again the form of the inverse relationship between moisture content and temperature for collapse was similar to those found for stickiness and for collapse during freeze drying. Tsouroflis et al. (1976) therefore suggested that similar mechanisms must prevail for all three phenomena, in line with the present analysis. In order to test the model proposed here, experiments were made to determine whether or not stickiness occurs at a more-or-less constant value of viscosity within the predicted range of lo6 to lo8 Pa-sfor an amorphous-powder system having various moisture contents. This required the selection of a suitable solution to be studied, measurement of its viscosity as a function of temperature and moisture content, and determination of conditions of temperature and moisture content which yield stickiness.
Preparation of Materials Solutions consisting of 87.5% sucrose and 12.5% fructose, w/w, were chosen as a simple model of dehydrated fruit juices, for which stickiness is a major concern. The use of simple sugars, such as sucrose, fructose, and glucose, approximates fruit juice compositions because these sugars amount to over 95% of the dissolved solids in most juices (Bellows, 1972). Fructose was added in the lowest ratio found to preclude sucrose crystallization reliably for the conditions experienced by the superconcentrated solutions used in this work. Two types of material were required for this work-bulk, homogeneous liquid solutions for viscosity determinations, and powder for sticky-point determinations. The method used for bulk-solution preparation was dissolution of a suspension of sugar crystals in heated water, followed by evaporation to concentrate the samples (Flores-Luna, 1979). Rapid cooling was then used to minimize degradation reactions and inhibit crystallization through a sharp increase in viscosity. Final moisture contents were dependent upon evaporation time and temperature and could be predicted after experience was gained. This procedure was similar to open-pan cooking, which is used in the confectionery industry for the manufacture of high-boiled sweets (Lees and Jackson, 1973). Sucrose hydrolysis was minimized since heating times were short, the pH (around 8.0) corresponded to the minimum rate of sucrose hydrolysis (Kelly and Brown, 1978/79),and fructose, a hydrolysis product, was already present in a significant amount. The final product was a transparent, straw-colored liquid (93-98% sugar) with a very high viscosity and free of crystals and air bubbles.
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982 449
Powder samples were prepared by freeze drying a 25% wfw aqueous sucroseffructose solution and crushing the porous product to yield particles 1-10 pm in size. The amorphous powder was extremely hygroscopic; therefore all operations involving powder handling and storage were carried out in a dry box under low-humidity conditions. Powder samples with moisture contents varying from 2.0 to 7.0% w/w were obtained by equilibrating thin layers of powder over saturated salt solutions or sulfuric acid solutions in vacuum desiccators.
Methods of Moisture Analysis The primary standard used for moisture analyses was the Karl Fischer titration (Mitchell and Smith, 1980). The method was used directly for powder samples, with a platinum-tungsten electrode assembly similar to that of Almy et al. (1940), the contacting procedure described by Johnson (1945), and direct titration. Measured moisture contents could be replicated within f0.1% H20. For bulk-solution samples, the Karl Fischer method was used to calibrate measurements made with an Abbe refractometer (Downton, 1981). Because of the slow approach of the viscous solutions to a steady-state reading within the refractometer, readings of refractive index were arbitrarily recorded 100 min after loading, even though further changes in indicated refractive index (up to 0.0013, or 0.45% w/w indicated solute content) were still occurring. For the range of compositions encountered in this work, the moisture content indicated by the Karl Fischer titration was about 1% w/w (absolute basis) higher than that corresponding to a linear (in weight fraction) extrapolation of weighted-average literature refractive-index data above 85% and 95% w/w for sucrose and fructose, respectively (Downton, 1981). Viscosity Measurements The principal technique used for measurement of absolute viscosity was the well-known falling-ball method (Barr, 1931; Bacon, 1936). This approach was favored since it allows the use of simple equipment, covers a large part of the viscosity range of interest, and, because of low shear, minimizes the tendency toward shear-induced crystallization during the measurement. If the Reynolds number is much less than unity, the viscosity is given by Stokes' law
Corrections were made for wall effects (Altrichter and Lustig, 1937). Bulk solutions with varying compositions (2.0-7.0% HzO wfw) were prepared in 0.50-L graduated cylinders. These samples were placed in a constant-temperature oil bath maintained at 20,40, 60, or 80 "C. Solid metal spheres were guided into the samples in such a way as to prevent entrainment of air bubbles and distortion of the axial travel of the sphere. There was a f2.3% random average deviation of measured velocities within a given run (Flores-Luna, 1979). A Weissenberg rheogoniometer was used for supplementary measurements in the upper range of viscosities, where the falling-ball method required long times. The Weissenberg rheogoniometer is a plate-and-cone rotational viscometer, highly instrumented and developed to measure rheological properties over a wide range of stress or shear rate in both tangential and normal planes (Van Wazer et al., 1963). Stress and shear-rate conditions are uniform within the fluid sample, unlike other viscometers. A low
I / T x lo3 K - I 10'2
2 9
I
,
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31 I
32
,
,
33
34 I
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35
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0 Folling boll 0 Rheogoniometer A Rheogoniometer w r t h crysIoll8zotion suspected
105
EO
70
I
1
I
60
50
40
I
30
1
-
I
20
T , "C
Figure 2. Viscosity of the sugar solution w. reciprocal temperature.
shear rate was used to avoid non-Newtonian effects, although isolated explorations did not reveal any of these. Operating procedures used are described elsewhere (Ho, 1978; Flores-Luna, 1979). Some tiny sugar crystals were noted in the bulk of some of the rheogoniometer samples after complete runs were finished. These measurements may have been less precise, since it was not possible to determine when incipient crystallization took place during the measurements or to see if any air bubbles were entrapped in the samples. Data obtained through the falling-ball and rheogoniometer methods are plotted semilogarithmically vs. reciprocal temperature in Figure 2. For the two concentrations where crystals appeared in the rheogoniometer measurements and therefore some uncertainty exists, dashed curves are drawn following the general trends observed for the falling-ball data at higher concentrations. Similar extrapolations are made for each concentration up to lo1' mPa.s. Results follow trends similar to those shown by previous data for other aqueous sugar solutions at lower viscosities (Flores-Luna, 1979). The well-known WLF equation, used widely for polymeric systems, characterizes the measured viscosities from this work well using freevolume concepts, as is shown by Soesanto and Williams (1981). In addition, those authors have made proposals for estimating these viscosities in terms of molar volumes of the individual components.
Sticky-Point Measurements The test used to determine sticky points of the amorphous sugar powder was that developed by Lazar et al. (1956). In it a previously hydrated powder sample is contained in a test tube which is closed to the atmosphere via a rotating mercury seal. The tube is then immersed in a constant-temperature water bath. The bath temperature is slowly raised while the powder is intermittently stirred by hand with a small propeller embedded in the sample. At a certain temperature, which depends upon the moisture content of the powder, the force required to turn the stirrer increases sharply. This is, in effect, the instantaneous caking temperature, and it is denoted the sticky-point temperature. The bath temperature was raised about 1 "C every three minutes at temperatures well removed from the sticky point, and about 1"C every 5 min as the sticky point was approached. Heating was assumed to be slow enough so that the powder temperature was the same as the bath temperature. The propeller was turned manually, 1/4 turn every other second. The test tube was firmly tapped periodically to ensure good powder contact with the stirrer. Within about 5 "C of the sticky point, a very slight resistance was encountered to stirring. Within 2 or 3 "C of the sticky point, the powder formed small clumps which fell apart upon tapping the test tube. At the sticky point,
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Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
501 2 551
2c .
I
I
i
i
Table I. Viscosities at Which Stickiness Occum (Interpolated from Figure 4 )
I
I
45
2.02 2.87 3.26 3.62 4.19 5.80 6.61
C
3.0
2.0
IO
4.0
5.0 6 0
7.0
H20 ( d r y basis1
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Figure 3. Sucrose/fructose sticky-point curve. I / T x lo3 K - ' lC~2
2.9
, Wl%
, 0 ~ ~
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3
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33
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1 '03'lsb
7b
So
5b
40
0:
io
I
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Figure 4. Viscosities of the sugar solution at the sticky point.
there was a sharp increase in the force required to turn the stirrer. End points were found to be clearly and precisely discernible. Replicate measurements gave the same sticky point, within f l K. Sample stirring could have been carried out mechanically instead of manually. Brennan et al. (1971) noted that the current to a stirrer motor increased sharply at the sticky point. Experimental sticky-point temperatures for the sucrose/fructose model powder are shown in Figure 3. The curve drawn through the data is similar to results obtained for similar systems by previous researchers (Lazar et al., 1956; Notter et al., 1959; Lazar and Morgan, 1966; Brennan et ai. 1971).
Discussion Sticky points of the sucrose/fructose powder are replotted in Figure 4,this time superposed upon the curves representing the viscosity data. All of the experimental points lie well within the predicted critical viscosity range and fall within the more limited range of 0.32 X 1O'O to 4.0 X 1O'O mPa.8, as shown in Table I. These two features-the relative constancy of the viscosities at the sticky point, and the fact that this viscosity falls within the range predicted by the model-support the proposed quantitative model as a good description of the stickiness phenomenon, based upon a correct interpretation of the mechanism of stickiness. The proposed mechanism can be used to explain the degree of success of past approaches taken to the stickiness problem. Established techniques of equipment modification and control primarily involve cooling the nearly dry particles or subjecting them to low-humidity conditions, as noted above. Both of these changes strongly raise the viscosity of the material composing the powder particles. Similarly, when higher-molecular-weight additives-such as gums, pectins, or maltodextrin-are used as drying aids, they serve to increase the viscosity at a given moisture
50.8 42.3 41.5 35.0 34.5 19.8 19.5
0.32 1.3 0.32 1.6 0.50 4.0 1.3
content and can raise the viscosity sufficiently to avoid stickiness. This is similar to the beneficial effects of these substances in raising the collapse temperature in freeze drying (Bellows and King, 1973) and deterring structural collapse of freeze-dried powders (Tsouroflis et al., 1976). The inverse relationship between sticky-point temperature and powder moisture content is also directly explained by the proposed mechanism. The critical viscosities found in this work were nearly constant at 1O'O mPa-s. In order to achieve a given viscosity, the moisture content must decrease as temperature increases, as shown in Figure 4. Thus, a particular relationship between sticky-point temperature and moisture content, such as shown in Figure 3, is determined by maintaining near-constancy of the critical viscosity of a material. Collapse temperatures for turning powders into a fused mass are generally lower than sticky-point temperatures for a given substance (see, e.g., Tsouroflis et al., 1976) because of the much longer times over which the process occurs (larger 7 in the numerator of eq l),despite the greater distances over which flow may have to occur. Similarly, critical moisture contents for caking during storage should be somewhat lower than those for instantaneous stickiness, at the same temperature. With a more quantitative and mechanistic understanding of the phenomenon of stickiness, a common ground exists for future research and process improvements in the area. This knowledge can be applied to suggest novel methods for overcoming the problem or for predicting under what conditions stickiness will occur so that it may be controlled.
Acknowledgment This research was carried out under Grants No. ENG 76-17270 and CPE-8006786 from the National Science Foundation. One of the authors (J. L. F-L.) also received partial support from Consejo Nacional de Ciencia y Tecnologia, Mexico. Nomenclature D = particle diameter, m d = diameter of metal sphere, m g = acceleration due to gravity, m/s2 K = fraction of the particle diameter required as bridge width for a sufficiently strong interparticle bond k = dimensionless proportionality constant T = temperature, K T = glass transition temperature, K = sticky-point temperature, K uT = metal sphere terminal velocity, m/s Greek Letters y = surface tension, N/m p = viscosity, Pa.s p = solution density, kg/m3 pa = metal-sphere density, kg/m3 T = time required for stickiness to occur, s Literature Cited
2
Airny, E. 0.;Griffin, W. 72(7). 329.
C.;Wllcox, C.S. Ind. Eng. Chem., Anal. Ed. 1040,
45 1
Ind. Eng. Chem. Fundam. 1982,21, 451-456
Altrichter, F.; Lustlg, A. Phys. Z . 1937,38, 786. Bacon, L. R. J. Franklin Inst. 1938,227, 251. Barr, 0. "A Monograph of Viscometry"; Oxford: London, 1931, Chapter 1, p 1. Bellows. R. J. PhD. Dissertation, University of Callfornia, Berkeley, 1972. Bellows, R. J.; King, C. J. Cry&b/ogy 1972,9, 559. Bellows, R. J.; King, C. J. AIChESymp. Ser. 1973,69(132), 33. Brennan, J. 0.; Herrera, J.; Jowltt, R. J. Food Techno/. 1971,6 , 295. Downton, G. E. M.S. Thesis, University of California, Berkeley, 1981. Fiores-Luna. J. L. M.S. Thesis, University of California, Berkeley, 1979. Gupta, A. S. "Spray Drying of Cltrus Juices", presented at American lnstltute of Chemical Engineers, Annual Meeting, Miami Beach, Nov 1978a. Gupta, A. S. US. Patent No. 4 112 130, 1978b. Ho, P. M.S. Thesis, University of California, Berkeley, 1978; p 249. Johnson, C. M. Ind. Eng. Chem., Anal. Ed. 1945, I7(5),312. Jones, G. 0. "Glass"; Methuen: London, 1956; p 5. Kelly, F. H. C.; Brown, D. W. Sugar Technoi. Rev. 1978l79,6 , 1. Lazar, M. E.; Brown, A. H.; Smith, G. S.; Wong, F. F.; Llndquist, F. E. Food Technoi. 1958, 10, 129. Lazar, M. E.; Morgan, A. I., Jr. food Techno/. 1988. 20(4), 531.
Lees, R.; Jackson, E. B. "Sugar Confectionery and Chocolate Manufacture"; Leonard Hill: Aylesbury, G.B., 1973. Mitchell, J.; Smith, D. M. "Aquametry: A Treatise on Methods for the Determination of Water", in "Chemical Analysis Series", 2nd ed.; Wiley-Interscience: New York, 1980 Vol. 5, Part 3. Notter, G. K.; Taylor, D. H.; Downes, N. J. Food Technol. 1959, 73, 113. Peleg. Y.; Mannhelm, C. H. J. Food Techno/. 1989,4 , 157. Peleg. M.; Mannheim, C. H. Powder Technoi. 1973, 7 , 45. Peleg. M.; Mannheim, C. H. J. Food Process Resen,. 1977, I , 3. Rumpf, H. Chem. Ing. Tech. 1974,46(1), 1. Schubert, H. Chem. Ing. Tech. 1973,45(6), 396. Soesanto, T.; Williams, M. C. J. Phys. Chem. 1981,8 5 , 3338. Tsouroflis, S.; Flink, J. M.; Karel, M. J. Sci. Food Agric. 1978, 27, 509. Van Wazar, J. R.; Lyons, J. W.; Kim, K. Y.: Colweil, R. E. "Viscosity and Flow Measurement", Intersclence: New York, 1963, p 113. White, G. W.; Cakebread, S. H. J. Food Technoi. 1988, 7 , 73.
Receiued for review October 15, 1981 Accepted July 16, 1982
Solid-Liquid Mass Transfer in Segmented Gas-Liquid Flow through a Capillary Vaslllos Hatrlantonlou and Bengt Andersson Department of Chemical Reaction Engineering, Chalmers University of Technobgy, S-4 12 96 Gijteborg, Sweden
The mass transfer of benzoic acid in a segmented gas-liquid flow in a tube was studied. The inner wall of the tube was coated with benzoic acid. A mathematical model describing the mass transfer was developed and a computer simulation was found to agree quite Well with the experimental data. A simple power law model describing the Sherwood number dependence of the variables was also proposed. The solid-liquid mass transfer for the segmented flow was found to be much greater than the mass transfer of continuous liquid flow without gas plugs.
Introduction A common difficulty in processing the three-phase reacting system, gas-liquid in the presence of a solid catalyst, is caused by the limiting mass transfer rate between the phases. A reactor with a monolithic "honey comb" catalyst support and a specially designed gas-liquid flow has been used in order to increase the rate of mass transfer. The monolith contained a large number of axial channels, which formed the catalyst support structure of the reactor system (to be published). The purpose of this work is to describe the flow and the mass transfer phenomena occurring in a single channel of the monolith effected by the segmented flow, which consists of well-separated plugs of gas and liquid. Due to internal recirculation of the liquid in the plugs (Figure l), the mass transfer to and from the liquid is enhanced compared to the mass transfer in a continuous liquid flow without gas plugs. Among the characteristics of this flow are the enhanced radial dispersion (Horvhth et al., 1973a) and the reduced axial dispersion (Skeggs, 1957). Moreover, the liquid film between gas and the solid wall is of negligible thickness, which improves the mass transfer from the gas to the wall. This reactor design obviously allows a more direct contact between wall and gas. Some studies have been made on this kind of system which indicate that the above-mentioned segmented or slug flow offers good possibilities for obtaining high mass transfer. This flow type and its applications have been studied by, among others, Horvith et al. (1973a), who measured the radial transport in slug flow through circular pipes with immobilized enzyme on the inner wall. They 0196-43 13/82/1021-045 1$0 1.25/0
also derived (1973b) a mathematical model for this novel reactor. Other studies on this subject have been carried out by Skeggs (1957), Oliver and Hoon (1968a,b), Snyder and Adler (1976), Satterfield and Ozel (19771, Vrentas et al. (1978), and Oliver and Wright (1964). Duda and Vrentas (1971) developed an analytical solution to describe the steady, closed streamline velocity field within a cylindrical cavity with a uniformly translating wall at low Reynolds numbers. Experimental Section The tube dimensions used in our experiments are the same as those of the above-mentioned monolith channels. The inner wall of the tube was coated with solid benzoic acid instead of catalytically active material. In this coating procedure melted benzoic acid was poured into a glass tube of suitable diameter, where it was allowed to cool. The thickness of the solid film was adjusted by a well-centered steel rod inside the tube. Two different tube diameters were used. The length of the tubes was 0.17 m, and their inner diameters after coating with benzoic acid were 2.350 and 3.094 mm, respectively. The reactants, water and air, were made to flow first through an empty glass tube which enabled visual investigation. The empty tube was fitted at the top of the coated tube. The inner diameters of the empty tube and the solid film were the same, Le., 2.350 and 3.094 mm, respectively. The flow through the tube contains alternately gas and liquid plugs with laminar profiles. The values of the total linear velocity for both tube diameters were determined to be between 0.079 and 0.13 m/s, corresponding to Reynolds numbers between 259 and 424, respectively. 0 1982 American Chemical Society
