PAUL Y. McCORMICK
MATHEMATICS PENETRATES DRYING TECHNOLOGY Computers begin to explore the complexities of moisture movement and heat flow u bstantial advances have been made in formulating S drying theory, and mathematical approaches are becoming more important as computers capable
of solving complex equations are increasingly available. During 1961 and the first quarter of 1962, the period covered by this review, important studies have appeared on the mechanism of moisture movement and heat flow. The studies, both experimental and mathematical, are concerned specifically with porous sheets, fibers, particulate solids in layer form, and spray droplets. Dehydrated and freeze-dried food products have received major attention also. Dehydrated foods now take just under 2% of the consumer’s food dollar ( 2 ) . Future outlets for these together with freeze. dried products probably will be mostly in soups (now a market of more than $500 million a year, of which 6yo is for dehydrated mixes and 2% for frozens), institutional markets, overseas exports, and military and camping supplies. At its plant in Camden, N. J., Campbell freeze-dries several ingredients for soups (20). Also, T. J. Lipton has recently installed freeze-drying facilities, and hopes to reduce drying costs to 2l/2 to 3l/2 cents per pound of moisture removed (20). A review of freeze-drying plant concepts is available (16) together with a list of manufacturers which make freeze-drying equipment. For dehydrated foods, foam-mat drying has been improved (9) to enhance the drying characteristics of fruit and vegetable juices and to yield products more readily reconstituted in water. Rapid drying is attributable to moisture movement by capillarity in the liquid films separating the foam bubbles. Improved reconstitution results from the honeycomb structure of the dry solids. Edible foam stabilizers are used-e.g., soybean protein, albumin, sucrose fatty acid esters, and glyceryl monostearate. Perforated trays or conveyors with air through circulation are employed for drying the foamed products. I n another foam-formation process, designed to improve the operation of spray dryers (6) compressed air is injected into the feed liquid through a mixing device located between the pressure pump and atomizing nozzle. Injection of the gas produces a foam and the
AUTHOR Paul Y . McCormick is a Senior Engineer in the Engineering Service Division, Engineering DeFartment, E. I. du Pont de Nemours Co., Inc., Wilmington, Del.
relatively large surface of the foamed droplets increases drying rates. The dry product takes the form of thinwall hollow spheres. This technique, when used for spray-drying cottage cheese whey, increases particle size about 100~o-i.e., from 50 to 60 microns without foaming to 110 to 130 microns. Application to other difficult-to-dry materials is suggested. The “shot-from-guns” technique, of cereal fame, is being developed for dehydrating vegetables such as carrots and potatoes (78). Partially dried pieces are heated in a pressure vessel to develop an internal steam pressure of 30 to 60 p.s.i. When this pressure is suddenly released, internal superheated water flashes and gives the vegetable pieces a porous structure. This porosity not only facilitates final drying, but reduces rehydration time for the consumer from 15 to 30 minutes to approximately 5 minutes. I n fluidized-solids developments, NarHPOI. 1 2 H z 0 wasdehydrated experimentally ( 3 ) . This salt loses water in three stages: 1 2 H z 0 to 7H20 to 2H20 to the anhydride. By uniformly drying in a small-scale unit (300gram batch capacity) and controlling temperature, each form can be produced separately. Correlation of drying data from particle sizes of 0.21 to 1.72 mm. indicates that the process is gas-phase controlled. The degree of process control obtainable is demonstrated by the fact that, as long as a higher degree of hydration exists, no dehydration to the next lower form occurs. Fundamentals
Work has continued on the “psuedo-wet-bulb temperature” (tpwb)which exists beneath the liquid boundary during falling-rate drying of thick porous solids, Experiments (73) with a 16- to 20-mesh silica sand demonstrated that a psuedo-wet-bulb temperature also exists in particulate solids having fairly large pore sizes. This confirms earlier tests on bundles of natural and synthetic fibers. A correlation to evaluate (tpwb) as a function of physical and thermal properties of the drying system, and equations to predict drying rate and moisture content as a function of drying time, were derived and reduced to graphical form. Validity of this work is limited to porous solids; water-sand, ethyl alcohol-sand, water-wool fiber, and water-Terylene were the materials studied. Experiments in segregating dissolved salts from granular solids in layer form are reported (12). For convection drying, solute concentration increased rapidly at the VOL. 5 4
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dryiiig surface, because of liquid rnoveincnt during rhc constant-rate period. Back diffusion of the solute during this period was neyligible. However, solute distribution in the final product is fairly uniform if drying is interrupted a t or near the critical moisture level, and if, before final drying, a period is allowcd for solute to redistribute by diffusion. The period required for diffusion was 48 to 192 hours. Similar results were also obtained by inverting the bed after the constantrate drying was completed. I n drying china clay by conduction, solute conccntrated at both the free and heated surfaces. This confirmed earlier work which showed that vaporization occurs at both surfaces with intermittent stages of condciisation and vaporization witliin the solids. The potcntial for using added solutes to determine drying chdracteristics and tlie mechanism of moisture movement i n other materials is apparent. Cylinder Drying
In a study of heat transfer and Lsater removal on uiifcltcd cylinder dryers (75),drying equations werc clcldoped by deriving a simplified form of the Fourier lieat equation for steady-state heat flow. Xumerical solutions, obtained by finite difference approximations werc prozrammed on a digital computer. M:itli the program, sheet temperature and moisture removed at any point on an unfelted cylinder dryer can bc calculated, provided suitable parameters of cylinder-tosheet, heat transfer coefficient, cylinder temperature and atmospheric conditions are specified. Data obtained by using the equations agreed with that obtained experimentally. T h e program, although concerned primarily with paper drying, m a y be applicable to other materials o n heated drums and cylinders. Later, this approach was applied to heat and mass transfer on the felted section of cylinder dryers ( 7 4 ) . Again theoretical equations were solved by a numerical method, using finite difference equations which Ivere programmed on a computer. Experimental data on internal sheet temperatures, sheet moisture loss, and felt moisture gain, demonstrated that, at cylinder temperatures above the boiling point, vaporization-condeiisation cycles existed within the sheet. Drying on felted cylinder sections is attributable primarily to liquid movement resulting from gas pressure gradients. Felt capillary suction effects were small. -4s expected, effect of trapped gas film increased substantially with surface temperature and sheet-moisture content. For heat transfer in single, slot-ty-pe impingement jets, a general correlation was derived ( 4 ) ,based on the concept of turbulent flow in both the jet and boundary layer for jets located close to the impingement surface. Parameters of Nusselt, Reynolds, and Prandtl numbers were used. The earlier work on multiple jets by Friedman and Mueller was summarized, and an “index of performance” number (heat transfer us. power consumed) was evaluated for various systems. 52
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Spray Drying
Accuracy in predicting drop-six distribution from liquid atomizers is important becausc size of the largest droplet usually controls retention time and chamber dimensions. For specially designed converging- and impingement-type pneumatic atomizers, a correlation was developed (5),relating median droplet size to thc ratio of air to liquid flow, air mass velocity, and length of the air-liquid interface. T h e correlation is specific to tlie nozzles investigated and applicable within certain limits to sprays having mass median droplet diameters between 5 and 30 microns. HoLvever, extension of the correlation to include commercial atomizers appears promising. iMethods for correlating drop size distributions are reviewed ( 7 7) and spray patterns produced by centrifugal spray nozzles were investigated, using seven liquids with viscosities between 1 and 10 cp. For particle size determination, spray droplets were collected in liquid nitrogen and screened. An immersion sampling technique for collecting spray droplets has been developed (79),and a sonic nozzle capable of producing uniform droplet sizes has been claimed ( 7 ) . Operating and safety controls for spray dryers are reviewed (70, 77) together with control concepts for rotary and conveyor dryers ( 7 0 ) . A method for calculating evaporation rate of a spray injected into a heated-wall cylindrical column has been devised ( 7 ) , using an extension of the Hottel-Cohen analysis of radiant heat transfer to an absorbing gas. Absorption of radiant energy in the evaporating droplet boundary-layer was analyzed approximately ( 8 ) . ,4t atmospheric pressure, boundary-layer absorption is small, hence the temperature gradient and rate of heat transfer at tlie droplet surface are not affected. These heat-transfer studies are of interest primarily in conncction with the “atomized suspension” spray dr)-er, developed in Canada, which employs hot-wall radiation for heat transfer to the spray. LITERATURE CITED (1) Chem. Eng. 68, 18, 84-6 (1961). (2) Food Eng. 33, 9, 42 (1961). (3) Ciborowski, J., Mlodzinski, B., Ian’. Chemist 38, 447, 252 (1962). (4) Daane, R. .4.> H a n S. T., Tappi 44, 1, 73-80 (1961). (5) Gretzinger, J., Marshall, 1%’. R., Jr.; A.2.Ch.E.J. 7, 312-18 (1961). (6) Hanrahan, F. P., Webb, B. H., Food Eng. 33, 8 , 37-8 (1961). (7) Hoffman, T. W’.,Gauvin, I V . H., Can. J . Chem. Eng. 39, 5 , 179-88 (1961). (8) Ibid., 39, 6, 252-9 (1961). (9) Morgan, A . I., others, Food Technol. 15, 1, 37-9 (1961). (10) McKinney, A. H., Chem. Eqg. 68, 9, 79-82 (1961). (11) Nelson, P. A,, Stevens, W.F., A.2.Ch.E.J. 7, 80-6 (1961). (121 Newitt. D. M.. others, Trans. Inst. Chem. Eners. (London) ‘ 38, 273-8’(1960). ’ (13) Nissan. A. H.. others. A.2.Ch.E.J. 6. 406-10 (1960). j14j Nissan; A. H.; George, H. H., 2bid.,’7, 635-41 (1961). (15) Nissan, A. H., Hansen, D., Ibid., 6, 606-11 (1960). (16) Peterson, M. S., Food Technol. 16, 3, 18-20 (1962). (17) Rasmussen, E. H., Bull. Am. Ceram. Soc. 39, 12, 732-4 (1960). (18) Roberts, N. E., Food Eng. 33, 9, 45 (1961). (19) Tate, R. W., A.I.Ch.E.J. 7 , 574-77 (1961). (20) Trauberman, L., Food Eng. 32, 11, 98-9 (1960). Y~
