4T- if) / miiiiiiiii iiiimimiiiifliiiil 1—- W, 31293 300630 4095 i LIERAEEY f Mommas; irate .. L University / This is to certify that the thesis entitled Dl FFUSION OF FLAVOR COMPONENTS IN CONCENTRATED MALTO-DEXTRIN SOLUTIONS presented by Edwin Mark OosTing has been accepted towards fulfillment of the requirements for M. S. degreein Chemical Engineering m0 .M Major professor Date AuguswL 3, I982 0-7639 MSU RETURNING MATERIALS: Place in book drop to ,1 Q J 6853' LIBRARJES remove this checkout from ”- your record. FINES will be charged if book is returned after the date stamped below. . a 3 i991 DIFFUSION OF FLAVOR COMPONENTS IN CONCENTRATED MALTO-DEXTRIN SOLUTIONS BY Edwin Mark Costing A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1982 ABSTRACT DIFFUSION OF FLAVOR COMPONENTS IN CONCENTRATED MALTO-DEXTRIN SOLUTIONS by Edwin Mark Costing The diffusivities and the vapor-liquid equilibrium coefficients of the flavor components, l—hexanol and 2-butanone, were measured in concentrated malto—dextrin solutions by newly developed techniques. Accurate deter- mination of these parameters required complete material balances of the two phases and control of the water concen- tration in the measurement cell. The diffusivities of the flavor components through malto-dextrin solutions were correlated with water content using the Stokes-Einstein group, Du/T. The correlation took the form, Dp/T = K" W3 , where K" is an adjustable constant, W is the water weight fraction, and B = -4. Measurements were also made of the vapor-liquid partition coefficients and the activity coefficients of l-hexanol and 2-butanone in malto-dextrin solutions. The activity coefficients were shown to be strong functions of temperature and solids concentrations. Viscosity data were obtained for the malto-dextrin solutions for use in correlating the diffusion coefficients. The solution viscosities were shown to correlate with water 8 content as u = AW , where A and B are temperature dependent constants. ® Copyright by Edwin Mark Costing 1982 To: Lynda, Kelli and Mark iii ACKNOWLEDGEMENTS I would like to thank Dr. Eric A. Grulke for his direction and support throughout this effort and Dr. J. Ian Gray for the use of his laboratory facilities. I would also like to thank Ekong A. Ekong for his work on the Weissenberger Rheogoniometer. I am especially indebted to my wife, Lynda, for typing and editing this manuscript and for her support and understanding. iv TABLE OF CONTENTS LIST OF TABLES. ................ . ..... . ................... vii LIST OF FIGURES ............. . ............................ .ix NOMENCLATURE .............................................. xi INTRODUCTION ............................................... 1 LITERATURE REVIEW.. ....... . ...................... . ......... 5 Droplet Drying ...................... .......... ..... ...5 Slab Drying. O O I O C O C O I O C O O O O O O O O O O C O O O C O O O O O O O O O O O O O O O O 6 Spray Dryj-ng. O O O O O O O O O O O O O O O ....... O O O O O O O O O O O O O O O O O O O 8 Vapor-Liquid Equilibrium Data ............. ...........16 Diffusivity Measurements.. .......... ................22 Diffusivity correlations in pure solvents.......22 Diffusivity measurements in malto-dextrin SOlutionSOOOOOOOOOOIOOO......OOOOOOOOOO0......25 EXPERIMENTAL METHODS......... ..... . ...... ... .............. 33 Constant Temperature Bath... ....... . ....... ... ...... ..33 Syringe................. ............................. 35 Syringe Mantle.......................................35 Diffusion Cells......................................37 Diffusion Trays ...................... . .......... .....40 Manometer............................................42 Materials............................................42 Experimental Procedure...............................44 Malto-dextrin solution preparation ...... . ....... 44 Solution density measurement....................45 Viscosity measurements..........................46 Diffusion Experiment ................................. 48 Concentrated malto-dextrin solutions............48 Dilute malto-dextrin solutions..................58 Effects of pH on Coefficients .......... . ............. 59 Calculation of Diffusion Coefficients........ ..... ...60 RESULTS AND DISCUSSION ............................ . ....... 64 SOlution DenSj-ty. O O O O O O O O O O I O O O O O O O O O I O ..... O O O O O O I 0 .64 Viscosity Correlations ....... ... ......... ..... ....... 64 Vapor-Liquid Equilibrium Coefficients................72 Diffusion Coefficients...............................83 pH EffectSOOOOOOOOOOOOOOO0.0.0.... ........ 00.0.0.0...98 V CONCLUSIONS.... ..... . ............ ........................101 RECOMMENDATIONSOO00.0.0000.........OOOOOOCOOOOO0.0.000000102 APPENDIX I - RAW DATA AND CALCULATED RESULTS.............103 APPENDIX II.- SAMPLE CALCULATIONS............. ......... ..120 APPENDIX III - VISCOSITY CORRELATION ATTEMPTS ..... .......l32 APPENDIX IV I EARLY EXPERIMENTS ...................... ....139 LITERATURE CITED ..... ... ................................. 145 vi NUMBER 10 11 12 13 14 15 16 17 18 19 LIST OF TABLES CHEMICALS AND SOURCES... ................. . ........ 43 CHEMICAL AND PHYSICAL DATA -- AMAIZO FRO-DEX® 10..43 VOLUME OF WATER ADDED TO DIFFUSION CELLS..... ..... 51 AMOUNTS OF DIFFUSANT ADDED TO DIFFUSION CELLS ..... 53 GAS CHROMATOGRAPH COLUMN AND CONDITIONS ......... ..55 MALTO-DEXTRIN SOLUTION DENSITY (g/ml) ............. 65 CONSTANTS FOR THE DENSITY CORRELATION, EQUATION 26 ..... ...0.....0.... ..... .....0..0....67 EXTRAPOLATED VALUES OF WATER AND MALTO-DEXTRIN 'DENSITY AND ACTUAL VALUES OF WATER DENSITY......67 VISCOSITY OF MALTO-DEXTRIN SOLUTIONS (Cp) ......... 68 CONSTANTS FOR EQUATION 42 ......................... 71 CONSTANTS FOR EQUATION 48.............. ........... 73 ACTIVITY COEFFICIENT CALCULATED FROM THE PIEROTTI CORRELATION.0......0...0..00...0.......80 ACTIVITY COEFFICIENTS CALCULATED FROM SOLUBILITY DATA..................... ..... .......81 CONSTANTS FOR EQUATION 57.................. ....... 90 VALUES OF 8 FOR DIFFUSANTS IN SIMPLE SUGAR SOLUTIONS...... ......... ................ ........ 97 HIGH SOLIDS DATA FOR 2-BUTANONE AT 60° C.... ..... 104 HIGH SOLIDS DATA FOR 2-BUTANONE AT 75° C ........ .105 HIGH SOLIDS DATA FOR 2-BUTANONE AT 90° c. ........ 106 HIGH SOLIDS DATA FOR 1-HEXANOL AT 60° C..........107 vii NUMBER 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 HIGH SOLIDS DATA FOR l-HEXANOL AT 75° C .......... 108 HIGH SOLIDS DATA FOR l-HEXANOL AT 90° C .......... 109 LOW SOLIDS DATA FOR 2-BUTANONE ................... 110 LOW SOLIDS DATA FOR 1-HEXANOL .................... 111 DIFFUSION DATA FOR 2-BUTANONE .................... 112 DIFFUSION DATA FOR l-HEXANOL ..................... 113 THE STOKES-EINSTEIN GROUP DATA, LOG (Du/T) ....... 114 ACTIVITY COEFFICIENT DATA FOR Z-BUTANONE AND 1-HEXANOL ...................................... 115 pH DATA FOR HEXANOL AT 90° C ..................... 116 DIFFUSION DATA FOR pH SAMPLES .................... 117 GAS CHROMATOGRAPH STANDARDS FOR HIGH SOLIDS SAMPLES ....................... 0.0.00.0... ...... 118 GAS CHROMATOGRAPH STANDARDS FOR LOW SOLIDS ‘ SAMPLES00000000000..00 000000 000.000.00.0000000.119 VOLUME RATIO AND DIFFUSION PATH LENGTH FOR THE DIFFUSION SAMPLES ............. . ....... . ........ 127 EINSTEIN CONSTANT K FOR EQUATION 100.............133 CONSTANTS FOR EQUATION 105. ...................... 135 CONSTANTS FOR EQUATION 108. ...................... 137 CONSTANTS FOR EQUATION 109.. .............. . ...... 137 CONSTANTS FOR EQUATION 110 ............ . ........... 138 viii NUMBER 10 11 12 13 14 15 LIST OF FIGURES CONSTANT TEMPERATURE BATH ......................... 34 CROSS SECTIONAL VIEW OF HEATED GAS SAMPLING SYRINGE...... ................... ... ............. 36 CROSS SECTIONAL VIEW OF DIFFUSION CELL ............ 38 DIFFUSION TRAY AND WIRE HOOK ............ . ......... 41 UPTAKE BY A SLAB FROM A STIRRED SOLUTION OF LIMITED VOLUME .............. ......... ........... 63 DENSITY VS. WEIGHT PERCENT SOLIDS. ................ 66 LOG D vs. LOG W FOR MALTO-DEXTRIN SOLUTIONS ....... 69 VAPOR-LIQUID EQUILIBRIUM COEFFICIENT VS. WEIGHT PERCENT SOLIDS FOR l-HEXANOL IN MALTO-DEXTRIN SOLUTIONS 0000000 . 0 0000000000000 0 00000000 . 0000000 7S VAPOR-LIQUID EQUILIBRIUM COEFFICIENT VS. WEIGHT PERCENT SOLIDS FOR Z-BUTANONE IN MALTO-DEXTRIN SOLUTIONS ..... ..00000000 ............. 000.000.00.76 ACTIVITY COEFFICIENT VS. WEIGHT PERCENT SOLIDS FOR 1-HEXANOL IN MALTO-DEXTRIN SOLUTIONS. ....... 77 ACTIVITY COEFFICIENT VS. WEIGHT PERCENT SOLIDS FOR 2-BUTANONE IN MALTO-DEXTRIN SOLUTIONS ....... 78 LOG D VS. WEIGHT PERCENT SOLIDS FOR l-HEXANOL IN MALTO-DEXTRIN SOLUTIONS......................84 LOG D VS. WEIGHT PERCENT SOLIDS FOR Z-BUTANONE IN MALTO-DEXTRIN SOLUTIONS. o o o ooooo o o o o o o o o ooooo 85 LOG (Du/T) VS. LOG W FOR l-HEXANOL IN MALTO-DEXTRIN SOLUTIONS. 0 0 0 0 0 0 0 . 0 . 0 ...... . . ..... 87 LOG (Du/T) vs. LOG w FOR 2-BUTANONE IN MALTO-DEXTRIN SOLUTIONS. o o o o o o o o o o o ooooooooooooo 88 ix NUMBER 16 17 18 19 LOG (Du/T) VS. LOG W FOR MENTING'S DATA.. ..... ....93 EFFECTS OF pH ON LOG D AND K FOR 1-HEXANOL.. ..... .99 GLASS CAPILLARY DIFFUSION TUBE ................. ..140 GLASS DIFFUSION CELL ............ . ................ 141 Symbol NOMENCLATURE Explanation English Letters: A A A A I > S w 00 3’ 3’ 3’ on S TD WO Slab surface area Constant in equation 25 Constant for equation 41 Constant for equations 9, 42, and 107 Diffusant gas chromato- graph peak area Internal standard gas .chromatograph peak area Standard gas chromatograph peak area Constant for equation 108 Constant for equation 109 Constant for equation 110 Constant in equation 25 Constant for equation 41 Constant for equations 9, 42, and 107 Constant for equation 108 Constant for equation 109 Constant for equation 110 Biot Number for mass transfer Concentration xi Units cm2 cmz/sec g/ml unitless unitless unitless unitless unitless unitless unitless (g/mlil/2 g/ml unitless unitless unitless unitless unitless g/ml xii Symbol Explanation Units English Letters: C Constant for equations 9 unitless and 43 C' Constant in equation 16 unitless Ci Concentration of compo— g/ml nent 1 CL Liquid phase diffusant g/ml concentration CSTD Standard concentration g/ml CV Vapor phase diffusant g/ml concentration Cw Water concentration g/ml C1 Concentration of compo- g/ml nent 1 ACl Concentration difference g/ml of component 1 at t>0 AC1° Concentration difference g/ml of component 1 at t=0 C2 Concentration of compo- g/ml nent 2 AC2 Concentration difference g/ml Of component 2 at t>0 AC2° Concentration difference of g/ml component 2 at t=0 D Constant for equations 4 unitless and 44 D Diffusivity cmZ/sec DA Diffusivity of component A cmZ/sec DAB Diffusivity of component A cmZ/sec in component B Dw Diffusivity of water cmzlsec Symbol DA DW AH AH Explanation Frequency factor for diffusivity Diffusivity of component 1 due to a concentration gradient in component 1 Diffusivity of component 1 in water Diffusivity of component 1 due to a concentration gradient in component 2, cross diffusion coefficient Diffusivity of component 2 due to a concentration gradient in component 1, cross diffusion coefficient Diffusivity of component 2 due to a concentration gradient in component 2 Constant for equations 9 and 43 Activation energy for diffusion of component A in water Activation energy for self- diffusion of water Activation energy for viscosity Activation energy for viscosity Of water Constant for equations 9 and 44 Heat of vaporization of solvent Heat of vaporization of water Flux of component 1 xiii Units cmzlsec cmz/sec cmz/sec cmZ/sec cmzlsec cm2/sec unitless Kcal/g mole Kcal/g mole Kcal/g mole Kcal/g mole unitless Kcal/g mole Kcal/g mole g/cm2 sec Symbol Explanation English Letters (cont.): Jz K Kl K" x: Flux of component 2 Boltzmann constant Constant in equations 17, 24 and 100 Vapor-liquid equilibrium coefficient, concentration based Constant for equation 55 Constant for equations 57 and 105 Vapor-liquid equilibrium coefficient, mole fraction based Gas phase mass transfer coefficient Base ionization constant Gas phase mass transfer coefficient Vapor-liquid concentration ratio at long time Liquid phase mass transfer coefficient Overall mass transfer coefficient ‘ Vapor-liquid concentration ratio at short time Vapor-liquid equilibrium coefficient Slab thickness Average molecular weight of solution xiv Units g/cm2 sec 9 cmzlsec2 °K unitless unitless unitless unitless unitless cm/sec unitless cm/Sec unitless cm/sec cm/sec unitless unitless cm g/g mole Symbol English Letters (cont.): MD MS 2 8323 DL DV SL TL TV Explanation Diffusant molecular weight Molecular weight of malto-dextrin Mass of solute at time t Molecular weight of water Mass of solute as t approaches infinity Avogodro's Number Running index Diffusant liquid molar concentration Diffusant vapor molar concentration Malto-dextrin liquid molar concentration Total liquid molar concen- tration Total vapor molar concen- tration Water liquid molar concentration Number of carbon atoms in solute molecule Number of carbon atoms in solvent molecule Total absolute pressure Saturated vapor pressure Saturated vapor pressure of component i Non-zero positive roots of equation 37 XV Units g/g mole g/g mole g/g mole unitless unitless g mole/m1 g mole/ml g mole/m1 g mole/m1 g mole/ml g mole/ml unitless unitless Torr Torr Torr unitless Symbol English Letters (cont.): R R *9 fife-{ran < m IDL“ U) STD Z 2! <1 .< < 2 <1 < <3 < O Explanation Ideal gas law constant Ideal gas law constant Linear regression correla- tion coefficient Molecular radius of compo- nent A Solution deflection reading Standard deflection reading Solids weight fraction Solubility Total solubility Absolute temperature Time or flow time Dimensionless time Water flow time Percent uptake Molar volume of component A Molar volume of component B Liquid volume Sample volume Solids volume Standard volume Vapor volume Water volume Water weight fractiOn Diffusant weight xvi Units Kcal/g mole °K ml Torr/g mole °K unitless CH1 unitless unitless unitless g/ml g/ml °K sec unitless sec unitless ml/g mole ml/g mole ml ml m1 m1 m1 ml unitless 9 Symbol Explanation English Letters (cont.): WIs WS X Internal standard weight Sample weight Distance Diffusant liquid phase mole fraction Saturated liquid mole fraction of component i Association parameter Diffusant vapor phase mole fraction Greek Letters: WWW Vapor-liquid mass ratio Cell constant' Constant for equation 55 Constant for equation 57 Activity coefficient Activity coefficient of component 1 Activity coefficient of component i at infinite dilution Activity coefficient for solute at infinite dilution Activity coefficient of solute in water Viscosity Viscosity of component B Relative viscosity xvii Units 9 9 cm unitless unitless unitless unitless unitless cm"2 unitless unitless unitless unitless unitless unitless unitless centipoise centipoise unitless Symbol Explanation Greek Letters (cont.): 115 uSTD Subscripts: STD Viscosity of solution Viscosity of standard Viscosity of water Frequency factor for viscosity Intrinsic viscosity Density Standard deviation of CL Standard deviation Of Cv Standard deviation of K Solids volume fraction Standard solution xviii Units centipoise centipoise centipoise centipoise unitless g/ml g/ml g/ml unitless unitless INTRODUCTION As the cost of energy rises, food storage systems requiring a minimum of energy are being sought. One of the oldest and most widely used methods of food preparation for storage is drying. Bomben, et a1. (1973), estimated food concentration costs in dollars per 1000 Kg of water removed for liquid foods based on 7,500 hours per year at a water removal rate of 150 to 1000 Kg per hour. Freeze drying was the most expensive, costing between $150 and $200 per 1000 Kg of water removed. The least expensive were spray drying at $15 to $50 per 1000 Kg water, reverse osmosis at $10 to $15 per 1000 Kg water, freeze concentration at $8 to $15 per 1000 Kg water, and double effect evaporation with aroma recovery at $6 to $15 per 1000 Kg water. Reverse osmosis and double effect evaporation still require spray or freeze drying to make a dry product. Spray drying is a fairly inexpensive method of drying and is applicable to most liquid foods. Perhaps the major disadvantage of spray drying as compared to freeze drying is the loss of volatile flavor components. Loss of flavors in the spray drying process can reduce the acceptability of the dried food. Flavor loss can be controlled if the basic mechanisms of spray drying are understood. The mass transfer of flavors l 2 from drying droplets depends on the basic physio-chemical characteristics of volatile flavor components in the food system. In spray dryers, volatile loss occurs in two zones. Near the nozzle, the liquid spreads into an extremely thin, turbulent film. The thin film provides a very large surface area for mass transfer. Depending on drying conditions, much of the water and volatile flavor com- ponents can be lost from the film. Farther away from the nozzle, drOplets are formed. Evaporation occurs on the surface of the drOplets. A zone of low water concentration (dry zone) occurs near the surface. The diffusivity of flavors in this dry zone is less than the diffusivity of water, so water diffuses faster than the flavors as the droplet dries. The important parameter in the drying of food droplets is the diffusivity of Volatile flavor compo- nents in food solutions over the water concentration experienced in spray drying. Two approaches may be taken to analyze a spray dryer. One may run experiments with a given spray dryer and vary parameters that he thinks are important. Correlations can then be used to identify how flavor component characteristics will vary with spray dryer operating conditions. Numerous experiments must be performed in order to characterize the spray dryer. Another approach to the problem would be to measure the physical and chemical characteristics of the flavor components and the liquid food. Using these 3 characteristics and the spray drying conditions, one could model the behavior of the flavor components and the liquid food material in a spray dryer. The model could be tested with a minimum number of spray drying eXperiments. NumeroUs experiments have been performed to measure the retention of flavor components during Spray drying. These experiments have done much to increase our qualitative understanding of spray drying. General mathematical models have not been proposed or solved for spray dryers mainly due to the lack of diffusion and equilibrium data for flavor components in food systems. Furthermore, there are few correlations which can be used to predict diffusi- vities and solubilities over the range of conditions ex- perienced by the droplets. Carbohydrate solutions have been used as surrogates for food liquids in spray drying experiments. The diffusivity and vapor-liquid equilibrium coefficient for various flavor components have been determined for sugar and malto-dextrin solutions, but these data were taken at room temperature and cannot be applied to spray dryer conditions. Also, no attempt has been made to correlate the data to a general correlation which could be extrapolated to higher temperatures or higher solids concentrations. The purpose of this study is to acquire diffusion and equilibrium data for a common flavor component in a model food system. An attempt was to be made to correlate the data in 4 a usable form. The ultimate goal of this research is to provide correlations to predict physical and chemical pro- perties of the flavor-food system over the range of condi- tions experienced by a drying droplet in the Spray dryer. These correlations are the tools necessary for a model of. the flavor loss during spray drying. LITERATURE REVIEW Many experiments have been performed in the spray dryer in order to understand the mechanisms of flavor loss. Auxiliary experiments have been performed on slab drying to try to explain the phenomena Observed in spray dryers. It is interesting to note how the theory and experiments have developed from simple experiments on the drying of single drops (Menting and Hoogstad, 1967) to measurements of the retention profile Of acetates in Spray drying sugar solutions (Kieckbusch and King, 1977). Dr0plet Drying In some of the earliest experiments, Menting and Hoogstad (1967) studied the retention of acetone, benzene, ethanol and ethyl acetate in a drying droplet of malto-dextrin solutions suspended on a wire in an air current. They used radioactive-labeled volatiles in their study. They observed the formation of a film on the drop surface which was permeable to water, but not acetone, benzene, ethanol or ethyl acetate. The film formed faster with higher initial solids concentration. Throughout the. experiments, the drop temperature was constant, as measured by a thermocouple inside the drop. Saravacos and Meyer (1968) observed that retention 5 6 of volatile aroma compounds during vacuum drying of grape juice and pectin solutions was dependent on the relative volatility of the compounds and the beginning solids concentration of the solutions. The most volatile compounds exhibited the least retention. Percent retention was enhanced by starting with more concentrated fruit juices. Slab Drying In slab drying experiments with malto—dextrin solutions, Menting, et al. (1970b), observed that the retention of acetone was a function of the solids content of the initial solutions. Varying amounts of agar-agar were added to gel the solutions. They showed an increase from 0% to about 70% retention of acetone in solutions of 0 to 700 g/l initial dry matter. They also reported that loss of acetone from the drying Slab stopped below a certain moisture content. The acetone content in the slab remained Constant after the transition from a constant drying rate period to a falling rate period. The transition in drying modes was determined by the tempera- ture in the malto-dextrin slab. An increase in the relative humidity of the drying air increased the time at which the constant rate period ended and when acetone loss ended. Using the concentration-dependent diffusion coefficients measured in a complimentary study (Menting, et al., 1970a), the observed loss of water and acetone was predicted. 7 Through some simple analyses, they determined that the value of the group KWOBiWO should be greater than 4 for the surface of a drying droplet to be in equilibrium with the drying air almost immediately after the onset of drying for dry air. KWO is the vapor-liquid equilibrium coefficient of the flavor component for the solution to be dryed at the initial drying temperature. BiWO was the Biot Number for mass transfer and equaled kA'I’DA where k ' was the gas phase mass transfer coefficient. The A value of 4 for K Bi corresponded to immediate film W0 ”W0 formation at the drop surface. This also corresponded to the maximum retention Of flavor components. Menting, et al. (1970b) also concluded that K was a function of the woBiwo relative humidity of the drying air. Thijssen (1971) concluded that retention of flavors from liquid foods was independent of their volatilities relative to water. Instead, the controlling factor was the diffusivity of the flavor component through the drying liquid. The rate Of evaporation of flavor components could be described as molecular diffusion to the surface Oftflualiquid with zero concentration at that surface. He stated that the reason for retention of flavors was their low diffusivity in the drying liquid as compared to the water diffusivity. The ratio DA/Dw (relative diffusi- vity) decreased very rapidly with increasing solids content and increasing size of flavor component for acetone and alcohols in malto-dextrin solutions. Below a certain 8 "critical water concentration," the relative diffusivity became small. The critical water concentration was defined as the water content where DA/DW becomes 1eSs than 0.01. Below this value of water concentration, the solu- tion became nearly impermeable to flavor components. Thus, the conditions in spray drying that lead to rapid water loss at the surface and the formation of a high solids content skin or film gave the best retention of flavors. Spray Drying In spray drying experiments with alcohols in malto- dextrin solutions, the maximum retention was obtained for the combination of high solids content of the feed and high feed temperatures. Both of these cause rapid film formation. The film should retard flavor diffusion. Rulkens and Thijssen (1972) have studied the effects of process variables on the retention of acetone and alcohols in Spray drying aqueous solutions of malto-dextrin. They concluded that the retention of volatiles in malto-dextrin solutions was independent of the relative volatility (i.e., vapor-liquid equilibrium coefficient). Retention increased with increasing molecule size of the volatile. At the low concentrations of the volatiles studied, retention appeared to be independent of volatile concen- tration. Given a low enough viscosity to ensure proper atomization, retention increased strongly with 9 increasing solids content. Thus, the maximum retention is Obtained at high feed concentrations and high feed temperatures. They also concluded that retention increased with decreasing air temperatures, but was insensitive to air temperatures at low solids concentration. A mathematical model for the concentration profiles of water and trace flavor component has been solved by Chandrasekaran and King (1972b). They used a ternary diffusion model for the fluxes in the slab. Data for the ternary diffusion coefficients was provided by a suppli- mentary work also by Chandrasekaran and King (1972a). The model was solved using the symmetrical Crank-Nicholsen implicit representation for a finite difference approxi- mation. The model predicted a maximum in the concentration profile for the flavor component just below the drying surface, at long times. Qualitatively, the maximum was due to shrinkage of the slab as water diffused to the surface. As the slab shrinks, the concentration of the flavor component builds up close to the moving surface. Drying experiments were performed on sucrose, fructose and orange juice containing 1.5% gelatin. These experi- ments gave flavor profiles qualitatively similar to the predicted profiles. The formation of a zone of high solids material (a skin or film) at the drying surface was responsible for the retention of the flavor component in the drying slab. Kieckbusch and King (1977) have made major 10 contributions to the understanding of spray dryer behavior. They studied the retention of volatile ace- tates at various distances from the atomizer for spray drying water and sucrose solutions. The observed retention of volatile components depends On whether the liquid or gas phase is controlling the volatile loss rate. They showed that a very large portion (60%) Of the volatiles were lost within 2 cm of the atomizer, which corresponds to the film-disintegration zone for 40% sucrose solutions. They also observed that the retention of acetates in water was substantially less than in sucrose solutions. More striking was the observation that the order of retention in water was the reverse of that in sucrose solutions. This was explained as the overall mass transfer resistance + -—— (1) where KL is the overall mass transfer coefficient, kL and kC are the individual liquid and gas phase coefficients, respectively, and K is the vapor-liquid equilibrium coeffi- cient. For water, ch is smaller than kL and KL is approximated by KL = KkC . (2) K increases with increasing molecular weight (Kieckbusch and King, 1979) and so KL increases also. So, the retention should decrease with increasing molecular weight at low solids content. This was observed in the experiment. 11 Mass transfer in the liquid phase controls the overall mass transfer for solutions of 40% sucrose. That is, kL is less than ch and so KL is represented by KL 5 kL . (3) Now, kL is proportional to the liquid diffusivity which is in turn proportional to the inverse of the molecular weight. So, KL should decrease with increasing molecular weight and the retention whould increase with increasing molecular weight. Further study of this system (Kieckbusch and King, 1980) demonstrates this hypothesis more. For 1% sucrose solutions, the retention is greatest for ethyl acetate and least for pentyl acetate. This indicates a gas-phase control of mass transfer because the vapor-liquid equili- brium coefficient is greatest for pentyl acetate. Thus, pentyl acetate is the most volatile and is retained the least. The diffusivity in the liquid phase should have some effect, but does not control the relative retentions in 1% sucrose solutions. The trend is reversed for 40% sucrose solutions. Retention is greatest for pentyl acetate and least for ethyl acetate. This indicates liquid phase control of mass transport. The liquid diffusivity decreases with increasing molecular weight. 80, pentyl acetate should have the lowest diffusivity and should have the highest retention. Of particular interest is the retention of acetates 12 in spray drying 20% sucrose solutions. The order of retention reverses at about 10 cm below the atomizer because the controlling phase for mass transfer changes. At distances of 0 to 10 cm, ethyl acetate has the highest retention, indicating gas phase mass transfer control. Beyond 10 cm, pentyl acetate has the maximum retention, indicating liquid phase mass transfer control. 50, within one spray dryer, the mechanism may switch from gas to liquid phase mass transfer control. Indeed, Kieckbusch and King made the general conclusion that the gas phase controls during drop formation and the liquid phase controls once the drop is formed. This is reasonable since there is considerable turbulent mixing in the atOmizer jet. But, once the drop has formed, viscous dissipation should reduce the mixing in the drop to zero. These effects can also be explained by the formation of a film on the drying drop. Once a film of high solids content is formed on the drop, the mass transfer will be controlled by the film since the diffusivity is a very strong function of percent solids of the film (this work). Kieckbusch and King (1980) also studied the effects Of liquid feed temperature, air temperature, air flow rate, and sugar molecular weight on the retention of ethyl acetate. Malto-dextrin solutions exhibited a greater retention of ethyl acetate than sucrose and malto- dextrin solutions having the same kinematic viscosity. This is most likely due to structural binding of ethyl 13 acetate to the malto-dextrin molecule. Malto-dextrin could form a helical structure in water solutions. During the drying process, ethyl acetate molecules Could become trapped inside of the helix. Sucrose would not exhibit such binding effects. A decrease in liquid feed temperature and an increase in air temperature both increased the retention. Since diffusivity is inversely proportional to feed temperature, the retention should increase at low feed temperatures. This argument cannot be used for the air temperatures, though. Instead, the increase in retention with increasing air temperatures may be attributed to the formation of a film at the higher air temperatures. Rulkens and Thijssen (1972) observed a reverse trend. They found that retention was decreased with increasing air temperatures. Their experiments were performed at considerably higher temper- atures than those of Kieckbusch and King. A temperature range of 110° C to 220° C was used by Kieckbusch and King, while Rulkens and Thijssen used a range of 210° C to 290° C. In Rulkens and Thijssen's experiments, the reduced retention can be explained by bubbling of the malto-dextrin droplets at the higher temperatures. Kieckbusch and King were able to predict the volatile loss very close to the nozzle using an expanding sheet, laminar flow model. Beyond the droplet formation distance, a solid sphere diffusion model was used. The expanding sheet model predicted volatile loss well, but the solid sic qua 10: (in £ me we 14 sphere diffusion model underpredicted the volatiles loss. In a study on the vacuum spray desorption of carbon dioxide, oxygen, Freon 114, and butane from deionized water, sodium chloride solutions and freshly acidified sea water, Simpson and Lynn (1977) observed large losses of the gasses before droplet formation. The degree of stripping observed was much greater than that predicted by the solid sphere model. Instead, up to 90% of the gas was stripped in the thin sheet formed at the spray nozzle. The amount of stripping was predicted by an expanding sheet model for mass transfer developed by Hasson, et a1. (1964). The model predicted the experimental observations very well. The reason for the high mass transfer rates from the water sheet is that before the sheet breaks into drops, it becomes very thin. The ratio of drOp diameter to sheet thickness ranges from 10 to 50. Since the diffu— sional path length in the sheet is very small, a large quantity of gas is desorbed from the sheet. A similar explanation might be used for the large loss of volatiles close to the spray nozzle in spray drying sucrose and malto-dextrin solutions (Kieckbusch and King, 1980). Reineccius, et al. (1978) studied the retention of methyl ketones in spray drying of milk systems of different fat contents. The retention increased with molecular weight of the ketone. It was found that the retention was 15 improved for fat contents of up to 21%. Above that value, the retention was reduced. Retention should be improved by the addition of some fat, since the ketOnes are soluble in fat. High fat contents, however, lead to a continuous fat phase which will serve as a path for diffusion out of the drying particle. The spray drying literature discussed show some parallels. The primary observation to be made is that volatile retention is enhanced when a film of high solids impermeable to volatile flavors is formed on the drying drOplet. This film acts as a barrier to larger flavor molecules through selective diffusion (Rulkens and Thijssen, 1972). The diffusivity of flavor molecules is substantially lower than the diffusivity of water in the film. The Optimum conditions in spray drying liquid foods are the conditions at which the film is formed the most rapidly. Large amounts of volatiles can be lost in the expanding liquid film at the spray nozzle. Volatile components can diffuse out of the film due to the short diffusional path length (Simpson and Lynn, 1977). Cracks can develop in the drying drOplet which enhance the volatile loss rate (Rulkens and Thijssen, 1972). If the droplets are heated too much, the water may volatilize. Bubbling within the drOplet may cause the skin to rupture, releasing much of the volatile flavor. There is a lack of information regarding the diffusivity and partition coefficients of volatile components in model foods. 16 If correlations can be developed which can predict the diffusivity and partition coefficient of flavor components in model foods, then mathematical models based on balances of heat, mass and momentum can be developed. In this fashion, the basic principles of spray drying may be more easily understood. Vapor-Liquid Equilibrium Data The vapor-liquid equilibrium coefficient is an impor- tant consideration in designing spray dryers. The vapor-liquid equilibrium may be defined in a number of ways. The convention used here is C . K=EX (4) L where CV and CL are molar or mass concentration of the solute in the vapor and liquid phase, respectively. A more typical definition is :2 K x (5) where x and y are the mole fraction of solute in the vapor and liquid phases. In the malto-dextrin System, the average molecular weight of the liquid phase is not well defined since the molecular weight of the malto-dextrin is not well defined. In these measurements, the vapor phase contained an unknown ratio of water and air. There- fore, the vapor-liquid equilibrium coefficient was based on Equation (4). 17 According to thermodynamic equilibrium, at low to moderate pressures, the mole fraction vapor-liquid equilibrium coefficient, K, is represented as sat R. = Y. F (6) t is the saturation vapor pressure of component where Pisa i, Yi is the activity coefficient for component i and P is the total pressure (Prausnitz, 1969). In partially soluble systems, the solubility of component i is related to the activity coefficient by *1 e fii. (7) where x1 is the solubility of species i. Compounds with very low solubilities will have high activity coefficients and, therefore, high vapor-liquid equilibrium coefficients (Bomben, et al., 1973). For very dilute flavors in food systems, the activity coefficient is often a constant with respect to the concentration of flavor component. At very low concentration of solute, the activity coefficient approaches a constant value, the activity coefficient at infinite dilution, vim. That is, 11m Y1 = Yi (8) Ci+0 where C1 is the concentration of species 1. So, 71” is a good approximatiOn to 71 for flavor components at finite, 18 small concentrations. The activity coefficients at infinite dilution have been correlated for a number of organic compounds in water and other solvents by Pierotti,et a1.(l959). The correlation is n log Y1 = A + B —l + 5; + D(n1 — n2)2 + £1 (9) n2 n1 2 where A - F are adjustable constants depending on the type of solute (component 1) and solvent (component 2), nl and n2 are the number of carbon atoms in the solute and solvent, respectively. The constants A - F are given for a temperature range of 25° to 100° C. This correlation should be useful in predicting the vapor-liquid equilibrium coefficient of volatiles in water. Buttery, et a1. (1971) used this correlation to calculate the vapor-liquid equilibrium coefficients of alkanals and 2—alkanones at 25° C. The calculated results were slightly higher than the experimental values. The solubility of homologues tend to decrease with increasing chain length. Davis (1968) measured the solu- - C bility of C aldehydes in water at 25° C. He found 5 9 that the solubility decreased from 22.00 g/l for pentanal to 0.11 for nonanal. The natural logarithm of the solubility was shown to be a linear function Of the carbon chain length. Nishino and Nakamura (1978) measured the same trends for alcohols, amines and aliphatic acids. They also found that the solubilities demonstrated minima over 19 the temperature range studied. Data presented by Stephen and Stephen (1963) Show a minimum solubility for l-hexanol at about 50° C and a minimum for 2-butanone at about 90° C. This has been explained in terms Of an increase in partial molar enthalpy of the solute with a temperature increase which results from the breakdown of the water structure surrounding the nonpolar alkyl .chain. Since the solubilities of alcohols, amines, ketones and aldehydes are not linear with temperature, it is expected that the corresponding activity coeffi- cients are also non-linear with temperature. Air-water vapor-liquid equilibrium coefficients at 25° C for aldehydes, ketones, and esters have been measured by Buttery, et a1. (1965, 1969, and 1971). In all of his studies, Buttery measured the concentration of the volatile component in the vapor and liquid phases using , a gas chromatograph. Liquid concentrations were well below the saturation levels, typically 5 - 200 ppm. The vapor-liquid equilibrium coefficient was Shown to be a strong function of the carbon chain length. For each homologous series, the natural logarithm of the vapor- liquid equilibrium coefficient was a linear function Of the number of carbon atoms in the carbon chain. The activity coefficients for ethyl alcohol, n—hexanal and various esters in sucrose and d-fuctose solutions were measured by Chandrasekaran and King (1971 and 1972a). The amount of volatile component was measured 20 in the vapor above a solution containing a known initial concentration of volatiles. The liquid-phase concentration of volatiles was not measured. The activity coeffiCient was calculated from the ratio of volatile concentration above the sugar solution to the volatile concentration above water. In all cases, the same amount of volatile component was added to the solution and allowed to equili- brate between the vapor and liquid phase. The activity coefficient in water was calculated from the correlation by Pierotti, et a1. (1959). Chandrasekaran and King also found that a plot of log Vb versus log CW gave one straight line for the volatile components in fructose. In this case, 7 and Y0 are the activity coefficients for the volatile component in the sugar solution and water, respectively and Cw is the water concentration. The Significant finding here is that all Of the flavor components for one sugar fit a single, master curve. But, since the flavor component did not interact with the sugar, the value of the activity coeffi- cient should be proportional to the water concentration. Kieckbusch and King (1979 and 1980) measured the vapor-liquid equilibrium coefficients for a number of acetates in aqueous solutions of sucrose, maltose, dextran, dextrin, malto-dextrin, Brazil-Santos coffee extract, and commercial instant coffee over a temperature range of 25° to 40° C. They also measured the vapor-liquid equilibrium coefficients in mineral oil, peanut oil, and 21 coffee Oil. In their experiments, Kieckbusch and King added a known amount of acetate to a special thermostated bottle containing a known amount of water. For pure water solutions, samples of both the gas and liquid phases were analyzed with a gas chromatograph and the vapor-liquid equilibrium coefficient calculated. Only the vapor was sampled for solutions containing dissolved solids. The vapor-liquid equilibrium coefficient for the sugar solutions were calculated from the ratio of the concentration in the vapor above the sugar solutions to the vapor above water. In each case, the same amount of volatile was added to the solutions. The pressure in the bottles was atmospheric since a small sampling hole in the bottle cap was left Open throughout the experiments. Some volatile component may have been lost, but this was ignored. The results of these experiments showed that the vapor-liquid equilibrium coefficient in water increased with increasing molecular weight. This was true at all temperatures. The vapor-liquid equilibrium coefficient for pentyl acetate increased with increasing solids content in sucrose, maltoSe and dextran solutions, but decreased with increasing solids content in malto-dextrin, dextrin, commercial instant coffee and Brazil-Santos coffee extract solutions. In this work, the vapor-liquid equilibrium coefficient was measured for l-hexanol and 2-butanone. .The concentration 22 in the liquid and vapor phases were measured. It is important to measure both since some sorption may occur on the experimental apparatus that is not accOunted for by a simple mass balance. Diffusivity Measurements A critical component of any mathematical model Of a spray dryer is the diffusivity of water and flavor components in the model food system. Correlations for diffusivity must be developed which consider the effects of solids content of the solution, temperature, the type Of flavor and the type of dissolved solids. Diffusivity correlations in pure solvents. It is well known that diffusion, being a rate process, follOws Arrhenius' Law: ( E”) D = D ex - —— (10) 0 p RT where the activation energy, ED is a function Of the water content of the malto-dextrin solution. DAB “A T is a constant for a given solute B in a given solvent A. According to Stokes-Einstein theory, the group For large spherical particles (Bird, et al., 1960), T =4nR . (11) If solvent and solute molecules are the same size and can be 1/3 packed into a cubic lattice, RA may be replaced by _1_ (YA) _ 2 N resulting in T (12) 31519.11 _N_‘/3 2n . Since the Stokes-Einstein Equation applies only to spherical molecules, numerous empirical correlations have been proposed. Wilke and Chang (1955) found that D u _A%F—§ varies with the molecular weight of the solvent to the % power and with the molar volume of the solute to the -0.6 power for pure solvents. That is, D D X N 1/2 AB B = 7.4 x 10-9 ( B B) (13) T VA.6 where XB is an association parameter which is 2.6 for water, 1.9 for methanol, 1.6 for ethanol and 1 for unassociated solvents like benzene, ether, and heptane. Others have attempted to extend or refine the Wilke-Chang equation. Othmer and Thakar (1953) based their correlation on Eyring rate theory. Viscosity and diffusivity vary as exponential functions of absolute temperature, D = D ex —— 14 o 0 RT) ( ) u = “0 exp RT . (15) Taking the logarithms and substituting for 1/RT yields ED log D = E— log n + C'. (16) u . E For a number of materials at low concentration, E— was u 24 shown to be approximately equal to -1.1. For solutes in water, Equation (16) becomes EDA log DA = §—— 109 uw + K (17) uW or E E log DA = E95 593 log “w + K . (18) DW uW Now, E E23 a ~1.1 (19) uw and the ratio of the activation energies is replaced by the latent heats of vaporization. The resulting empirical correlation becomes, _ 1.4 10‘“ DAB_ (1.1 AH /AH ) 05 (20) B W V 11w A “B Scheibel (1954) prOposed an emperical correlation based on data for water and a number of other solvents. 2/3 + D VA AB ”B = 8.2 x 10"8 A (21) __fir—— V 1/3 A Sitaraman, et a1. (1963) substituted the ratio Of latent heats of vaporization for the Wilke-Chang association parameter X. They arrived at 1/2 AH 1/3 msa _ - “a B T DAB — 5.4 x 10 3 -—- (22) 11 0. 3 o. s B AHA VA Reddy and Doraiswamy (1967) replaced the association 25 1 parameter with V 1/3 resulting in B DAB “E _ K MB ' 23 "7F’— — 1/3 ( ) (VA VB) where VB K = 1.0 x 10"7 for V‘ ; 1.5 (24a) A VB K = 8.5 x 10'8 for V‘ > 1.5 (24b) A NO rational was given for the substitution Of the associa- tion parameter with 1 . 1/3 VB Diffusivity measurements in malto-dextrin solutions. The first effort to measure the diffusion coefficient of volatile flavor compounds in malto-dextrin solutions was made by Menting, et al. (1970a). They measured the diffu— sivity of water, acetone and ethyl acetate over a wide range of solids content at 25° C. The water diffusivities were measured in drying experiments. The weight of a dish of malto-dextrin solution containing 1% agar-agar and benzoic acid was measured over a period of time. The air above the dish was maintained at a constant relative humidity. The diffusion coefficient was taken as an average of sorption and desorption experiments. The diffusivities of acetone and ethyl acetate were measured in one of two ways. For solutions above 20% water, a small sample containing a small amount of agar- agar was placed inside a thermostated flask. It was 26 assumed that the sample did not lose much water since the flask was small. A 10 ml mixture of acetone, ethyl acetate and benzene vapors was added to the flask. The concentration of flavor component in the vapor was measured from time to time by injecting 25 or 30 ul samples into a gas chromatograph. The diffusivity was calculated from the change in concentration in the vapor phase with time. The benzene was added as an internal standard for the vapor analysis. The concentration of benzene was assumed to be constant Since it is not soluble to any appreciable extent in water. The solids content of the malto-dextrin solutions was not measured even though it would have been very easy to do so. A radioactive tracer technique was used in malto-dextrin solutions containing less than 20% water. First, glass rods were coated with 50 wt-% malto-dextrin solutions of various thicknesses by drawing the rods out of the solution at a constant rate. The malto-dextrin was air dried at 80° C. Before use, the rods were placed in an enclosed container with a saturated salt solution at the desired relative humidity. They were then placed in a Similar container with similar salt solution with a small amount Of diffusant in the vapor. At selected times, the rods were removed and the malto-dextrin coating was dissolved in water. The resulting solution was analyzed with a scintillation detector for diffusant. The diffusivity was calculated from the change in the diffusant concentration 27 in the liquid with time. The solids content was not measured in these solutions. It is important to measure the solids content to be sure the experiment works properly. Menting found that the diffusivity was a strong function of the solids content. The diffusivity of acetone corre- lated with the water concentration, Cw as ._ - B . DA — A exp ( C 1/2) . (25) W Here A and B are arbitrary constants. No physical reason for correlating the data this way was given. Benzene, carbon tetrachloride and camphor diffusivities were measured at 20.1% water content using the same procedure. Methane diffusivity at 20.1% water content was measured by a desorption experiment. Methane was introduced into a flask containing a thin layer of malto—dextrin solution. The system was allowed to come to equilibrium. The methane was removed from the vapor by flushing the flask with air. The vapor phase concentration of methane was measured as a function of time and the diffusion coefficient calculated. From these experiments, it was Shown that log D was a linear function of the diffusant diameter. Other workers have measured the diffusion coefficients of flavor analogs in food systems. The ternary diffusion coefficients of dilute ethanol, ethyl acetate, n-butyl acetate and n-hexanal were measured in solutions of sucrose, d-glucose and d-fructose by Chandrasekaran and 28 King (1972). A stirred diaphram cell was used since the sugar concentrations were fairly dilute. The initial concentration of sugar was slightly different across the cell. The initial concentration of organic diffusant was zero on one side of the cell and a small value on the other side. The equations for the flux of organic (component 1) and water (component 2) were VC - D VC (26a) J = D 1 12 2 1 11 D VC - D VC (26b) J 21 1 22 2 2 (Chandrasekaran and King, 1972a). The flux of the sugar (component 3) was not independent of the water and organic fluxes. The cell diaphram equation for a binary system was AC° _ 1n (7R?) — 8 D t (27) where AC° and AC were the concentration differences across the cell at time equal to zero and t, respectively, and B was the cell constant. The equations for a ternary system were reduced to AC AC ° ——J%-= 1 - D11 + 20 D12 8 t AC1 AC1 2 AC2° + (D11 + D12 ”21’ + D12 (011+ ”22’ A C 1 2 2 5 2t + --- (28) and o _ o AC2 0AC2 = 021 + 022 AC2 B t AC1 AC1° AC2° ’ ”21 ( ”11 + ”22) + 32—? (”222 + ”12 ”21) 1 82 t2 2 + --- (29) In order to use these equations, one could have used values of AC for two values of t, or one or more of the diffusion coefficients must have been known from previous experiments. Chandrasekaran and King used literature values for D22 in sugar solutions, but the literature values for D22 (the water diffusion coefficient in sugar solutions), which Chandrasekaran and King used in their work, were actually sugar diffusion coefficients. The data for D22 corresponded to diffusion coefficients for sucrose and d-glucose solu- tions presented by Henrion (1964a, b), English and Dole (1950), and Gladden and Dole (1952).~ According to Chandrasekaran and King, D22 in 0 wt % sugar, the self- diffusion coefficient of water, was approximately 6.0 x 10" cmzlsec. Menting gave a value of 2.2 x 10"5 cmZ/sec for the water self—diffusion coefficient. Values for D22 in Chandrasekaran and King's paper were actually sugar diffusion coefficients which were significantly lower than water diffusion coefficients should have been. However, this did not invalidate their calculations. By inspecting equation 28, one sees that D22 appeared only in the quad- ratic terms. Thus, this error should not have introduced 30 much error in the organic component diffusivities, D11. Chandrasekaran and King (19723) made some rather interesting conclusions from their data. The ratio of the diffusivities of the organic components in a sugar solution to that in water (Dll/Dllo) showed a logarithmic relationship with water concentration, Cw. That is, log Dll/Dllo was approximately linear with log Cw or log W, where W was the water weight fraction. The significant observation was that the data for all organic components in all sugar solutions fit the same curve. The slope of the curve log Dll/Dllo versus log W was about 3.4 at 2980 K curve showed considerable scatter. They also calculated the activation energy for diffusion (ED) of ethanol and sucrose in sucrose solutions and the activation energy for the solution viscosity (Eu) at various weight percent sucrose. The diffusion data that they claimed was for water, was actually for sucrose in a sucrose solution. They showed that E was approximately D equal to Eu (in absolute value) for sucrose at low con- centrations. Above 20% sucrose, Eu became greater than ED. Henrion (1964a) found that Du/T for sucrose was a constant in dilute sucrose solutions from 25° to 750 C. Gladden and Dole (1952) also found that Eu and ED for glucose and sucrose became equal in very dilute solutions of glucose and sucrose. At increasing sugar concentrations, Eu became significantly greater than ED. 31 Since D and u are exponential functions of their activation energies divided by absolute temperature, if ED equals Eu' the product Du should be constant with temperature and Du/T Should be nearly constant with temperature. This could indicate that the mechanism for diffusion was_the same as that of viscosity at low concentration of diffusant. At high dilution, solute molecules Were far apart and could not interact with each other. They tended to diffuse the same way that solvent molecules flow. The resistance to flow (viscosity) is caused by shearing forces as solvent molecules slide past each other. At low concentrations, the resistance to solute diffusion should be caused by similar shearing forces between solute and solvent molecules. If the mechanism for diffusion and flow are the same, it is reasonable to expect their activation energies to be equal. At higher solute concentrations the solute molecules had more Opportunity to interact. They may diffuse in groups through the solvent. If they diffused in groups, the energy needed for each individual molecule to get through the solvent molecules (ED) Should have been less than the energy needed for individual solvent or solute molecules to slide past each other (Eu)' ED for the group as a whole should have been greater than ED for an individual molecule diffusing through the solvent. But, ED for each individual molecule in the group should have 32 been less than Eu' since the solvent molecules would have resisted the group at its boundaries, but would not have interacted with each individual molecule in the groUp. The existance of such a group was reasonable Since many organic molecules are known to hydrogen bond. Hydrogen bonding could have held the groups together as they diffused through the solvent. Through the efforts of Menting, et al., and Chandrasekaran and King, a considerable amount of diffusion data has been obtained. None of the investigators have made an effort to develop a general correlation for diffu- sivity over a range of temperatures and solids content. It is important to be able to correlate the diffusivity with temperature and solids content so that a continuous function for diffusivity is available for use in mathematical models for Spray dryers. EXPERIMENTAL METHODS Constant Temperature Bath A constant temperature bath (figure 1) was used to keep the diffusion cell at a constant temperature. A temperature bath with a relatively large volume was needed to keep the temperature as constant as possible. A glass fish tank with a clear Plexiglass¢”1 cover was used. The fish tank was 24 in. long, 12 in. wide, and 12 in. deep. The cover was made of a clear Plexiglass® sheet which was 3/8 in. thick. Plexiglass® was used because it is water resistant and transparent. The cover was made in two parts, each measuring 12 in. by 12 in. One half was stationary on the bath. Holes were drilled into this half to accomodate the cir- culating water heater, heated syringe tubes, and a thermo- meter. The other half acted as a removable cover. Strips of Plexiglass® were glued along the bottom edges of both halves of the cover to keep them in place. A Haake model E52 recirculating heater was used in the experiments. It provided temperature control to i 0.1° C. The circulating pump on the heater was used to pump hot water to the syringe mantle as well as to 1Registered Trademark, Rohm & Haas Co. 33 34 ‘f' 1| OS cm ID iYGON' TUBING ' ' ‘ HEATER {L _] fl HAAKE'moaeI £52 SAMPLING )r SYRINGE - 1 see Figure 2 ‘~R£CIRCULATING PUMP (L GLASS TEE TANK FIGURE 1. CONSTANT TEMPERATURE BATH 35 circulate the water in the bath. The Haake heater held the temperature to within 0.2° C at a bath temperature of 90° C with the bath cover removed for 15 minutes. A Haake thermometer with 0.5° C graduations was used. Insulation on the sides of the bath was kept to a minimum amount. Three layers of aluminum foil and one layer of corrugated cardboard provided enough insulation. Syringe A Hamilton 1.0 ml gas sampling syringe (figure 2) was used to sample the vapor. The syringe performed very well when used in conjunction with a Plexiglass® heating mantle. The relative standard deviations Of repetitive samplings was typically less than 1% of the mean. This type of glass syringe was rather fragile and care had to be taken to avoid physical and thermal Shock to it. Syringe Mantle A Plexiglass® syringe mantle (figure 2) was fabricated to accomodate the 1.0 ml gas-tight syringe. The body of the mantle was made of a Plexiglass® tube which was 1 1/4 in. in diameter with 3/8 in. thick walls. The tube was cut to the length of the syringe body. The ends of the mantle were made of 3/8 in. flat Plexiglass®. A hole just large enough for the syringe needle to fit through was drilled in the bottom end piece. A hole large enough for the body of the syringe to pass through was drilled in the 36 WATER INLET WATER OUTLET ( RUBBER GASKET ' Nu; NEOPRENE \‘oll- R'NG FIGURE 2. CROSS SECTIONAL VIEW OF HEATED GAS SAMPLING SYRINGE 37 top piece. The end pieces were glued to the body using cyano-acrylate glue. Two 3/8 in. holes were drilled near Opposite ends of the mantle body. Into these holes were glued two pieces of COpper tubing 1 in. long. The copper tubing acted as a connection for the water circulating tubing from the hot water bath. Each syringe was held in its mantle by a back plate which was fastened to the top end plate by means of two 1 in. bolts and 1/8 in. diameter nuts. A hole large enough for the plunger to pass through was drilled in the back plate. The syringe was placed in the mantle resting on two rubber seals. One seal was a small round rubber disk through which the needle was pierced. This sealed the front end of the syringe. The second seal was a 1 in. rubber "O" ring. This second seal fit over the body of the syringe and sealed the back of the syringe. Over the back of the syringe, the back plate was fastened. The pressure of the back plate against the syringe pressed the seals against the front and back ends of the mantle, making the seal. Diffusion Cells During the diffusion experiments, it was desired to place an adequate number of diffusion cells into the water bath at any one time. The most reasonable approach to thisrequirement was to use relatively small containers as diffusion cells (figure 3). It was found that 125 ml PIERCE 1 “52.182 “S fl . fl .. , \ \ m, MININERT VALVE wax \r N 125 ml *- SERUM BOTTLE DIFFUSION TRAY , 43% 0,, o FIGURE 2. CROSS SECTIONAL VIEW OF DIFFUSION CELL 39 serum bottles worked well for this purpose. It was necessary to sink the cells into the bath using some type of weight, so that the temperature was constant throughout the cell to prevent condensation Of either diffusant or water on the cell walls. The external volume of each cell was 200 m1 and its empty weight was 100 9, so, 100 g of 16 gauge lead shot was used to sink each cell. Lead shot was used becauSe it is relatively inert to organic solvents and it is very dense. The lead shot also served as a good level platform upon which to place the diffusion trays. The Shot was easily leveled in the bottom of the diffusion cells by Shaking the cell. ®1 A Pierce Mininert Valve was used to cap the diffu- sion cell. It provided a pressure tight seal up to at least 1.5 atmospheres. The body of the valve was made of Teflonq”2. The pressure seal was made at the mouth of the cell by a system which consisted of two rubber rings encased inside the base of the valve on which pressure was exerted by a threaded ring. The ring was turned down on the rubber rings which caused the base of the valve to bulge, making the seal. The valve mechanism was a sliding cylinder which passed through the axis of the valve at right angles to it. When the valve was Open, a needle could be inserted through the valve's axis into 1Registered Trademark, Pierce Chemical Co. 2Registered Trademark, I. E. du Pont de Nemours & CO. 40 the diffusion cell. When the valve was closed, the hole in the sliding cylinder was no longer in line with the valve axis and a needle could not be pushed through it. To prevent gas from escaping around the needle when it was inserted, a small Silicone septum was located above the sliding cylinder. 80, to use the valve, one would Slide the Teflon® cylinder to the Open position and insert the syringe needle through the body of the valve. Diffusion Trays In order to reduce the time needed to perform the experiments, a thin layer of solution was used. Since some of the solutions were not very viscous, small Teflon® trays (figure 4) were made to contain the solutions during the experiment. Teflon® was chosen because Of its inert characteristics. The outside dimensions of the trays were 1 1/8 in. long, 7/16 in. wide, and 1/8 or 7/32 in. thick. A pit 1.5 mm or 4.5 mm deep was machined into the middle of each tray. A small hole was drilled into one corner of each tray to provide a way to remove the trays from the diffusion cells. A small wire hook was used for this purpose. The hook was placed into the diffusion cell and through the small hole in the Teflon® tray. The hook was then used to place and position the trays in the diffusion cells and to remove.the trays from the diffusion cells. 41 DIFFUSION TRAY TOP VIEW CROSS SECTION C >0 ' Ian. I WIRE HOOK 1" 13 cm. .I : ) FIGURE 4. DIFFUSION TRAY AND WIRE HOOK 42 Manometer A U-tube manometer was used to measure the pressure in the cells. It was made from 3/8 in. O.D. glass tubing. The glass tube was bent so that one Side of the manometer tube was 38 cm tall and the other side was 72 cm tall. Triple distilled mercury was poured into the U-tube and a thin Tygon®l tube was attached to the short end. A 22 gauge, 3 in. long hypodermic syringe needle was affixed to the free end of this Tygonq” tubing. A 40 cm ruler was placed behind the long tube with the graduation increasing up. In this way, the level of mercury in the long tube could be Sighted through the tube.' The long tube was left open to the atmosphere. The pressure in the diffusion cells was measured by inserting the manometer needle into the cell and Observing the level in the U-tube. Materials Table 1 lists sources of the chemicals used in the experiments. The characteristics of the malto-dextrin, Fro-dex®2 10 are listed in table 2. The average molecular weight of the malto-dextrin was assumed to be 1641.2. Fro-dexqplo has an average chain length of 10 sugar mole- cules according to the American Maize Products Company. 1Registered Trademark, Norton, Inc. 2Registered Trademark, American Maize Products Co. 43 TABLE 1 CHEMICALS AND SOURCES Chemical Source Fro-dex® 10 Malto-dextrin American Maize Products CO. 2-Butanone Mallinckrodt, Inc. l-Hexanol Aldrich Chemical CO, Inc. l-Butanol ‘ Mallinckrodt, Inc. l-Pentanol Mallinckrodt, Inc. TABLE 2 CHEMICAL AND PHYSICAL DATA-- AMAIZO ,FRO-DEX® 10 Moisture 5.0% Dextrose Equivalent 10 S02 (M.W.) 40 ppm PH (1:1) 4.5 Weight per cu. ft. 30 lbs Carbohydrate Composition (Approx. D.B.) Monosaccharides 1% Disaccharides 4% Trisaccharides 5% Tetrasaccharides & Higher 90% 44 Experimental Procedure MaltO-dextrin solution preparation. Solutions of Fro-dex® 10 malto-dextrin in water were prepared on a weight basis with an accuracy of 1% absolute. About 12 g of the malto-dextrin was weighed into a 250 m1 beaker to within 0.1 g on a top-loading digital balance. About 5 g of deionized water was added in excess of the desired weight percentage. This water was added so that upon heating, the malto-dextrin would completely dissolve before the desired weight percentage was obtained. This excess of water was especially important when preparing the 70 and 80 wt % solutions because they had a tendency to become very viscous as water evaporated from them, making them very difficult to stir. After adding the water, the mixture was heated to 90° - 100° C on a hotplate, and was stirred continuously until the malto-dextrin completely dissolved. It was assumed that the malto-dextrin was in solution once the mixture was clear. The solution was stirred and period- ically weighed on a tOp-loading balance until enough water was lost to increase the weight percentage to that desired. A stream Of air was directed into the beaker of malto-dextrin solution while it was being heated to increase the evaporative water loss. When enough water was evaporated from the solution to make the desired weight percentage, it was allowed to cool to room temp- erature. The solution was weighed again and enough water 45 was added to replace the water lost to evaporation during cooling. Then the solution was stirred and the beaker was covered with Parafilm®l wrap. The solution was stored in a refrigerator at 10° C until needed. Storing the solutions this way prevented infestation by mold for at least three months. Solution density measurement. The density of malto- dextrin solutions was measured at varying temperature and weight percent solids using a glass pycnometer. Solu- tions of the malto-dextrin were prepared and placed in the pycnometer. Air bubbles were removed from the solutions by centrifuging the pycnometer at 2000 r.p.m. The more viscous 70 and 80 wt % solutions were heated to 60° C and then centrifuged to speed the displacement of trapped air. After the pycnometer had been filled with solution at room temperature, it was held in a 1000 m1 beaker containing 600 ml Of water. Clamps and a ring-stand were used to hold the pycnometer in the beaker so that the pycnometer was just covered with water. The beaker of water served as a constant temperature bath. An 8 cm long, Teflon® coated, magnetic stirring bar was placed in the beaker. The beaker rested on a stirring hotplate. A thermometer was held in the water by means of clamps and a ring-stand. At the onset of the experiment, the pycnometer was clamped into place in the beaker and the hotplate was 1Registered Trademark, American Can Co. 46 turned on. The beaker was heated at a rate of about 0.5° C per minute. As tflua desired temperature was approached, the heat setting on the hotplate was reduced. When the exact temperature was reached, the heat setting was adjusted carefully to obtain a constant bath temperature. The temp- erature was held for 20 minutes to insure thermal equili- brium within the pycnometer. After the 20 minute period, the pycnometer was removed from the water bath and allowed to cool to room temperature. The pycnometer was then weighed to within 0.01 mg. The pycnometer was Opened with a pair of pliers and cleaned in hot water. The weight of the pycnometer was determined when it was empty and dry. The volume was calibrated with boiled, deionized water at the temperatures used in the experiment. The deionized water was boiled to remove dissolved carbon dioxide. Viscosity measurements. The viscosity of 30, 50 and 65 wt % solids solutions were measured at 60°, 75° and 90° C. An Ostwald-Fenske viscometer was used for the 30 and 50 wt % solids solutions. A Ferranti Couette viscometer of the coaxial cylinder type was used for the 65 wt % solids splution. The procedures are Similar to those discussed by Collins, et a1. (1973). The Ostwald- Fenske viscometer was clamped to a ring-stand and immersed in the constant temperature bath. Into the viscometer was pipetted 10 m1 of the solution. Ten minutes were allowed for the contents of the viscometer to reach the 47 bath temperature. Using a rubber pipette bulb, the solution was drawn up past the upper mark above the capillary and released. The flow time between marks was measured to .001 minutes with a timer. The flow- times for water and 30 and 50 wt % solutions were measured. the viscositycfifthe malto-dextrin solutions was calculated by taking the ratios of flow times for water and the malto-dextrin solutions. That is, t H = E; “W . (30) For the 65 wt % solids solution, the Couette viscometer was used. A 250 ml beaker containing about 150 ml Of the solution was clamped to a ring—stand and placed in the constant temperature water bath so that the water level was higher than the solution level. The viscometer was clamped above the beaker on the ring-stand so that the cylinders were immersed in the solution. The deflection meter needle was zeroed. The motor was turned on and the deflection reading was taken over a period of at least five minutes. The readings showed no change over the five minute period. The deflection reading represented the torque applied to the inner cylinder while the outer cylinder was rotating. This was repeated until three consecutive readings agreed. The deflection reading is prOportional to the viscosity of the liquid being tested. Pure glycerine was used to calibrate the viscometer. The deflection reading was taken for glycerin 48 at 38° C using the same rotation Speed and the same set Of cylinders. According to Ferranti, the resistance spring in the viscometer gives a linear diSplacement with applied force (Users Manual), the readings of the standard and the unknown solutions can be ratioed to give the ratio of the standard and unknown viscoSities. That is, R u =—i-u . S RStd Std (31) Where R is the deflection reading. Attempts were made to measure the viscosities of malto-dextrin solutions with concentrations greater than 65 wt % using a Weissenberger Rheogoniometer. However, the evaporation rate from the edge of a cone and plate assembly was so rapid that the solutions solidified before measurements could be obtained. Diffusion Experiment The diffusion coefficient and the vapor-liquid equilibrium coefficient were measured in aqueous malto- dextrin solutions containing 30, 50, 70 and 80 wt % solids and water. The vapor-liquid equilibrium coefficient was measured for 15 wt % solids solutions, also. The experiments were performed at 60°, 75° and 90° C. Concentrated malto-dextrin.solutions. For solutions containing 30, 50, 70 and 80 wt % solids, the experiments were performed using TeflonQ” diffusion trays inside the diffusion cells. The diffusion trays were filled with 49 malto-dextrin solution and the trays were placed in the cells. I The solutions were placed in the diffusion trays and diffusion cells in one of two ways, depending on their percent solids. The low-percent solids solutions (30 and 50 wt %) were pipetted into a diffusion tray already placed in a diffusion cell. A small wire hook was used to place the diffusion trays in their cells. The trays had to be tipped to place them in the diffusion cell, therefore, low percent solids solUtions were pipetted directly into the diffusion cells using a disposable pipette because they were not viscous enough to stay in the diffusion tray when it was tipped. High percent solids solutions (70 and 80 wt % SOlidS) were pressed into the diffusion trays with a metal spatula. The diffusion tray was then placed into a diffusion cell with the small wire hook. In the experiments, samples were of two types. Steady state samples were the samples with which the vapor— liquid equilibrium coefficient was measured. They were exposed to the diffusant until equilibrium was approached. Unsteady state samples were exposed to the diffusant for a short period. The diffusion coefficient was measured with the unsteady state samples. In order to maintain the malto-dextrin solutions at a constant weight percent during the experiment, deionized water.was injected into the diffusion cells before placing 50 them into the temperature bath. A 250 pl and a 50 ul syringewere used to inject the water. Table 3 gives the amounts of water added to the diffusion cells. For a given percent solids, the same amount was added at all temperatures. These amounts of water were determined from a simple experiment and trial-and-error. The simple experiment consisted of injecting varying amounts of water into diffusion cells containing a given percent solids solution and measuring the change in percent solids after about 24 hours. A rough estimate of the required amount of water was calculated. It was also noted if a skin was formed in the 24-hour period. Forma- tion of a skin on the solution was an indication of drying. The percent solids measured during the diffusion runs showed that the amounts of water added to the cells were reasonably close to the amounts needed. After the water was added to each of the sample cells, 'they were placed in the constant temperature bath for a period of time called the "conditioning period." Diffusant was added to the steady state sample cells before the conditioning period and to the unsteady state sample cells after the conditioning period. During the conditioning period, vapor-liquid equilibrium with respect to diffusant was approached in the steady state sample cells. Vapor-liquid equilibrium with respect to water was approached in all of the sample cells during this period. Regardless of the experiment temperature, each 51 TABLE 3 VOLUME OF WATER ADDED TO DIFFUSION CELLS Wt % Solids ul Water 30 160 50 100 70 50 80 30 52 set of samples were conditioned for 24 hours at 90° C. This was the total conditioning period for 90° C samples. The 75° C samples were conditioned at 75° C for another 48 hours after the initial 90° C conditioning. The 60° C samples conditioned at 90° C for 24 hours, 75° C for another 24 hours and, finally, for 72 hours at 60° C. So, the 90° samples received a total of 24 hours of conditioning, the 75° C samples received a total of 72 hours of conditioning and the 60° C samples received a total of 120 hours of conditioning. The approximate diffusivity of diffusant was deter- mined in early experiments. With these approximate values, an approximate run time was determined for each experimental condition using the solution to the unsteady state equation. Run times were targeted at 20% approach to steady state. Enough diffusant was added to both the steady state and unsteady state sample cells to bring the partial pressure of diffusant up to one—half of its vapor pressure. Table 4 gives the amounts of diffusant added at each temperature. Gaseous diffusants could easily be.used in this experimental apparatus. A gas tight syringe could be used to inject the diffusant into the cell. The head space of the diffusion cell was sampled using a 1 m1 Hamilton gas tight syringe. The syringe was heated to the water bath temperature inside a Plexiglassq” mantle as described earlier. The syringe 53 TABLE 4 AMOUNTS OF DIFFUSANT ADDED TO DIFFUSION CELLS Volume Of Liquid Diffusant (ul) Temperature l-Hexanol 2-Butanone 60° C 4.6 30 75° C 10.1 100 90° C 20.8 200 54 was cleaned by aspiration of water and methanol through the needle. The contents of the syringe was evacuated using an aspirator before each sample injection. Prior - to sampling the vapor, the pressure inside the cell was measured using a manometer. The syringe needle was plunged through the cell valve into the body of the cell. About 0.5 m1 of the vapor was drawn into the syringe and expelled back into the cell. This was done tO'fill the small void volume of the syringe with the vapor in the cell. Then 1.0 ml Of the vapor was drawn into the syringe. The syringe needle was drawn out of the cell and the sample was quickly injected onto the gas chro- matograph column. The needle was kept in the injection port for ten seconds to prevent loss of vapor through the port. Immediately after removing the syringe, the valve on the cell was closed. This process was repeated at least three times and the results of the best two injections were averaged. Aqueous solutions of the diffusant were used as standards. Standard curves of peak area versus weight injected were linear in their entire range. The gas chromatograph column and conditions are tabulated in table 5for the vapor and liquid samples. A Hewlet- Packard 5840A gas chromatograph with a flame ionization detector was used. After the vapor had been analyzed, the cell was removed from the water bath and liquid samples were taken. 55 TABLE 5 GAS CHROMATOGRAPH COLUMN AND CONDITIONS Liquid Samples Vapor Samples COlumn 5% Carbowax 20 M 5% SP 2100 Column Temp. 115° C 110° C Detector Temp. 400° C 400° C Nitrogen Flow 60 ml/min. 40 ml/min. Injector Temp 140° C 130° C Carrier Gas N N 2 2 56 The time that the cell was removed from the bath was recorded as the end of the experiment. The valve was removed from the diffusion cell and the cell was flushed for about two seconds with clean air. Air flushing was necessary to remove the diffusant and water vapor from the cells so that they did not condense on the liquid samples. The liquid sample was then removed from the Teflon® trays. Half of the sample was used to determine the percent solids and half was used to determine the concentration of diffusant. Samples were taken in one of two ways. Less viscous 30 and 50 wt % solids solutions were sampled with a disposable pipette when the diffusion trays were inside the cells. Solutions of 70 and 80 wt % solids were sampled after the diffusion trays were removed from the Cells. A spatula was used to scrape the solution out of the tray. The liquid sample for the percent solids determination was weighed to within 0.01 mg into a preweighed aluminum dish. The weight of the sample was recorded. The sample was dried at 110° C for 48 hours. The sample was allowed to cool to room temperature in a dessicator and then weighed. The dry weight of the sample and dish were recorded. Prior to their use, the aluminum dishes were dried at 110° C for at least 24 hours to remove any volatiles absorbed on the dish surface. The portion of the liquid sample for the concentration determination was weighed into a preweighed 6 ml serum 57 bottle. A small amount of internal standard was added to~ the vial and the vial was weighed again. Internal stan- dards for l-hexanol and 2-butanone were l-butanol and 1-pentanol, respectively. 'The weights of the vial, the vial plus sample, and the vial with sample and internal standard were recorded to within 0.01 mg. The vial was filled to the tOp with deionized water. A silicone rubber septum with a Teflon® coating on one side and an aluminum crimp cap was used to cover the vial. The septum was placed with the Teflon® side toward the solution in the vial. The aluminum cap was placed over the septum and crimped down. The septa were used to prevent volatile loss prior to the liquid analysis. Concentrated liquid standards containing a known ratio of diffusant to internal standard were prepared. The approximate amount of malto-dextrin that was contained in the samples was weighed into the standard serum vial. Two drOps of the concentrated standard solution containing a known weight ratio of diffusant to internal standard were pipetted into the vial. The vial was filled to the tOp with deionized water and a septum was crimped on the tOp of the vial. Liquid samples of 3 ul were injected onto a gas chromatograph column. At least three duplicate injections were done for each sample. The gas chromatograph column and conditions are listed in table 5. Since there was some malto-dextrin in the sample, the glass wool in the 58 injector end of the column was changed before each set of samples. Also, the detector was kept at 400° C (its maximum temperature) during the runs to prevent fouling of the detector by volatile components of the malto-dextrin. Dilute malto-dextrin solutions. The diffusion coefficient of 2-butanone and l-hexanol was measured in water. The vapor-liquid equilibrium coefficient of each was measured in water and 15 wt % solids solution. Water or 15 wt % malto-dextrin solution was placed in 2 ml screw-tOp vials in the diffusion cells. Wire lOOpS were attached to the neck of the vials so that they could be removed from the cells without spilling the contents. The vials were placed in the very bottom of the diffusion cells and lead shot was banked up against the vials to keep them vertical. After the vials had been positioned inside the cells, 1.4 ml of the liquid was placed in each Of them. -To maintain the humidity in the cell, 200 pl of deionized water was added to the vapor Space. The gas sampling procedure was the same as that used for the concentrated solutions. Before the conditioning period of 24 hours, diffusant was added directly to the steady state sample vials. Diffusant was added directly to the sample vials to ensure fast equilibrium in the steady state samples. After the conditioning period, diffusant was injected into the unsteady state sample cells. Care was taken not to get any diffusant in the unsteady 59 state vials. The diffusant was dropped onto the lead shot at the bottom of each diffusion cell containing unsteady state samples. The beginning of the experiment was recorded as the time at which the diffusant was injected into the cell. At the end of the experiment, after the gas had been sampled, the valve was removed from the cell and the sample vial was quickly removed and capped. After the samples had cooled to room temperature, they were directly injected onto a gas chromatograph column. Triplicate 3 ul injections were used. A standard of known concentration was injected with the same syringe used to inject the samples. The same syringe was used to insure accurate volume reproduction. All other details of the analysis follow the procedure for concentrated malto-dextrin solutions. Effects of pH on Coefficients Solutions of constant pH were prepared by adding 1.0 ml of a pH buffer solution to 20 g of 50 % wt solids malto-dextrin solution. Phosphate buffer solutions were used (Weast, 1975). For the pH 6.0 and 8.0 stock solutions, 2.4 g and 0.2 g of monobasic sodium phosphate was weighed into a 100 m1 beaker. To this, 50 ml of deionized water was added. The pH was adjusted to 6.0 and 8.0 with a saturated solution of dibasic sodium phosphate. This solution was diluted to 100 ml in a volumetric flask. 60 These 50 wt % solutions were run at 90° C in the same way that all of the other solutions were. The diffu- sivities and equilibrium coefficient of the pH 6 and 9 solutions were compared to that of the unbuffered solution. The pH of the unbuffered solution was 4.3. -Calculation of the Diffusion Coefficients The diffusivities of l-hexanol and 2-butanone were measured by performing an unsteady state experiment. A quasi-steady state experiment using a fritted diffusion cell was impossible to do here because the viscosity of the high solids malto-dextrin solutions were extremely large. It would be impossible to stir a malto-dextrin solution at a solids content of 80%. The only option left was to do an unsteady state experiment using diffusant in the vapor phase. In these experiments, a small amount of liquid diffu- sant was added to the cell. It was assumed that the liquid diffusant evaporated and mixed very rapidly. The vapor phase was not mixed Since the diffusivity of gasses is at least 1,000 times the diffusivity of the liquid. The physical situation in the experiments may be described as diffusion from a stirred solution of limited volume. Crank (1975) discusses the solution of this diffusion problem. The diffusion equation is 2 3c 8 c (32) 61 where c is the diffusant concentration, t is time, x is distance and D is the diffusivity. The initial condition is c = 0, 0 < x < l, t = 0 (33) where 1 is the slab thickness. The boundary conditions are ac - - o 34 5; — 0, 1 — 0, t > ( ) and KV V 8C _ _ fig = .7i_.§E - D 8t, x 1, t > 0 (35) where Vv is the vapor volume, K is the vapor-liquid equilibrium coefficient and A is the Slab surface area. This means that the concentration at the slab surface changes with time. .The solution to this equation is most easily obtained using the Laplace transform. In the form Mt/Mm, where M and Man are the mass of solute in the slab at time t t and at infinity, the solution is 20 (l + a) m n=1 1 + a + aqn2 exp (-an2/12) (36) where qn is the non-zero positive root of tan qn r aqn (37) where V °=Kv—V (38) L . This form is good for all values of t, but is very difficult 62 to solve numerically. A simpler form is Mt fi— -- (1 + a) [1 - exp (T/OLZ) erfc ( T/a2)1/2]' (39) on where T = Dt/lz. This solution works well for small values of T. The solution behavior is shown in figure 5. The numbers on the graph represent the percent uptake, U. U is represented by, ”=1+a. (40) Notice that Mt/ M00 is a linear function of Tli/2 for 0% uptake. The linearity in the curve decreases with increasing percent uptake. Notice also the extremely: rapid change in Mt/M0° for 99% uptake. For systems that have small vapor-liquid equilibrium coefficients, the diffusant is absorbed rapidly. .D can be calculated in an iterative fashion using equation 39. Values of Mt/M0° and a are substituted and values of T are guessed until the correct value is found. 63 I. I T I r 1 I I I 1.. -I / , 1. 99 q 08» . . 0.6 3” . 8 . I \ 40 1 z. 2 0.4~ 0 .. 0.2~ ~ 0 ' (£2 ‘ d4 ‘ 0.6 ' 0'8 ‘ in FIGURE 5. UPTAKE BY A SLAB FROM A STIRRED SOLUTION OF LIMITED VOLUME RESULTS AND DISCUSSION Solution Density The density of the malto-dextrin solutions was measured over the range of experimental conditions used in the diffusion experiments. The density (table 6 and figure 6) was linear with S and fit the form 0 = A + BS. _ (41) Table 7 gives A, B and the correlation coefficient, r, calculated for the data. Table 8 gives the density extrapolated from equation 41 at 0 and 100 wt % solids and the density Of water (Weast, 1975). Since the extrapolated values are approximately 3% below the actual values of water density, the solutions are nearly ideal. Viscosity7C0rrelations The viscosity of malto-dextrin solutions was measured so that the group %# could be calculated from the diffusion data. Table 9 and figure 7 give the viscosity in centi- poise for various percent solids and temperatures. The values of viscosity at 0 wt % are for water (Bennet and Meyers, 1974). The viscosity was a dramatic function of solids content, increasing over three orders of magnitude from 0 wt % solids (water) to 63 wt % solids. Temperature 64 65 TABLE 6 MALTO-DEXTRIN SOLUTION DENSITY (g/ml) Temperature (° C) Wt % Solids 60° 75° 90° 30.9 ' 1.119 1.110 1.099 47.0 1.202 1.193 1.181 67.5 1.317 1.307 1.296 66 1.4 I: DENSITY (g/ml) i2 1.0 30 so» ‘4 92:3 non" FIGURE 6. 50 60 70 WEIGHT ZSOLIDS DENSITY VS. WEIGHT PERCENT SOLIDS 67 TABLE 7 CONSTANTS FOR THE DENSITY CORRELATION, EQUATION 26 Temperature (° C) A B r 60° 0.9503 0.5414 0.9998 75° 0.9420 0.5390 0.9998 90° 0.9309‘ 0.5388 0.9996 TABLE 8 EXTRAPOLATED VALUES OF WATER AND MALTO-DEXTRIN DENSITY AND ACTUAL VALUES OF WATER DENSITY Density (g/ml) Temp. Water Water Malto-dextrin (° C) (Actual) (Extrapolated) (Extrapolated) 60° 0.9832 0.9503 0.4917 75° 0.9749 0.9420 0.4810 90° 0.9653 0.9309 0.4697 68 TABLE 9 VISCOSITY OF MALTO-DEXTRIN SOLUTIONS (cp) Temperature (° C) Wt % Solids 60° 75° 90° 0 0.4688 0.3799 0.3165 31.1 6.15 4.18 3.03 47.2 43.46 26.68 16.69 63.2 757 359 197 69 WEIGHT % SOLIDS ‘0 20 40 60 80 8'7 3 *- .. 2 )- .. ’5 IL :1. c1 .2 l r - o _ A 60°C _ o 75°C I 90°C -17 1 1 A n 1 l I 1 j 0.0 -0.2 -0.4 -0.6 -o.8 log W FIGURE 7. LOG D vs. LOG W FOR MALTO-DEXTRIN SOLUTIONS 70 also had a marked effect on the viscosity. Since the viscosity was to be used to calculate %% at a number of values of percent solids, a correlation for viscosity was desired as a function of both tempera— ture and solution concentration. It was also desired to extrapolate the viscosity above 63.2 wt % solids because of the rapid increase in viscoSity with increasing solids content. Numerous equations were fit to the data with varying success (see appendix III). The simplest correlation that gave good agreement was log N = A + B log W . (42) This form showed the best correlation coefficients. Table 10 gives the constants and the correlation coeffi- cients. Since the constants A and B are based on the log of the viscosity, they Should be a linear function of %. That is, _ E A — C + T (43) _ E B — D + T . p (44) Linear regression analysis of A and B versus % gave A = -2.325 + 65%;” , r = 1 (45) and B = 4.162 — 9%,4—4 , — -o.9994 . (46) The total correlation became (651.9 - 3844 log W) . (47) HH‘ log n = -2.325 + 4.162 log W + 71 TABLE 10 CONSTANTS FOR EQUATION 42 Temperature. (° C) A B r 60° -0.3681 -7.3834 -0.9994 75° -0.4523 -6.8584 -0.9996 90° -0.5297 -6.4313 -0.9995 72 Viscosity data for sucrose and dextrose (Stephen and Stephen, 1963) were correlated to the same form, 1 (48) log u‘= C + D log W + T (E + F log W) . The constants C, D, E, and F, and the maximum correlation coefficient are given in table 11. C and D are fairly constant for the sugars studied. E and F Show a decreasing trend with increasing molecular weight. E is the activa- tion energy for the viscosity of water. E Should be a constant. So, the only parameter which shows a signifi- cant variation with the molecular weight of the solute is F. F represents the magnitude of the effect of W on the activation energy. Since W is less than 1, a decrease in W (increase in percent solids) will cause an increase in the viscosity activation energy. For malto-dextrin, Eu = 652 - 3844 log N (49) an increase in percent solids causes an increase in the viscosity activation energy. Since equation 48 worked well for sucrose over a very wide temperature range, it was assumed to be generally valid. Vapor-Liquid Equilibrium Coefficients The vapor-liquid equilibrium coefficient, K, was calculated from the experimental results. K is defined as C K = E! (50) L where C and C are the concentration diffusants in the V L 73 vvmmI «mm ma.¢ ~m.mi mmm.o com I com ¢.H~ma cfiuuxOOIouHoz moami mow va.¢ mv.~I mmm.o 6mm I omH m.~¢m mmouoom HHmNI can ah.m vs.~( ham.o com I 6mm oma mmowuxmo E m o O A 8 o. 098m 6859 wasomsoo Edeflxmz musumwmema pnmflmz Hmanomaoz mc ZOHB_ . z: 50 75°C . a 90°C .— 2 . \ I 30 F ~ 0 20 40 I 50 80 WEIGHT zsouos FIGURE 11. ACTIVITY COEFFICIENT vs. WEIGHT PERCENT SOLIDS FOR Z-BUTANONE IN MALTO-DEXTRIN SOLUTIONS 79 not show a minimum. The general trends in the activity coefficient for 2-butanone agreed with this. For the most part, y for 2-butanone was relatively constant compared with y for l-hexanol. That was why K showed, at most, a very weak minimum for 2—butanone. The activity coefficient at 0 wt % solids was calcu- lated from other sources. Table 12 gives values of y” for l-hexanol and 2-butanone calculated from the Pierotti correlation (equation 9). Table 13 gives 7 for saturated solutions of l-hexanol and 2-butanone in water (equation 7) calculated from solubility data. The Pierotti correlation best approximated the data presented here. Most of the data for 1-hexanol was in the range of y” at 500 and 1000 C, calculated from the Pierotti correlation. The data for 2-butanone fell slightly above the expected values calculated from the Pierotti correlation at 50° and 100° C. The general trends in y with respect to temperature were pre- dicted by the Pierotti correlation with the exception of 2-butanone at 90° C. The activity coefficients calculated from solubility data did not predict the absolute values of 7, but did predict the general trends in the data with the exception of 2-butanone at 90° C. According to solubility data and the Pierotti correlation, y for 2-butanone should show a general increasing trend from 60° to 90° C, but y at 90° C was between 7 for 75° and 60° C. This discrepancy might have been due to experimental error or, more likely, 80 TABLE 12 ACTIVITY COEFFICIENT CALCULATED FROM THE PIEROTTI CORRELATION Activity Coefficient, y Temp. . (° C) l-Hexanol 2-Butanone 50° 613.8 36.9 100° 319.9 41.1 81 TABLE 13 ACTIVITY COEFFICIENTS CALCULATED FROM SOLUBILITY DATA 1-Hexanol 2-Butanone Temp. Solubility Solubility (° C) (wt. %) Y (wt. %) Y 30° 0.545 1100 21.9 15.3 50° 0.515 1160 17.5 19.9 70° 0.565 1060 16.2 21.7 90° 0.68 880 16.1 21.8 110° 0.89 670 17.7 19.6 Source: Stephen and Stephen, 1963 82 was a true representation of the behavior of y. The activity coefficient calculated from the solu- bility data showed a maximum at 90° C. Since the solubility of 2-butanone was significantly greater than the concentra- tions of 2-butanone used in this study, the activity coefficients calculated from solubility data cannot be directly compared with the data presented here. What the data did show is that there was a maximum in Y as a function of temperature and that the maximum occured at 90° C for high 2-butanone concentrations (solubility data) and at 75° C at low concentrations (this work). The behavior of y as a function of S showed some interesting results. The activity coefficient was a much stronger function of S for l-hexanol than for 2-butanone. Since y was inversely proportional to solu- bility, a decrease in 7 should be interpreted as an increase in solubility or affinity of the solute to the solution. Therefore, the strong decrease in y versus 8 in the l-hexanol data should be interpreted as a strong affinity of 1-hexanol molecules to malto-dextrin molecules. Since y was a much stronger decreasing function of solids content for l-hexanol than for 2-butanone, l-hexanol molecules luui a much higher affinity toward malto-dextrin than did 2-butanone. The stronger affinity of l—hexanol toward malto-dextrin as compared. with 2-butanone was most likely due to hydrogen bonding. The alcohol should have hydrogen bonded to the malto—dextrin 83 due to the hydroxyl group present. The ketone should have shown less hydrogen bonding with the malto-dextrin mole- cules since it does not have a hydroxyl group. I For 2-butanone, the maximum in y as a function of temperature disappeared as the solids content increased. The maximum disappeared at about 20 wt % solids (figure 11). The disappearance of the maximum in y indicated basic differences in attractive forces between 2-butanone and water, and between 2-butanone and malto-dextrin. The maximum in y in water solutions has been explained as the formation and subsequent breakdown of ice-like structures of water formed around the non—polar part of the solute molecule as the temperature rises (Nishino and Nakamura, 1978). As the solids content increased, the maximum in y disappeared. This indicates that the attraction of 2-butanone to malto-dextrin was not a result of structural changes similar to those exhibited by water. Whatever attraction there was between 2-butanone and malto—dextrin, was probably due to very weak hydrogen bonding. Diffusion Coefficients The diffusivity of l—hexanol and 2-butanone in malto-dextrin solutions*was a strong function of the solids content. Figures 12 and 13 show the log of the diffusivity versus the percent solids of the malto-dextrin solution. One should notice two trends in the diffusivity. 84 _‘. . 90°C I -5 T :3 u o .l 60°C -6. . A A a \ -7 - - '8 j 4 L 1 1 4 4 1 WEIGHT 7. SOLIDS FIGURE 12. LOG D vs. WEIGHT PERCENT SOLIDS FOR l-HEXANOL IN MALTO-DEXTRIN SOLUTIONS 85 - , 90°C - Lag D -8 l I J l 1 J 1 l 20 40 60 80 WEIGHT X SOLIDS FIGURE 13. LOG D vs. WEIGHT PERCENT SOLIDS FOR Z-BUTANONE IN MALTO-DEXTRIN SOLUTIONS 86 First, the diffusivity decreased by several orders of magnitude from 0 to 80 wt % solids. Second, one should notice that the diffusivity decreased significantly with decreasing temperature. Du Figures 14 and 15 show log 7F-versus log W where W is the water weight fraction. The values of %# were calcu- lated from the diffusivity data and the malto-dextrin solution viscosity data. Notice that the data gave a straight line when plotted in this fashion. There was considerable scatter in the data, though. Correlations for diffusivities of organic components from the literature were tried as a first evaluation of the data (equations 11 to 24). However, they did not work m. T solutions. MB, which was used in the literature correla- well to predict of organic solutes in malto-dextrin tions, was assumed to be the average molecular weight of the solution, ”B = MN Ms Mw + (MS - MW) w where MW is the molecular weight of water and MS is the average molecular weight of the malto-dextrin. The (53) correlations showed a slight decrease in log %# below w = 1. The data showed a slope of about 4 times that of the correlations. Most of the emperical correlations for %¥ have the general form DH —T— = KMBIIZ (54) 87 WEIGHT % SOLIDS O 20 40 . 60 80 '4 I I I T 1 WILKE 8: CHANG, 1955 SITARAMAN, el al., 1963 2 SCHEIBEL, 1954 3 OTHMER 8: THAKAR, I953 . . O -7- II D l 1 A 2 I 3 -8 A 90°C 0 75 °C I 60°C _9 7 1 1 I 1 n 1 1 1 0 -0.2 -04 -0.6 -O.8 L09\N FIGURE 14. LOG (Du/T) vs. LOG W FOR l-HEXANOL IN MALTO-DEXTRIN SOLUTIONS 88 WEIGHT 1 SOLIDS _30 20 40 60 30 90 I WILKE & CHANG, I955 SITARAMAN, et al., 1963 2 SCHEIBEL, I954 ' -4_ 3 OTHMER & IHAKAR, 1953 ‘A -5 - 9 1: \ :1 9. u 3 A -6 .- -7 I .. 2 ' fl { 3 -8 1 1 l 1 1 1 1 1 I 1 0 -0.2 -0.4 -O.6 -O.8 -I.O Log W FIGURE 15. LOG (Du/T) VS. LOG W FOR 2-BUTANONE IN MALTO-DEXTRIN SOLUTIONS 89 It would be reasonable to assume that a correlation for %g in malto-dextrin solutions should have a similar form. That is, D11 _ i "B —T— — K MB (55) where B < 0. For high values of W, . Mw (56) so, D“ = K" W8 (57) or log %# = log K" + 8 log W . (58) Linear regression analysis was done on the data at each temperature and for all of the data combined. Table 14 shows the results of those regression analyses. Log %# correlated better for individual temperatures than for all the temperatures, but, given the poor correla- tion coefficients (r in table 14), it was not reasonable to draw any conclusions with respect to trends in K" and B with temperature. Given the scatter in the data (see figure 14 and 15), one could only conclude that K" and 8 are relatively constant with respect to temperature. This conclusion is consistant with literature correlations for-%¥ . The literature correlations discussed earlier 'were all independent of temperature. Given-P-B does not vary with temperature, one may also T conclude that the activation energy for diffusion, ED is 90 TABLE 14 CONSTANTS FOR EQUATION 57 Temp. Compound (° C) Log K" B r l-Hexanol 60° -8.23 -4.41 -0.895 75° -7.95 -4.16 -0.979 90° -7.57 -2.87 -0.962 _All _ _ _ Temp. 7.89 3.70 0.919 2-Butanone 60° -7.58 -5.23 -0.984 75° -7.31 -3.79 -0.989 90° -6.86 -3.25 -0.982 All _ _ Temp. 7.73 3.96 -0.961 91 equal to the negative of the activation energy for vis- cosity, Eu. Chandrasekaran and King (1972a) made a similar conclusion for ethanol in sucrose solutions. They found that ED for ethanol was equal to EU for sucrose solutions from 0 to 70 wt % sucrose between 25° and 35° C. ED for sucrose in these solutions was substantially lower than ED for ethanol and En. At low sucrose concentrations, ED for sucrose approached Sn and ED for dilute ethanol. Othmer and Thaker (1953) obtained a range of values for ED/Eu of -l.07 to -1.15 for water, calcium chloride, phenol, mannitol and sucrose over a temperature range of 10° to 50° C. The significance of this conclusion is that the activation energy for diffusivity may be obtained from simple viscosity measurements. Viscosity is very easily measured over a wide range of temperatures and solids content. The diffusivity, however, is, at best, difficult to measure. With one series of diffusion experiments at one temperature and viscosity measurements over the temperature range and percent solids content, one could generate a complete set of diffusivity values a T Other workers have not tried to correlate their data if the dependence of on solids content were known. in this manner. The viscosity of malto—dextrin must be known to use the data of Menting, et al. (1970a), but it can be estimated from equation 47. The malto-dextrin viscosity was estimated at 21.5° C and values for-%% for the data from Menting, et al., for water, acetone, 92 ethyl acetate, benzene, camphor, and carbon tetrachloride were calculated. Figure 16 shows the results of these calculations. The intercept for each compound at log W = 0 is different due to differing molecular volumes. One may see a general trend in all of the data. For high water contents, the 510pe of the log gF-versus log W curve has a slope of approximately -4 for ethyl acetate, acetone, benzene and carbontetrachloride. At higher solids content (low values of W), the curves level off. In work involving unsteady state diffusion in aqueous solutions of malto-dextrin, it is very important to measure the final water content after the diffusion experiment has been performed. Since Menting, et al., did not measure the final moisture content in their experiments, there is reason to believe that their diffusion data at the high solids content may not be accurate. In all of Menting's work, the water content of the final sample was assumed, not measured. For water contents above 30 wt % water, samples were equilibrated in a flask containing a large amount of malto-dextrin solution at the desired weight percent water for 15 hours. The sample was placed in the 200 ml glass flask, and the diffusion run was made. It was assumed that the moisture content did not change due to the small volume of the flask. This is probably a reasonable assumption since the vapor pressure of water at 21.5° C is quite low. The 93 WEIGHT :5 souos 30 2O 40 6O 80 90 . ACETONE V 0 ETHYL ACETATE vwmzn O BENZENE 40133011 TETRACHLORIDE -4. OCAMPHOR ‘ LogW FIGURE 16. LOG (Du/T) VS. LOG W FOR MENTING'S DATA 94 change in the concentration of diffusant with time in the vapor phase was measured. For water contents below 30%, the change in the concentration of the diffusant with time in the liquid phase was measured. Due to the extremely low concentra- tion of diffusant in the liquid phase, the diffusant concentration was measured with a radioactive tracer technique. Glass bars were coated with 50 wt % solids malto-dextrin by drawing them out of the solution at a constant velocity. These rods were air blown dry at 80° C. In order to obtain the desired percent solids for the experiment, the malto-dextrin coated rods were placed in a closed container with a constant humidity salt solution. The experiment was carried out in another chamber similar to the first, except that 1% radioactive labled acetone or other diffusant was added to the constant humidity salt solution. Rods were removed periodically and the concentration of diffusant was measured. The diffusivity was calculated from the initial slope of the curve of Mt/M0° versus t1/2. This experimental method is excellent and should produce very good results. The question that should concern anyone performing such experiments is whether the assumptions made are correct. Menting assumed values of the weight percent solids in this experiment. He assumed that the solutions come to equilibrium above the constant humidity solutions, but he 95 did not measure the percent solids in any of his experiments after the experiment had been completed. In the present work, the solids content of every solution was measured and, in fact, it was found necessary for determining accurate data. 21 T data (figure 16), the diffusion coefficients measured for According to the trends in log in Menting's ethyl acetate and acetone were low below moisture content of 30 wt %. One might look at it another way. Perhaps the assumed water content of the malto-dextrin solutions was significantly higher than the actual water content in the experiment. If the malto-dextrin coated bars were not equilibrated long enough with the constant humidity solutions, the water content could have been significantly lower than the assumed value. In the present work, the solids content of every solution was measured. Examination of the trends in %§ for Menting's data indicate that there may have been some discrepancy between the assumed solids content and the actual solids content. This might explain why log-%% is not linear with log W below a water content of 30 wt % water. The data for water diffusivity are linear to a water content of about 10 wt % water. The data presented here for l-hexanol and 2-butanone indicate that log %# is approxi- mately linear to a water content of 20 wt % water. The data also indicate that the slope of the log %# versus log W line is -4 for all of the diffusion data in 96 malto-dextrin solutions so far. This is an important result, since a considerable amount of diffusion data can be approximated if this holds for all diffusants in malto-dextrin. Chandrasekaran and King (1972a) showed similar trends in their data for diffusion of various dilute organics in sugar solutions. All of their data for ethanol, ethyl acetate, n-butyl acetate and n-hexanal in solutions of d-fructose, d-glucose, sucrose and a mixture of the three correlate to one master plot at 25° C. When the data is plotted as log D11/D11o versus log W, the data all lie on the same line. D11 and D11° are the diffusivity of the dilute organic in sugar solution and in water, respectively. At 35° C, data were collected for ethanol and ethyl acetate in sucrose solution. These higher temperature data show the same behavior as the 25° C data, except there was less variation. The slope of the log Dll/Dllo versus log W curve should have the same slope as the log D11 versus log W curve. The viscosity correlates in a similar fashion. The slope of log u versus log W curve is known. The sum of the slopes of the log D versus log W curve and log u versus log W curve should give the lepe of the log %# curve, B. Table 15 gives the values of 8 curves for sugar solutions for data from Chandrasekaran and King (1972a). Notice that B is nearly constant. Also, 8 is considerably larger for malto-dextrin solutions than 97 TABLE 15 VALUES FOR 8 FOR DIFFUSANTS IN SIMPLE SUGAR SOLUTIONS Temperature (° C) 8 25° -0.9 35° -l.2 (Chandrasekaran and King, 1972) 98 for simple sugar solutions. This is probably due to the greater dependence of viscosity on solids content in the malto-dextrin solutions than in simple sugar solutions. From the experiments performed here and elsewhere, the following conclusions can be made. First, %§ is nearly constant with respect to temperature for dilute diffusants in sugar and malto-dextrin solutions. Second, the lepe of the log-%¥ versus log W curve is a constant depending on the type of dissolved solid. For malto-dextrin solutions, it is approximately equal to -4. For sugar solutions, it is about -1. pH Effects The effect of pH on the equilibrium coefficient, K, the diffusivity of l-hexanol in 50 wt % solids solutions at 90° C was studied. A pH range of 4.3 to 8 was consid- ered. The unbuffered solution had a pH of 4.3. Other solutions were buffered at pH6 and pH8. Outside of this range, the malto-dextrin breaks down. Figure 17 shows the variation in diffusivity and partition coefficient with pH. The diffusivity is nearly constant from a pH 0f 4 t0 3. The equilibrium coefficient increases a small amount over the range. The decrease in equilibrium coefficient with decreasing pH must be attributed to association with water. Since there is no effect of pH on the diffusivity, the association of l-hexanol with the malto-dextrin solutions is not pH 99 ‘50 I I I I a 0 3‘5)- 4.- {I A“ 1 I l O) 2 x 5: ‘D 2. r Li I I 4 5 6 7 8 pII FIGURE 17. EFFECTS OF pH ON LOG 0 AND K FOR 1-HEXANOL 100 dependent. So, association with water must be pH dependent. This would indicate that l-hexanol becomes more soluble in acidic solutions. Alcohols are slightly basic compared to water (Morrison and Boyd, 1973). They have the ability to accept a proton. ROH + H+ + R0H2+ (59) This reaction has the equilibrium constant KB. The equilibrium expression is [ROH2+] + = KB (60) [ROH] [H l where [ ] denotes concentration. Rearranging, we get [ROH2+] = KB [ROH] [n+1 (61) The solubility in neutral solution is a constant, S, equal to the concentration of unprotonated alcohol, [ROH]. The concentration of the protonated alcohol is [ROH2+] = KB 5 [n+1 (62) The total solubility of the alcohol, ST' is ST = s + [ROH2+] . (63) Substituting, sT = s (1 + KBIH+]) . (64) So, the total solubility increases with increasing hydronium ion concentration or with decreasing pH. This gives the observed result that K decreases with decreasing pH. CONCLUSIONS 1. The vapor-liquid equilibrium and activity coefficients for l-hexanol and 2-butanone in aqueous malto-dextrin solutions are a strong function of temperature. 2. The diffusivity of flavor components in aqueous malto-dextrin solutions can be correlated using the Stokes- Einstein group. Log (Du/T) was shown to be a linear func- tion of log W for l-hexanol and 2-butanone at 60° to 90° C (this study) and for acetone and ethyl acetate and water at 21.5° C (Menting, et al., 1970a). The 510pe of the log (Du/T) versus log W line was about -4 for all of the diffusion data in the literature to date. 3. The diffusion coefficient is not affected by pH. The vapor-liquid equilibrium of 1-hexanol is dependent on pH. The solubility is increased at low pH due to increased ionization of alcohol. 4. The viscosity of aqueous sucrose, glucose and malto-dextrin solutions was correlated with the water weight fraction (W). The log u was a linear function of log W. The activation energy of viscosity, B11 was also shown to be a linear function of log W. 5. The density of aqueous malto-dextrin solutions was a linear function of weight percent solids. 101 RECOMMENDATIONS l. The experimental methods developed here should be used on other food systems like solutions of simple sugars, milk solids and coffee. 2. The diffusivity of flavor components of widely varying molecular weight in malto-dextrin in the 60° to 90° C range should be measured to test the validity of the Stokes-Einstein group correlation. 3. The diffusivity and vapor-liquid equilibrium of water in malto-dextrin solutions in the 60° to 90° C range should be measured. 4. Models for spray dryers should be developed and the correlations for diffusivity and the vapor-liquid equilibrium data should be used to predict flavor reten- tion in malto—dextrin. The calculated model could then be compared with actual spray drying data. 102 APPENDICES APPENDIX I RAW DATA AND CALCULATED RESULTS The following tables (tables 16 through 20) give raw data and calculated results for the diffusion experi- ments performed in this study. Data for the standards is presented in tables 30 and 31. The relative standard deviation (olx) and standard deviation (0) values in the tables are for the data in the columns to their immediate left. Samples A and B were steady state samples and samples C and D were unsteady state samples in all of the tables. The calculated results were calculated using the equations in Appendix II. 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AEUV 8. u Hmflfifiz H z\ 2 H z\ s H z\ z mHmEmm 0 com 0 amp 0 com AOdemmIH mom 0 .2 mxo 73 x n. :53 n 39.—um o .3 .2 .8258: «o.— <._. m .< .00 mcocmusmnm 01¢de mH3\03 AMHMJE Puma Hem—yam mmHmEmm AMEN“. vumccmum 0 ¢\ > onwocmum canvaq Unaccmuw nomm> mom mamH.b mm.m mH com mamo.o ~o.m mm.m 3 com mHmo.o ma.m oo.m ma emu mHmo.o Hm.v oo.m 3 omn mHmo.o mh.m ¢~.m ma coo mHmo.o vm.m vN.m 3 com AOdemmIH ommo.o mv.m .mm.v ma .3 com ommo.o No.5 mv.m ma .3 amp omwo.o v>.m ¢¢.m ma .3 com mcocmusmlm AHs\m. .He. mHmamm .o .. oumwcmum new .uoH x mama oH x osm< .aame o A. new > onwocmum pumocmum Unmccmum cstHq 02¢ Homm> oasqu Homm> mmnmzdm mQHAOm 30A MOh mQfiflQZdBm mmdeOdeommU m<0 Hm mqm<fi APPENDIX II SAMPLE CALCULATIONS Vapor Concentration, CV The concentration of the diffusant in the vapor phase was determined using an external standard technique. In early runs, a series of injections of standard produced a standard curve of peak area versus volume of injection for each run. These standard curves were linear. So, in sub— sequent runs, 5 pl injections were used to calibrate the response. The external standard technique is outlined by Gudzinowicz (1967). The equation used to calculate the vapor phase concentration was AD ( CSTDVSTD) ASTD 0 II "U | (65) The following is an example for l-hexanol, 60° C, sample 30 A. P = 1.078 atm 4.42 x 106 1.0 m1 STD = 0.3153 g/ml < f) ‘< > /A = 5.207 x 10‘11 m1 STD STD 120 121 . _ 4.43 x 106 CV - (1.078) ( 1.0 ml ) (0.03153 g/ml) x (5.207 x 10'"11 ml) CV = 7.866 x 10‘6 g/ml Liquid Concentrations, CL The concentration of diffusant in the liquid phase was measured in one of two ways. For low percent solids samples (less than 30 wt % solids), an external standard technique similar to the vapor phase analysis was used. An internal standard technique was used for the rest of the samples (Gudzinowicz, 1967). Low solids samples were injected directly onto the gas chromatograph (G. C.) column. The G. C. response was calibrated using 3 ul injections of an aqueous standard solution. The liquid phase concentration was AD CSTDV STD CL = vD A (66) s STD ' ' In this case, VS = VSTD = 3 ul or CL = A CSTD . (67) STD The following is an example for l-hexanol, 60° C, sample W A. A A = 2.677 x 106 C = 0.03153 g/ml 5.643 X 107 3’ ll 2.677 x 106 5.643 x 106 ) (0.03513 g/ml) 122 CL = 1.496 x 10‘3 g/ml Samples containing greater than 30 wt % solids were analyzed by the internal standard technique outlined by Gudzinowicz (1967). A standard solution containing a known weight ratio of diffusant and internal standard was injected. The weight ratio of diffusant weight to sample weight was 10.52 115(3) (1'2) (63) Ws AIs WS AD STD WIS STD . The concentration in the liquid phase was C=p—-‘3. (69) The density was shown to be a linear function of weight percent solids. p = A + BS . ' _ (70) The constants A and B were obtained by a least-squares fit of the density data for 30, 50, 70 and 80 wt % solids solutions. The liquid concentration was A W A W CL = (A + BS) (IX-2) (—Wl§) (XI—S) (W2) (71) IS 5 D STD IS STD . The following is an example for l-hexanol, 60° C, sample 30 A. A = 0.9503 g/ml B = 0.5414 g/ml S = 0.343 123 U 0.03881 > IS 2 I IS — 0.01352 9 2 = 0.16540 9 AI ) ID STD w ) IS STD S (I) 6.353 I. 0.1102 ”I 2 0 ll [0.9503 g/ml + (0.5414 g/ml) (0.343)] (0.03881) x ( 0.01352 g 0.16540 9 CL 2.523 x 10‘3 g/ml ) (6.353) (0.1102) Vapor-Liquid Equilibrium Coefficient, K In this work, the vapor-liquid equilibrium coefficient, K, was defined as the ratio of vapor and liquid concentra- tions at equilibrium or or, simply, (72) (73) where equilibrium between the bulk vapor and liquid phases is assumed. The following is an example for l-hexanol, 60° C, sample 30 A. CV = 7.866 x 10" g/ml 124 cL = 2.523 x 10"3 g/ml = 7.866 X 10"6 g/ml 2.523 x 10'3 g/ml K K = 3.118 X 10'3 Vapor-Liquid Equilibrium Coefficient Standard Deviation, OK The relative standard deviation of a calculated value (eg. K) is the square root of the sum of the squares of the relative standard deviations of each measured value (Skoog and West,1976). That is, the relative standard deviations for the partition coefficient was 0 0 2 o 2 K _ cv CL —-K -/ ( —C ) + (——C ) (74) or Ocv 2 0CL 2 O 0 K ( -——-) + ( -—-) (75) K C C V The following is an example for l-hexanol, 60° C, sample 30 A. U 7?! = 0.0132 V U 7?! = 0.0029 L 0 = 3.118 x 10-3 f(0.0132)2 + (0.0029)2 0.042 x 10-3 Q ll 125 Diffusivity, D The solution to the unsteady state diffusion equation is given by Crank (1975) as Mt T T M— = (1 + a) [1 — exp (—> erfc <—)1/2] (76) w 02 02 ' Mt/ M0° is the ratio of the bulk concentration of diffusant in the liquid phase at time t to the bulk concentration at steady state. This ratio may be represented as Mt ke —— = ——9 (77) M on Where keq and kt are not equilibrium constants, but are convenient ratios of concentrations for calculation purposes. They are defined as .. _‘_’ eq - CL (78) at large values of t, and as C kt = 5‘1- (79) L at small values of t. In this work keq = K (80) since equilibrium is reached at large values of t. The ratio of the mass of diffusant in the vapor phase to the mass of diffusant in the liquid phase at steady state was a, or a = ;E = ————- (81) 126 or a = K —— (82) Table 32 gives valuesofVV/VL for the samples. Dimension- less lime, T, is defined as T = _ (83) To obtain a diffusivity from the data, Mt/Mco and a were first obtained. Mt/M0° was calculated from the steady state and unsteady state concentration ratios and k was taken as the keq that has a weight percent solids value closest to the weight percent solids of the short time sample being calculated. The following is an example for 1-hexanol, 60° C, sample 30 C. k = 8.723 x 10‘3 t k = 3.118 x 10‘3 eq 23 _ 3.118 x 10’3 M _ m 8.723 x 10"3 0.7347 22 M00 The value of a was calculated using equation 82. The following is an example for 1-hexanol, 60° C, sample 30 C. K = 3.118 x 10'3 V —Y = 889.0 VL 127 TABLE 32 VOLUME RATIO AND DIFFUSION PATH LENGTH FOR THE DIFFUSION SAMPLES Sample vV /vL 1 (cm) W 114.3 1.8 30, 50 296.3 0.45 70, 80 889.0 0.15 128 p H (3.118 x 1073) (889.0) 0.9240 9 I) The unsteady state diffusion equation (equation 76) was solved by trial and error for T. The following is an example for l-hexanol, 60° C, sample 30 C. M t _ i; — 0.7347 c = 0.9240 0.7347 = (1 + 0.9240) 1 - exp [ T ] (0.9240)2 T 1/2 X erfc [ ] (0.9240)2 . T T1/2 0.7347 = 1.9240 1 e exp a-gggg) erfc 6‘5536 Trial and error gives T = 0.2095. Given a dimensionless value of time, T, the diffusi- vity was obtained by rearranging equation 83. 2 D = 111?— (84) The following is an example for 1-hexanol, 60° C, sample 30 C. T 0.2095 1 0.45 cm t = 2779 sec (0.2095) (0.45 cm)2 2779 sec D: 1.526 x 10'5 cmz/sec U (I 129 Activity Coefficient, y The activity coefficient, y, was calculated from the vapor-liquid equilibrium data, K. The molar vapor-liquid equilibrium coefficient was defined as x P The vapor phase mole fraction was Y = ——- (86) where nDV and nTV were the diffusant and total vapor molar concentrations, reSpectively. The diffusant molar con- centration was 0 n = —V- (87) DV MD where CV was the vapor phase mass concentration of diffusant and MD was the diffusant molecular weight. Assuming an ideal gas for the vapor phase, nTV.became _._P_ nTv ‘ RT (88) where P wasifluatotal pressure, R was the ideal gas constant and T was absolute temperature. The vapor mole fraction became y =.— (89) x = -——- (90) 130 where nDL and nTL were the diffusant and total liquid molar concentration, respectively. The diffusant liquid molar concentration was n = .5 (91) DL MD . The total liquid molar concentration was = + nTL nDL + nWL nSL (92) where nWL and nSL were the water and solids (malto-dextrin) liquid molar concentration, respectively. The diffusant concentration was assumed to be negligible. The water and solids concentration became WP n = ——- (93) WL MW and SO “31. " (a; ‘9‘” where p was the solution density, S and W were the solids and water weight fraction, and MW and MS were the water and solids molecular weight. The water and solids weight fractions were related by w = 1 - S. (95) The density was correlated by p = A + BS . (96) So, the liquid mole fraction became C _ L MD(A+BS) ( “w +31%) . 131 The activity coefficient was calculated by sat = P X Y P )c or = KRT (A + BS) 1 - S 31 Y sat M M . P w' S The following is an example for l-hexanol, 60° C, sample 30 A. K = 3.118 x 10'-3 R = 62,400 :mnfolTé’er T = 333.2 °x A = 0.9503 g/cm3 B = 0.5388 g/cm3 S = 0.343 psat = 11.10 Torr Mw =18.01 g/g mole MS = 1641.2 g/g mole Y (3.118 x 10") (62,400 gcmmzl'remfx) (333.2 ox) 11.10 Torr x[0.9503 g/cm3 + 0.5388 g/cm3 (0.343)] x ( 1 - 0.343 )( 0.343 ) 1641.2 g/g mole 18.01 970 mole y = 243 (98) (99) APPENDIX III VISCOSITY CORRELATION ATTEMPTS An extention of the Einstein equation was used to fit the data (Willey and Macosko, 1978) - JL = 2 ”R — u l + 2.5 ¢ + K 0 W where 0 is the volume fraction. An ideal mixing rule was assumed for water and malto-dextrin, ¢= VS VS + VW where S v=— S 08 and W v=— W pw or 1 ¢= p 1 + g —§ pw where S is the solids weight fraction, W is the water weight fraction, and DW are the density of pure 0S (100) (101) (102) (103) (104) malto-dextrin and water, respectively. K in equation 100 was a strong function of the percent solids. Table 33 132 EINSTEIN 133 TABLE 33 CONSTANT K FOR EQUATION 100 Temperature (°C) Wt % Solids 60° 75° 90° 31.1 153 180 220 47.2 370 498 661 63.2 2202 3348 5724 134 gives calculated values for K. This correlation does not work because it is meant for use with suspension_of spheres. The malto-dextrin studied here has, on average, a chain length of 10 dextrose molecules. (In solution, the malto-dextrin molecules should not be spheres. There should be a much greater dependency of the viscosity on the mean molar volume of the solution, since the malto- dextrin chains should extend when a shearing force is exerted on them. Numerous empirical correlations were tried. One of which was the Martin equation (Bird, et al., 1960), u - us = us In] C exp (K" [n] C) (105) where “S is the solvent viscosity, C is concentration in g/ml, K" is an adjustable parameter and [u] is given by lim u - 1‘S [u] = --—-—- (106) C+0 us This equation correlated very well. Table 34 and the correlation coefficient, r, gives In], K" for the temp- eratures at which the viscosity was measured. This correlation was not used in the calculations because it was fairly complex and the density was not measured over the entire range of percent solids of interest. Menting, et al. (1970a), have shown that the diffusi- vity of acetone correlates well with exp (BCW'1/2). That is, log D = A + Bcw'l/2 (107) Since the diffusivity and viscosity might have a similar 135 TABLE 34 CONSTANTS FOR EQUATION 105 Temp. (°C) [(1] K" r 60° 1.51 2.48 0.994 75° 1.67 2.07 0.996 90° 1.76 1.83 0.994 136 mechanism, the form of a correlation for viscosity should follow the same form. That assumption is indeed correct. Loq u correlates well with Cw'l/z. Table 35 gives the constants for the viscosity correlation of the form, log 0 = A2 + BZCW'1/2 . (108) This equation correlates as well as the Martin equation. Since C is a function of the water fraction, W, a correlation in the form of log n = A3 + 83w-1/2 (109) was used. This correlation worked better than the one 4 4 based on Cw‘l/z. Table 36 gives the constants A3 and B3 and the correlation coefficient. It was also found that log n correlates well with W”2 although not as well as with W‘l/2 or Cw'llz. The correlation becomes 10g 0 = A + B wl/2 . (110) Table 37 gives the constants A4 and B4 and the correlation coefficient. 137 TABLE 35 CONSTANTS FOR EQUATION 108 Temp. (°C) A2 52 r 60° -7.82 7.45 0.994 75° -7.38 6.89 0.994 90° -7.06 6.46 0.994 TABLE 36 CONSTANTS FOR EQUATION 109 Temp. (°C) A3 B3 r 60° -5.20 49.3 0.999 75° -4.94 45.8 0.999 90° -4.74 42.9 0.999 138 TABLE 37 CONSTANTS FOR EQUATION 110 Temp. (°C) A4 1.34 r 60° 17.58 1.86 -0.994 75° 1 16.08 1.73 -o.994 90° 14.83 1.62 -0.994 APPENDIX IV EARLY EXPERIMENTS Previous workers had measured D and K by measuring changes in either the vapor or liquid phase concentration. Early experiments in this study were conducted on the same philosophy. The first attempts at measuring the diffusivity and the partition coefficient of l-hexanol were performed using heavy walled capillary tubes (figure 18). Malto- dextrin solutions were placed inside the capillary tubes with a disposable glass pipette for the low solids solutions. High solids solutions were drawn into the capillary tubes by drawing a vacuum on one end of the capillary tube and placing the other end into a beaker of hot solution. One end of the tube was sealed with several layers of Teflon® tape and a Teflonqy cap. The capillary tubes were then placed upright inside the diffusion chamber in a 50 m1 beaker. For the equilibrium partition measurements, a thin layer (approximately 0.3 cm thick) of malto-dextrin solution was poured into a 25 ml beaker. This beaker was placed in the diffusion chamber (figure 19) along with the capillary tubes. The diffusion chamber was then placed in the constant temperature water bath and 139 140 HEAVY WALL , GLASS CAPILLARY 7.9 cm TEFLON IAPE \ IEFLON CAP-o L— J "L‘ —+(—— 02 cm FIGURE 18. GLASS CAPILLARY DIFFUSION TUBE 141 .1 10 cm. (anon SIOPCOCK—’ {O r _ GROUND GLASS —-+\ JOINT 15"“. WEIGHT — FIGURE 19. GLASS DIFFUSION CELL 142 the chamber was completely submerged in the water to prevent condensation of water or hexanol on any part of it. Approximately 4 hours were allowed for the contents of the diffusion chamber to reach the water bath tempera- ture. Then the chamber was removed from the bath and a 25 ml beaker containing about 10 m1 of l-hexanol was placed in the diffusion chamber along with the samples. The chamber was immediately returned to the water bath. The time at which the l-hexanol was introduced into the diffusion chamber was recorded as the starting time for the run. The l-hexanol was allowed to diffuse into the samples for 4 to 48 hours, depending on the percent solids of the sample. Samples of low percent solids solutions were taken by inverting the diffusion tube above a 5 ml serum vial. High percent solids samples were pushed out of the diffu- sion tube with a metal rod. Samples were taken at different times for each temperature and percent solids. In each run, the very last sample to be taken was the vapor-liquid equilibrium coefficient sample. All samples were analyzed using the internal standard method described in the Experimental Method section. Vapor-liquid equilibrium coefficients were calculated based on the weight percent l-hexanol in the liquid phase and the saturated vapor pressure of l-hexanol. It was assumed that the total pressure inside the diffusion chamber was 1 atmosphere 143 since the chamber was opened prior to the introduction of l-hexanol. The partial pressure of water in the chamber was neglected. Using the technique just described, it was observed that the diffusion samples lost a considerable amount of water. A drop in the liquid sample capillary of as much as 1 cm.was observed for 30 wt % solids samples. A method for controlling the relative humidity above the samples was necessary. Pre-conditioning similar to that used by Menting, et al. (1970a), was tried. Saturated inorganic salt solu- tions were placed in the diffusion chambers in 25 ml beakers along with about 10 ml of malto-dextrin solution in a 25 ml beaker. All of the possible combinations of 30, 50, 70, and 80 wt % solids malto-dextrin solutions and saturated solutions of NaBr, KCl, LiCl, KC2H3O2 at 60° C were tried. After a conditioning period of 24 hours, all of the solutions had lost most of their water. Some of the solu— tions had lost so much water that they had to be chipped out of their beakers. Obviously, the vapor pressure of water above the malto-dextrin solutions was considerably greater than that above the saturated salt solutions. In another attempt, a beaker containing about 100 m1 of malto—dextrin solution was placed in the diffusion chamber along with the sample solutions. The 100 ml solution had the same percent solids as the samples. After a conditioning period of 24 hours at 60° C, the solutions 144 showed a water loss similar to that experienced with the saturated salt solutions. The solutions in the diffusion chamber lost a considerable amount of water. This method was rejected for two reasons. First, the solutions lost water during a 24-hour conditioning period. Second, and most important, it was decided that it was important to use a partial pressure of l-hexanol much lower than the saturated vapor pressure. 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