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Desorption isotherm of milk powders at elevated temperatures and over a wide range of relative humidity
Journal of Food Engineering 68 (2005) 257–264 www.elsevier.com/locate/jfoodeng
Desorption isotherm of milk powders at elevated temperatures and over a wide range of relative humidity Sean X.Q. Lin a, Xiao Dong Chen a
a,*
, David L. Pearce
b
Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand b Fonterra Research Centre, Private Bag 11-029, Palmerston North, New Zealand Received 18 November 2003; accepted 31 May 2004
Abstract In this paper, a detailed account of the measurement and analysis of equilibrium isotherm data, obtained using a specialized device built for the purposes of large temperature and humidity ranges, is provided. The measurements were for the desorption isotherms of milk powder (skim milk powder and whole milk powder) for which data have not been available for the range that is relevant to spray drying conditions. The experimental approach allowed us to avoid the problem associated with amorphous lactose, which is known to undergo a glass transition if the equilibration process takes too long. The data points were adequately fitted using the GAB model, in terms of both the moisture content and the temperature dependence. These results will be widely used in spray drying simulations or spray drier designs for dairy powder production. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherms; Correlations; Spray drying of milk
1. Introduction In the simulation of the drying of a single droplet of milk, the equilibrium vapour pressure of the milk is very important because it determines the mass transfer driving force. However, most milk powder sorption isotherms have been measured at around ambient temperature (Berlin, Anderson, & Pallansch, 1968; Heldman, Hall, & Hedrick, 1965; Warburton & Pixton, 1978). There have been very few reports for the temperature range 60–90 °C at relative humidities of up to 40% (Kockel, Allen, Hennigs, & Langrish, 2002; Pisecky, 1992). The exhaust air from a commercial spray drier falls into this temperature and humidity range. For isotherm measurements, samples can reach equilibrium with the moisture contained in the air by either a *
Corresponding author. Tel.: +64 9 373 5799x87004; fax: +64 9 373 7463. E-mail address: [email protected] (X.D. Chen). 0260-8774/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.05.036
dynamic method (Kockel et al., 2002; Papadakis, Bahu, McKenzie, & Kemp, 1993) or a static method (Heldman et al., 1965; Warburton & Pixton, 1978). In the dynamic method, the temperature and the humidity of the air are accurately controlled and air is continuously passed through the sample. In order to let the sample reach equilibrium with the air in a relatively short time (within 3 h) the sample must have the largest surface area possible when exposed to the humid air. One method used in previous research, to obtain the largest surface area possible, was to use a stirred fluidized bed (Kockel et al., 2002). Another method allowed humid air to pass through a cartridge that held the sample (Papadakis et al., 1993). With the dynamic method, the time to reach equilibrium was largely reduced to several hours (Kockel et al., 2002). In contrast, the static method leaves the sample in an environment in which the temperature and the humidity are controlled. Unlike the dynamic method, the air in this environment is static. Because the sample is a thick layer of powder with a
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comparatively small surface area, air cannot easily pass through the sample; hence the time to reach equilibrium may be as long as several weeks (Bell & Labuza, 2000). Lactose in milk powders presents special problems in sorption measurements. It can be either amorphous or crystalline. Amorphous lactose in milk powder holds more water than crystalline lactose. During the sorption experiment, particularly using the static method, crystallization of the amorphous lactose occurs in the milk powder sample. This phenomenon is well known (Berlin et al., 1968; Jouppila & Roos, 1994). Berlin et al. (1968) used an electronic recording microbalance to record gravimetric changes in a precise absorption and desorption experiment on the dehydration dairy products. A maximum in the sorption measurement was found at around a water activity of 0.5. This was attributed to the occurrence of morphology changes. Jouppila and Roos (1994) confirmed the phenomenon of the crystallization of lactose during a sorption experiment. In their study, the effect of lactose hydrolysis on water sorption and the effect of milk fat on lactose crystallization were investigated. Most isotherm measurement experiments are brought to equilibrium using the static method. As crystallization of lactose had to be avoided during the measurements, the static method was unsuitable espe-
cially at humidities above 50% RH. Hence the dynamic method was adopted. There are many models to fit the moisture isotherm of food products. In some models, such as the SPS (Papadakis et al., 1993), Keey (1992) and Henderson (1952) models, the temperature dependence is directly expressed in the equations. Other models, such as the BET and GAB models, do not include the temperature dependence relationship directly, but this relationship is reflected in the modelÕs coefficients, which are temperature dependent. As part of milk droplet drying studies, the drying conditions at high humidities were required. To model the droplet drying, a wider range of desorption isotherms was needed. In this research, the desorption isotherms of skim milk powder and whole milk powder were measured at elevated temperatures of 53–90 °C at up to 100% relative humidity (RH) by a dynamic technique. The results were fitted using some of the available models.
2. Experimental procedure and materials A schematic diagram of the experimental set-up is shown in Fig. 1. The sample (milk solution) was coated
Fig. 1. Schematic diagrams of the measurement system. (a) Moisture isotherm measurement set-up. 1––fan and heater; 2––drying chamber; 3––milk carrier; 4––Teflon sheet; 5––humid air outlet. (b) The metal shim tray (milk carrier) for holding the liquid samples.
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on to a milk carrier. The air from the humidity generator, where both temperature and humidity were controlled, was passed through the milk carrier at a flow rate of 20–30 standard litres per minute. The milk carrier was contained in a drying chamber and set on top of a mass balance, which measured the weight change of the sample. In this method, a thin layer of milk solution (about 0.07 mm after being totally dried) was coated on to a milk carrier (see Fig. 1(b)). The method used for coating the milk carrier was as follows. A stainless steel shim carrier was immersed in a milk solution of 25 wt%. The milk solution was reconstituted from commercially available milk powder and water. The coated carrier was then pre-dried in a hot air stream for several minutes. The above procedures were repeated several times to obtain thicker milk films. The pre-drying enabled the milk solution to adhere to the stainless steel shim and prevented the milk solution from running to the bottom of the carrier. The moisture content of the coated milk solution after pre-drying was about 0.2–0.4 kg/kg (solids basis) higher than the equilibrium moisture content. Pre-drying maintained a thin and even coating on the shim, thus reducing the time to reach equilibrium significantly. The pre-drying time was up to some 30 s, the air temperature used was 70 °C and the air velocity was 5 m s1. The size of the stainless steel shim (see Fig. 1(b)) was 21 mm by 30 mm and nine shims were set in parallel. Air (from the humidity generator) was passed through these shims at a speed of approximately 1 m s1. Because of the large heat and mass transfer area and the thin layer of the coating, the milk solution was able to reach equilibrium within 50 min. Fig. 2 shows a typical drying process of the sample during isotherm measurement. The coated milk carrier was placed in a drying chamber, which was installed inside a temperature-
0.66
Sample weight (g)
0.65 0.64 0.63 0.62 0.61 0.60 0
10
20
30
40
50
60
Drying time (min)
Fig. 2. Typical drying process of the sample during isotherm measurement (skim milk powder desorption, 69.5 °C, 72.8% RH).
259
controlled environment chamber. The temperature of this chamber was set at the same temperature as the drying chamber. Air from the humidity generator was introduced into the drying chamber and then passed through the milk carrier. The outlet for the humid air from the drying chamber was a 6 mm hole covered by a metal sheet, with enough room between the two to allow the air to flow out. This method ensured that the pressure of the drying chamber was just above ambient pressure and minimized the effect of the humidity from the environment on the drying chamber. Two thermocouples were placed approximately 5 mm from the milk carrier. One was used to control the temperature of the humidity generator and the other was used for temperature measurement of the drying chamber (i.e. equilibrium temperature of the desorption isotherm). The thermocouple used to measure the equilibrium temperature of the sample was calibrated with an accuracy of ±0.1 °C. The calibration method followed the approach taken by Nicholas and White (1982). The maximum temperature fluctuation of the drying chamber, where the milk powder was brought to equilibrium, was less than 0.1 °C. The weight change of the milk carrier (i.e. the sample flow) was measured using a balance with a repeatability of 0.001 g. During weighing, the drying air flow was cut off for 5 s; it was assumed that the humidity inside the drying chamber did not change because the outlet of the drying chamber was doubly separated from the environment. The interval between weighings was from 3 to 10 min. When a constant sample weight had been attained for at least 10 min, it was assumed that equilibrium had been reached (most samples had an equilibrium time of 20 min). To determine the dry solids content of the milk samples after desorption isotherm experiments, the samples were dried at 102 ± 2 °C for 3 h. The drying temperature and time which were used here are recommended by the Association of Official Analytical Chemists (Nollet, 1996). The area of the experimental set-up that supported the carrier and that was exposed to the humid air was designed to a minimum and was made with Teflon to minimize moisture sorption, which may have affected the final sample weights. Moisture sorption on the experimental set-up was carefully calibrated and excluded from the calculations. For the isotherm measurements in this study, the accuracy of the relative humidity was better than 1.5% RH and the repeatability was better than 0.3% RH. The accuracy of the moisture content measurement was better than 0.005 kg/kg. The desorption studies were conducted on spraydried skim and whole milk powders, with the gross compositions listed in Table 1.
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Table 1 Composition (wt%) of the skim and whole milk powders before reconstitution in water Skim milk powder
Whole milk powder
Fat Total protein Lactose Mineral Moisture
0.6 36.5 49.8 9.3 3.8
26.5 28.0 36.8 5.9 2.8
3. Results and discussion Fig. 3 shows a moisture desorption isotherm of skim milk powder at 69.4 °C. It shows the typical trend for foods containing sugar, with the equilibrium moisture content increasing sharply at high water activities, caused by the dissolution of lactose. The results of this study were compared with the reported values of Kockel et al. (2002) which were adjusted because the final drying condition (to determine the solids weight) of the reported values was 85 °C instead of 102 °C (International Dairy Federation, 1993). As suggested by Kockel et al. (2002), the moisture contents of their reported values were multiplied by a factor of 1.17 so that they could be compared with moisture contents measured in this study. The average difference between the reported values and the results of this study was 0.004 kg/kg. This difference was within the range of accuracy for this study. The closeness between the reported values of Kockel et al. (2002) and the results of this study is demonstrated in Fig. 4. After the experiments, all the samples were examined using scanning electron microscopy. Fig. 5 shows that the samples had a smooth surface rather than a rough surface covered in crystals or even tomahawk-shaped crystals as observed by Warburton and Pixton (1978). This suggested that crystallization of lactose did not take place.
1.4
Moisture content (kg/kg)
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 3. Moisture desorption isotherm for skim milk powder at 69.4 °C.
Moisture content (kg/kg)
Component
0.08
0.06
0.04
0.02 Exp. data(current) Exp. data Kockel et al. 0.00 0.0
0.1
0.2
0.3
0.4
Water activity (-)
Fig. 4. Comparison of measured data (current) with reported data (Kockel et al., 2002).
Fig. 5. Scanning electron micrograph of skim milk powder after the experiment (69.4 °C, aw = 0.63).
The desorption isotherm of skim milk powder was also measured at 52.6 and 89.6 °C. Fig. 6 shows the desorption isotherms of skim milk at 52.6, 69.4 and 89.6 °C. The isotherms showed a clear temperature dependence. However, the relationship was different at high and low humidities, divided by an inversion point. Below the inversion point, an increase in temperature resulted in a decrease in the equilibrium moisture content, which is widely accepted for the effect of temperature on the isotherm. Above the inversion point, the equilibrium moisture content increased with an increase in temperature for the same water activity. This phenomenon has been reported previously for food containing sugar (Maroulis, Tasmi, & Marinos-Kouris, 1988; Rahman, 1995; Tasmi, Marinos-Kouris, & Maroulis, 1990). The shift in water activity caused by temperature changes was explained as being mainly due to the change in water binding, the dissociation of water or the increase in solubility of a solute in water (Rahman, 1995). For the
S.X.Q. Lin et al. / Journal of Food Engineering 68 (2005) 257–264 1.0
1.4
52.6°C
52.6°C
1.2
69.6°C
69.4°C
0.8
89.6°C
Moisture content (kg/kg)
Moisture content (kg/kg)
261
1.0 0.8 0.6 0.4
89.5°C
0.6
0.4
0.2
0.2 0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Water activity (-)
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 6. Moisture desorption isotherms for skim milk powder at different temperatures.
Fig. 8. Moisture desorption isotherms for whole milk powder at different temperatures.
milk powder desorption isotherms at higher moisture contents, the increase in the solubility of lactose, caused by an increase in temperature, was the major influencing factor. This resulted in the equilibrium moisture content increasing with an increase in temperature. In this study, there was no clear inversion point because of measurement error and because of a large interval between the two measurement points. The inversion point ranged from a water activity of 0.3 to a water activity of 0.43. Fig. 7 shows the inversion points of the desorption isotherms for skim milk powder in the temperature range 53–90 °C. Fig. 8 shows the desorption isotherms of whole milk powder at different temperatures. Comparison of Figs. 6 and 8 showed that the whole milk powder had a lower equilibrium moisture content than skim milk powder at the same water activity. This may have been because the fat that is contained in whole milk powder is not
considered to be a water-absorbing component. When the moisture content was calculated on a non-fat basis, the desorption isotherms of skim milk powder and whole milk powder were essentially identical. As shown in Fig. 9, the moisture desorption isotherms for skim milk powder and whole milk powder based on non-fat solids at a temperature of around 70 °C were almost identical, which was also observed by Berlin et al. (1968) and Jouppila and Roos (1994) . The difference between the two isotherms was within the uncertainty of the moisture content measurement when the water activity was less than 0.80. The less close agreement above a water activity of 0.80 may have resulted from the uncertainty in the water activity measurement (i.e. in this range, the uncertainty of the water activity measurement was about 0.015). The desorption isotherms of skim milk powder and whole milk powder were essentially identical at temperatures of 53 and 90 °C when the
1.4 Moisture content on non-fat basis (kg/kg)
Moisture content (kg/kg)
0.2
0.1
52.6°C 69.4°C 89.6°C
0.0 0.0
Skim milk, 69.4°C
1.2
Whole milk, 69.6°C
1.0 0.8 0.6 0.4 0.2 0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 7. The inversion points (or range) of the moisture desorption isotherms for skim milk powder at different temperatures.
0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 9. Moisture desorption isotherms for skim milk powder and whole milk powder based on non-fat solids.
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1993), Keey (1992), Henderson (1952) and other models, which incorporate the temperature dependence directly. Least squares curve fitting (automated curve fitting software: TableCurve2D) was used. However, these fits were not successful because the temperature dependence of the experimental data was different in the different water activity ranges, divided by the inversion point. In contrast, the GAB and BET equations for n-layers (Do, 1998) fitted these data very well. The GAB equation for curve fitting has the following form:
Moisture content (kg/kg)
0.2
0.1
52.6°C 69.6°C
X eq ¼
89.5°C
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Ckm0 aw ð1 kaw Þð1 kaw þ Ckaw Þ
ð1Þ
where Xeq is the equilibrium moisture content, aw is the water activity, m0 is the monolayer moisture content and C and k are constants related to the temperature. DH 1 C ¼ C 0 exp ð2Þ RT DH 2 k ¼ k 0 exp ð3Þ RT
Water activity (-)
Fig. 10. The inversion points (or range) of the moisture desorption isotherms for whole milk powders at different temperatures.
moisture content was calculated on a non-fat basis (data not shown). Similar to skim milk powder, the desorption isotherm for whole milk powder had an inversion point. Fig. 10 shows the details of the desorption isotherms at a range of water activities. The inversion point ranged from a water activity of 0.28 to a water activity of 0.40. The measured data for skim milk powder and whole milk powder were fitted using SPS (Papadakis et al.,
where T is the absolute temperature, R is the gas constant and DH1 and DH2 are heats of sorption of water. Tables 2–5 list the GAB constants of skim milk powder and whole milk powder at different temperatures.
Table 2 GAB constants by direct regression of skim milk powder Temperature (°C)
52.6 69.4 89.6
GAB constants
Fit standard error
(kg/kg) m0
C
k
0.06245 0.06067 0.06887
10.42 15.72 4.04
0.873 0.937 1.047
(kg/kg) m0
C
k
0.04290 0.04264 0.04049
8.78 13.07 5.24
0.909 0.956 1.106
0.005 0.02 0.002
Table 3 GAB constants by direct regression for whole milk powder Temperature (°C)
52.6 69.6 89.5
GAB constants
Fit standard error
0.003 0.01 0.0006
Table 4 GAB constants by indirect regression for skim milk powder Temperature (°C)
GAB constants
Fit standard error
(kg/kg) m0
C
k
52.6 69.4 89.6
0.06156 0.06156 0.06156
15.83 10.01 6.207
0.866 0.940 1.050
0.007 0.02 0.005
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263
Table 5 GAB constants by indirect regression for whole milk powder Temperature (°C)
GAB constants (kg/kg) m0
C
k
52.6 69.6 89.5
0.04277 0.04277 0.04277
9.20 7.70 6.20
0.904 0.956 1.020
The direct regression constants were estimated from a group of experimental data that had the same absorption temperature. Based on the direct regression, monolayer moisture contents were obtained at different temperatures. Then the average of the monolayer moisture contents was taken (the constant at 90 °C was not used, because the experimental data had only limited points of water activity up to 0.50). In the indirect regression, the average monolayer moisture content obtained from the direct regression was used and then the constants C and k of the GAB equation were again estimated from the regression. From Tables 2–5, the fit standard errors of the indirect regressions had no significant increase compared with those of the direct regressions. The indirect regressions also resulted in constant values for the monolayer moisture contents of the skim milk powder and whole milk powder, which were 0.06156 and 0.04277 kg/kg respectively. The reported monolayer moisture content values of skim milk powder are 0.0425 kg/kg (absorption at 26 °C) (Lomauro, Bakshi, & Labuza, 1985) and 0.051 kg/kg (absorption at 24 °C) (Jouppila & Roos, 1994). Because the values in this study were obtained from desorption experiments, the monolayer moisture contents obtained were reasonable. The values of C (indirect regression) for skim milk powder and whole milk powder decreased when the temperature was increased and were related to the temperature according to Eq. (2) (DH1 = 24,831 J/mol, C0 = 0.001645, R2 = 0.9999 for skim milk powder and D H1 = 10,485 J/mol, C0 = 0.1925, R2 = 0.998 for whole milk powder). The values of k (indirect regression) increased with an increase in temperature and were related to the temperature according to Eq. (3) (DH2 = 5118 J/ mol, k0 = 5.710, R2 = 0.996 for skim milk powder and DH2 = 3215 J/mol, k0 = 2.960, R2 = 0.999 for whole milk powder). The predictions of the GAB model showed good agreement with the experimental data (not shown graphically here). The average differences between the measured data and the model predictions for water activities up to 0.95 were 5.4% and 3.6% for skim milk powder and whole milk powder respectively. The original experimental values of the equilibrium moisture contents of skim milk powder and whole milk powder are listed in Appendices A and B.
Fit standard error
0.007 0.01 0.003
4. Conclusions A new dynamic isotherm measurement method was developed. This method largely reduces the equilibrium time, which is the key to obtaining the isotherms for food materials with crystallizable components. Using this method, data on the desorption isotherms of skim milk powder and whole milk powder at elevated temperatures (up to 90 °C) and high humidities (up to 100% RH) were obtained. The desorption behaviours at three temperatures (53, 70 and 90 °C) showed that there was a temperature dependence. Various formulae for the equilibrium moisture content were used in an attempt to fit the experimental data. The GAB model yielded the best fit for water activities of up to 0.95.
Appendix A Temperature (°C)
Water activity
Equilibrium moisture content (kg/kg)
52.6
0.977 0.902 0.798 0.636 0.486 0.326 0.168
0.598 0.288 0.191 0.133 0.103 0.067 0.046
69.4
1.000 0.987 0.932 0.820 0.728 0.632 0.484 0.325 0.166
1.303 0.808 0.449 0.262 0.202 0.158 0.108 0.071 0.045
89.6
0.538 0.430 0.324 0.217 0.111
0.133 0.096 0.069 0.050 0.026
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Appendix B Temperature (°C)
Water activity
Equilibrium moisture content (kg/kg)
52.6
0.965 0.925 0.867 0.775 0.637 0.483 0.324 0.170
0.345 0.267 0.195 0.141 0.092 0.063 0.048 0.034
69.6
0.998 0.953 0.932 0.859 0.795 0.654 0.505 0.324 0.164
0.926 0.462 0.380 0.255 0.185 0.113 0.073 0.051 0.032
0.539 0.381 0.240 0.106
0.089 0.056 0.035 0.019
References Bell, L. N., & Labuza, T. P. (2000). Moisture sorption: practical aspects of isotherm measurement and use (pp. 43–45). St. Paul, MN: American Association of Cereal Chemists, Inc. Berlin, E., Anderson, B. A., & Pallansch, M. J. (1968). Water vapor sorption properties of various dried milks and wheys. Journal of Dairy Science, 51, 1339–1344.
Do, D. D. (1998). Adsorption analysis: equilibrium and kinetics (pp. 96– 98). London: Imperial College Press. Heldman, D. R., Hall, C. W., & Hedrick, T. I. (1965). Vapor equilibrium relationships of dry milk. Journal of Dairy Science, 48, 845–852. Henderson, S. M. (1952). A basic concept of equilibrium moisture. Agricultural Engineering, 33, 29–31. International Dairy Federation, (1993). Dried milk and dried cream: determination of water content. IDF Standard 26A. International Dairy Federation, Brussels, Belgium. Jouppila, K., & Roos, Y. H. (1994). Water sorption and timedependent phenomena of milk powders. Journal of Dairy Science, 77, 1798–1808. Keey, R. B. (1992). Drying of loose and particulate materials. New York: Hemisphere. Kockel, T. K., Allen, S., Hennigs, C., & Langrish, T. A. G. (2002). An experimental study of the equilibrium for skim milk powder at elevated temperature. Journal of Food Engineering, 51, 291–297. Lomauro, C. J., Bakshi, A. S., & Labuza, T. P. (1985). Evaluation of food moisture sorption isotherm equations, Part II: milk, coffee, tea, nut, oilseeds, spices and starchy foods. Lebensmittel-Wissenschaft and Technologie, 18, 118–124. Maroulis, Z. B., Tasmi, E., & Marinos-Kouris, D. (1988). Application of the GAB model to the moisture sorption isotherms for dried fruits. Journal of Food Engineering, 7, 63–78. Nicholas, J. V., & White, D. R. (1982). Traceable temperatures: an introductory guide to temperature measurement and calibration (pp. 77–96). DSIR Science Information Division, Wellington, New Zealand. Nollet, L. M. L. (1996). Handbook of food analysis (Vol. 1, pp. 71–72). New York: Marcel Dekker, Inc. Papadakis, S. E., Bahu, R. E., McKenzie, K. A., & Kemp, I. C. (1993). Correlations for the equilibrium moisture content of solids. Drying Technology, 11, 543–553. Pisecky, J. (1992). Water activity of milk powders. Milchwissenschaft, 47, 1–68. Rahman, S. (1995). Food properties handbook (pp. 46–47). New York: CRC Press. Tasmi, E., Marinos-Kouris, D., & Maroulis, Z. B. (1990). Water sorption isotherms of raisins, currants, figs, prunes, and apricots. Journal of Food Science, 55, 1594–1597. Warburton, S., & Pixton, S. W. (1978). The moisture relations of spray dried skimmed milk. Journal of Stored Products Research, 1, 43–58.
Desorption isotherm of milk powders at elevated temperatures and over a wide range of relative humidity Sean X.Q. Lin a, Xiao Dong Chen a
a,*
, David L. Pearce
b
Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand b Fonterra Research Centre, Private Bag 11-029, Palmerston North, New Zealand Received 18 November 2003; accepted 31 May 2004
Abstract In this paper, a detailed account of the measurement and analysis of equilibrium isotherm data, obtained using a specialized device built for the purposes of large temperature and humidity ranges, is provided. The measurements were for the desorption isotherms of milk powder (skim milk powder and whole milk powder) for which data have not been available for the range that is relevant to spray drying conditions. The experimental approach allowed us to avoid the problem associated with amorphous lactose, which is known to undergo a glass transition if the equilibration process takes too long. The data points were adequately fitted using the GAB model, in terms of both the moisture content and the temperature dependence. These results will be widely used in spray drying simulations or spray drier designs for dairy powder production. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherms; Correlations; Spray drying of milk
1. Introduction In the simulation of the drying of a single droplet of milk, the equilibrium vapour pressure of the milk is very important because it determines the mass transfer driving force. However, most milk powder sorption isotherms have been measured at around ambient temperature (Berlin, Anderson, & Pallansch, 1968; Heldman, Hall, & Hedrick, 1965; Warburton & Pixton, 1978). There have been very few reports for the temperature range 60–90 °C at relative humidities of up to 40% (Kockel, Allen, Hennigs, & Langrish, 2002; Pisecky, 1992). The exhaust air from a commercial spray drier falls into this temperature and humidity range. For isotherm measurements, samples can reach equilibrium with the moisture contained in the air by either a *
Corresponding author. Tel.: +64 9 373 5799x87004; fax: +64 9 373 7463. E-mail address: [email protected] (X.D. Chen). 0260-8774/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.05.036
dynamic method (Kockel et al., 2002; Papadakis, Bahu, McKenzie, & Kemp, 1993) or a static method (Heldman et al., 1965; Warburton & Pixton, 1978). In the dynamic method, the temperature and the humidity of the air are accurately controlled and air is continuously passed through the sample. In order to let the sample reach equilibrium with the air in a relatively short time (within 3 h) the sample must have the largest surface area possible when exposed to the humid air. One method used in previous research, to obtain the largest surface area possible, was to use a stirred fluidized bed (Kockel et al., 2002). Another method allowed humid air to pass through a cartridge that held the sample (Papadakis et al., 1993). With the dynamic method, the time to reach equilibrium was largely reduced to several hours (Kockel et al., 2002). In contrast, the static method leaves the sample in an environment in which the temperature and the humidity are controlled. Unlike the dynamic method, the air in this environment is static. Because the sample is a thick layer of powder with a
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comparatively small surface area, air cannot easily pass through the sample; hence the time to reach equilibrium may be as long as several weeks (Bell & Labuza, 2000). Lactose in milk powders presents special problems in sorption measurements. It can be either amorphous or crystalline. Amorphous lactose in milk powder holds more water than crystalline lactose. During the sorption experiment, particularly using the static method, crystallization of the amorphous lactose occurs in the milk powder sample. This phenomenon is well known (Berlin et al., 1968; Jouppila & Roos, 1994). Berlin et al. (1968) used an electronic recording microbalance to record gravimetric changes in a precise absorption and desorption experiment on the dehydration dairy products. A maximum in the sorption measurement was found at around a water activity of 0.5. This was attributed to the occurrence of morphology changes. Jouppila and Roos (1994) confirmed the phenomenon of the crystallization of lactose during a sorption experiment. In their study, the effect of lactose hydrolysis on water sorption and the effect of milk fat on lactose crystallization were investigated. Most isotherm measurement experiments are brought to equilibrium using the static method. As crystallization of lactose had to be avoided during the measurements, the static method was unsuitable espe-
cially at humidities above 50% RH. Hence the dynamic method was adopted. There are many models to fit the moisture isotherm of food products. In some models, such as the SPS (Papadakis et al., 1993), Keey (1992) and Henderson (1952) models, the temperature dependence is directly expressed in the equations. Other models, such as the BET and GAB models, do not include the temperature dependence relationship directly, but this relationship is reflected in the modelÕs coefficients, which are temperature dependent. As part of milk droplet drying studies, the drying conditions at high humidities were required. To model the droplet drying, a wider range of desorption isotherms was needed. In this research, the desorption isotherms of skim milk powder and whole milk powder were measured at elevated temperatures of 53–90 °C at up to 100% relative humidity (RH) by a dynamic technique. The results were fitted using some of the available models.
2. Experimental procedure and materials A schematic diagram of the experimental set-up is shown in Fig. 1. The sample (milk solution) was coated
Fig. 1. Schematic diagrams of the measurement system. (a) Moisture isotherm measurement set-up. 1––fan and heater; 2––drying chamber; 3––milk carrier; 4––Teflon sheet; 5––humid air outlet. (b) The metal shim tray (milk carrier) for holding the liquid samples.
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on to a milk carrier. The air from the humidity generator, where both temperature and humidity were controlled, was passed through the milk carrier at a flow rate of 20–30 standard litres per minute. The milk carrier was contained in a drying chamber and set on top of a mass balance, which measured the weight change of the sample. In this method, a thin layer of milk solution (about 0.07 mm after being totally dried) was coated on to a milk carrier (see Fig. 1(b)). The method used for coating the milk carrier was as follows. A stainless steel shim carrier was immersed in a milk solution of 25 wt%. The milk solution was reconstituted from commercially available milk powder and water. The coated carrier was then pre-dried in a hot air stream for several minutes. The above procedures were repeated several times to obtain thicker milk films. The pre-drying enabled the milk solution to adhere to the stainless steel shim and prevented the milk solution from running to the bottom of the carrier. The moisture content of the coated milk solution after pre-drying was about 0.2–0.4 kg/kg (solids basis) higher than the equilibrium moisture content. Pre-drying maintained a thin and even coating on the shim, thus reducing the time to reach equilibrium significantly. The pre-drying time was up to some 30 s, the air temperature used was 70 °C and the air velocity was 5 m s1. The size of the stainless steel shim (see Fig. 1(b)) was 21 mm by 30 mm and nine shims were set in parallel. Air (from the humidity generator) was passed through these shims at a speed of approximately 1 m s1. Because of the large heat and mass transfer area and the thin layer of the coating, the milk solution was able to reach equilibrium within 50 min. Fig. 2 shows a typical drying process of the sample during isotherm measurement. The coated milk carrier was placed in a drying chamber, which was installed inside a temperature-
0.66
Sample weight (g)
0.65 0.64 0.63 0.62 0.61 0.60 0
10
20
30
40
50
60
Drying time (min)
Fig. 2. Typical drying process of the sample during isotherm measurement (skim milk powder desorption, 69.5 °C, 72.8% RH).
259
controlled environment chamber. The temperature of this chamber was set at the same temperature as the drying chamber. Air from the humidity generator was introduced into the drying chamber and then passed through the milk carrier. The outlet for the humid air from the drying chamber was a 6 mm hole covered by a metal sheet, with enough room between the two to allow the air to flow out. This method ensured that the pressure of the drying chamber was just above ambient pressure and minimized the effect of the humidity from the environment on the drying chamber. Two thermocouples were placed approximately 5 mm from the milk carrier. One was used to control the temperature of the humidity generator and the other was used for temperature measurement of the drying chamber (i.e. equilibrium temperature of the desorption isotherm). The thermocouple used to measure the equilibrium temperature of the sample was calibrated with an accuracy of ±0.1 °C. The calibration method followed the approach taken by Nicholas and White (1982). The maximum temperature fluctuation of the drying chamber, where the milk powder was brought to equilibrium, was less than 0.1 °C. The weight change of the milk carrier (i.e. the sample flow) was measured using a balance with a repeatability of 0.001 g. During weighing, the drying air flow was cut off for 5 s; it was assumed that the humidity inside the drying chamber did not change because the outlet of the drying chamber was doubly separated from the environment. The interval between weighings was from 3 to 10 min. When a constant sample weight had been attained for at least 10 min, it was assumed that equilibrium had been reached (most samples had an equilibrium time of 20 min). To determine the dry solids content of the milk samples after desorption isotherm experiments, the samples were dried at 102 ± 2 °C for 3 h. The drying temperature and time which were used here are recommended by the Association of Official Analytical Chemists (Nollet, 1996). The area of the experimental set-up that supported the carrier and that was exposed to the humid air was designed to a minimum and was made with Teflon to minimize moisture sorption, which may have affected the final sample weights. Moisture sorption on the experimental set-up was carefully calibrated and excluded from the calculations. For the isotherm measurements in this study, the accuracy of the relative humidity was better than 1.5% RH and the repeatability was better than 0.3% RH. The accuracy of the moisture content measurement was better than 0.005 kg/kg. The desorption studies were conducted on spraydried skim and whole milk powders, with the gross compositions listed in Table 1.
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Table 1 Composition (wt%) of the skim and whole milk powders before reconstitution in water Skim milk powder
Whole milk powder
Fat Total protein Lactose Mineral Moisture
0.6 36.5 49.8 9.3 3.8
26.5 28.0 36.8 5.9 2.8
3. Results and discussion Fig. 3 shows a moisture desorption isotherm of skim milk powder at 69.4 °C. It shows the typical trend for foods containing sugar, with the equilibrium moisture content increasing sharply at high water activities, caused by the dissolution of lactose. The results of this study were compared with the reported values of Kockel et al. (2002) which were adjusted because the final drying condition (to determine the solids weight) of the reported values was 85 °C instead of 102 °C (International Dairy Federation, 1993). As suggested by Kockel et al. (2002), the moisture contents of their reported values were multiplied by a factor of 1.17 so that they could be compared with moisture contents measured in this study. The average difference between the reported values and the results of this study was 0.004 kg/kg. This difference was within the range of accuracy for this study. The closeness between the reported values of Kockel et al. (2002) and the results of this study is demonstrated in Fig. 4. After the experiments, all the samples were examined using scanning electron microscopy. Fig. 5 shows that the samples had a smooth surface rather than a rough surface covered in crystals or even tomahawk-shaped crystals as observed by Warburton and Pixton (1978). This suggested that crystallization of lactose did not take place.
1.4
Moisture content (kg/kg)
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 3. Moisture desorption isotherm for skim milk powder at 69.4 °C.
Moisture content (kg/kg)
Component
0.08
0.06
0.04
0.02 Exp. data(current) Exp. data Kockel et al. 0.00 0.0
0.1
0.2
0.3
0.4
Water activity (-)
Fig. 4. Comparison of measured data (current) with reported data (Kockel et al., 2002).
Fig. 5. Scanning electron micrograph of skim milk powder after the experiment (69.4 °C, aw = 0.63).
The desorption isotherm of skim milk powder was also measured at 52.6 and 89.6 °C. Fig. 6 shows the desorption isotherms of skim milk at 52.6, 69.4 and 89.6 °C. The isotherms showed a clear temperature dependence. However, the relationship was different at high and low humidities, divided by an inversion point. Below the inversion point, an increase in temperature resulted in a decrease in the equilibrium moisture content, which is widely accepted for the effect of temperature on the isotherm. Above the inversion point, the equilibrium moisture content increased with an increase in temperature for the same water activity. This phenomenon has been reported previously for food containing sugar (Maroulis, Tasmi, & Marinos-Kouris, 1988; Rahman, 1995; Tasmi, Marinos-Kouris, & Maroulis, 1990). The shift in water activity caused by temperature changes was explained as being mainly due to the change in water binding, the dissociation of water or the increase in solubility of a solute in water (Rahman, 1995). For the
S.X.Q. Lin et al. / Journal of Food Engineering 68 (2005) 257–264 1.0
1.4
52.6°C
52.6°C
1.2
69.6°C
69.4°C
0.8
89.6°C
Moisture content (kg/kg)
Moisture content (kg/kg)
261
1.0 0.8 0.6 0.4
89.5°C
0.6
0.4
0.2
0.2 0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Water activity (-)
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 6. Moisture desorption isotherms for skim milk powder at different temperatures.
Fig. 8. Moisture desorption isotherms for whole milk powder at different temperatures.
milk powder desorption isotherms at higher moisture contents, the increase in the solubility of lactose, caused by an increase in temperature, was the major influencing factor. This resulted in the equilibrium moisture content increasing with an increase in temperature. In this study, there was no clear inversion point because of measurement error and because of a large interval between the two measurement points. The inversion point ranged from a water activity of 0.3 to a water activity of 0.43. Fig. 7 shows the inversion points of the desorption isotherms for skim milk powder in the temperature range 53–90 °C. Fig. 8 shows the desorption isotherms of whole milk powder at different temperatures. Comparison of Figs. 6 and 8 showed that the whole milk powder had a lower equilibrium moisture content than skim milk powder at the same water activity. This may have been because the fat that is contained in whole milk powder is not
considered to be a water-absorbing component. When the moisture content was calculated on a non-fat basis, the desorption isotherms of skim milk powder and whole milk powder were essentially identical. As shown in Fig. 9, the moisture desorption isotherms for skim milk powder and whole milk powder based on non-fat solids at a temperature of around 70 °C were almost identical, which was also observed by Berlin et al. (1968) and Jouppila and Roos (1994) . The difference between the two isotherms was within the uncertainty of the moisture content measurement when the water activity was less than 0.80. The less close agreement above a water activity of 0.80 may have resulted from the uncertainty in the water activity measurement (i.e. in this range, the uncertainty of the water activity measurement was about 0.015). The desorption isotherms of skim milk powder and whole milk powder were essentially identical at temperatures of 53 and 90 °C when the
1.4 Moisture content on non-fat basis (kg/kg)
Moisture content (kg/kg)
0.2
0.1
52.6°C 69.4°C 89.6°C
0.0 0.0
Skim milk, 69.4°C
1.2
Whole milk, 69.6°C
1.0 0.8 0.6 0.4 0.2 0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 7. The inversion points (or range) of the moisture desorption isotherms for skim milk powder at different temperatures.
0.0
0.2
0.4
0.6
0.8
1.0
Water activity (-)
Fig. 9. Moisture desorption isotherms for skim milk powder and whole milk powder based on non-fat solids.
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1993), Keey (1992), Henderson (1952) and other models, which incorporate the temperature dependence directly. Least squares curve fitting (automated curve fitting software: TableCurve2D) was used. However, these fits were not successful because the temperature dependence of the experimental data was different in the different water activity ranges, divided by the inversion point. In contrast, the GAB and BET equations for n-layers (Do, 1998) fitted these data very well. The GAB equation for curve fitting has the following form:
Moisture content (kg/kg)
0.2
0.1
52.6°C 69.6°C
X eq ¼
89.5°C
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Ckm0 aw ð1 kaw Þð1 kaw þ Ckaw Þ
ð1Þ
where Xeq is the equilibrium moisture content, aw is the water activity, m0 is the monolayer moisture content and C and k are constants related to the temperature. DH 1 C ¼ C 0 exp ð2Þ RT DH 2 k ¼ k 0 exp ð3Þ RT
Water activity (-)
Fig. 10. The inversion points (or range) of the moisture desorption isotherms for whole milk powders at different temperatures.
moisture content was calculated on a non-fat basis (data not shown). Similar to skim milk powder, the desorption isotherm for whole milk powder had an inversion point. Fig. 10 shows the details of the desorption isotherms at a range of water activities. The inversion point ranged from a water activity of 0.28 to a water activity of 0.40. The measured data for skim milk powder and whole milk powder were fitted using SPS (Papadakis et al.,
where T is the absolute temperature, R is the gas constant and DH1 and DH2 are heats of sorption of water. Tables 2–5 list the GAB constants of skim milk powder and whole milk powder at different temperatures.
Table 2 GAB constants by direct regression of skim milk powder Temperature (°C)
52.6 69.4 89.6
GAB constants
Fit standard error
(kg/kg) m0
C
k
0.06245 0.06067 0.06887
10.42 15.72 4.04
0.873 0.937 1.047
(kg/kg) m0
C
k
0.04290 0.04264 0.04049
8.78 13.07 5.24
0.909 0.956 1.106
0.005 0.02 0.002
Table 3 GAB constants by direct regression for whole milk powder Temperature (°C)
52.6 69.6 89.5
GAB constants
Fit standard error
0.003 0.01 0.0006
Table 4 GAB constants by indirect regression for skim milk powder Temperature (°C)
GAB constants
Fit standard error
(kg/kg) m0
C
k
52.6 69.4 89.6
0.06156 0.06156 0.06156
15.83 10.01 6.207
0.866 0.940 1.050
0.007 0.02 0.005
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Table 5 GAB constants by indirect regression for whole milk powder Temperature (°C)
GAB constants (kg/kg) m0
C
k
52.6 69.6 89.5
0.04277 0.04277 0.04277
9.20 7.70 6.20
0.904 0.956 1.020
The direct regression constants were estimated from a group of experimental data that had the same absorption temperature. Based on the direct regression, monolayer moisture contents were obtained at different temperatures. Then the average of the monolayer moisture contents was taken (the constant at 90 °C was not used, because the experimental data had only limited points of water activity up to 0.50). In the indirect regression, the average monolayer moisture content obtained from the direct regression was used and then the constants C and k of the GAB equation were again estimated from the regression. From Tables 2–5, the fit standard errors of the indirect regressions had no significant increase compared with those of the direct regressions. The indirect regressions also resulted in constant values for the monolayer moisture contents of the skim milk powder and whole milk powder, which were 0.06156 and 0.04277 kg/kg respectively. The reported monolayer moisture content values of skim milk powder are 0.0425 kg/kg (absorption at 26 °C) (Lomauro, Bakshi, & Labuza, 1985) and 0.051 kg/kg (absorption at 24 °C) (Jouppila & Roos, 1994). Because the values in this study were obtained from desorption experiments, the monolayer moisture contents obtained were reasonable. The values of C (indirect regression) for skim milk powder and whole milk powder decreased when the temperature was increased and were related to the temperature according to Eq. (2) (DH1 = 24,831 J/mol, C0 = 0.001645, R2 = 0.9999 for skim milk powder and D H1 = 10,485 J/mol, C0 = 0.1925, R2 = 0.998 for whole milk powder). The values of k (indirect regression) increased with an increase in temperature and were related to the temperature according to Eq. (3) (DH2 = 5118 J/ mol, k0 = 5.710, R2 = 0.996 for skim milk powder and DH2 = 3215 J/mol, k0 = 2.960, R2 = 0.999 for whole milk powder). The predictions of the GAB model showed good agreement with the experimental data (not shown graphically here). The average differences between the measured data and the model predictions for water activities up to 0.95 were 5.4% and 3.6% for skim milk powder and whole milk powder respectively. The original experimental values of the equilibrium moisture contents of skim milk powder and whole milk powder are listed in Appendices A and B.
Fit standard error
0.007 0.01 0.003
4. Conclusions A new dynamic isotherm measurement method was developed. This method largely reduces the equilibrium time, which is the key to obtaining the isotherms for food materials with crystallizable components. Using this method, data on the desorption isotherms of skim milk powder and whole milk powder at elevated temperatures (up to 90 °C) and high humidities (up to 100% RH) were obtained. The desorption behaviours at three temperatures (53, 70 and 90 °C) showed that there was a temperature dependence. Various formulae for the equilibrium moisture content were used in an attempt to fit the experimental data. The GAB model yielded the best fit for water activities of up to 0.95.
Appendix A Temperature (°C)
Water activity
Equilibrium moisture content (kg/kg)
52.6
0.977 0.902 0.798 0.636 0.486 0.326 0.168
0.598 0.288 0.191 0.133 0.103 0.067 0.046
69.4
1.000 0.987 0.932 0.820 0.728 0.632 0.484 0.325 0.166
1.303 0.808 0.449 0.262 0.202 0.158 0.108 0.071 0.045
89.6
0.538 0.430 0.324 0.217 0.111
0.133 0.096 0.069 0.050 0.026
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Appendix B Temperature (°C)
Water activity
Equilibrium moisture content (kg/kg)
52.6
0.965 0.925 0.867 0.775 0.637 0.483 0.324 0.170
0.345 0.267 0.195 0.141 0.092 0.063 0.048 0.034
69.6
0.998 0.953 0.932 0.859 0.795 0.654 0.505 0.324 0.164
0.926 0.462 0.380 0.255 0.185 0.113 0.073 0.051 0.032
0.539 0.381 0.240 0.106
0.089 0.056 0.035 0.019
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