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The prediction of moisture sorption isotherms for dairy powders
ARTICLE IN PRESS
International Dairy Journal 15 (2005) 411–418 www.elsevier.com/locate/idairyj
The prediction of moisture sorption isotherms for dairy powders Kylie D. Fostera,, John E. Bronlundb, A.H.J. (Tony) Patersonb a
Institute of Food, Nutrition and Human Health, Massey University—Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand b Institute of Technology and Engineering, Massey University, Private Bag 11222, Palmerston North, New Zealand Received 7 March 2004; accepted 5 August 2004
Abstract Moisture sorption isotherms were measured for whey protein isolate, high micellar casein and a milk protein concentrate powder. No temperature dependence was observed over the temperature range of 4–37 1C. At 50 1C the powders absorbed less moisture than observed at the lower temperatures. These isotherms were used to predict the isotherms for freeze-dried amorphous lactose/casein/ whey protein powders. An isotherm for micellar casein was predicted using a simple additive isotherm model and was used along with isotherms for whey protein and amorphous lactose to predict moisture sorption isotherms for commercial dairy powders. Predicted isotherms compared well with measured isotherms indicating that this simple additive isotherm model is suitable for predicting moisture sorption isotherms of dairy powders. Delayed lactose crystallisation was observed in lactose/whey protein powders when compared to lactose/casein powders over the same water activity range. r 2004 Elsevier Ltd. All rights reserved. Keywords: Moisture sorption isotherms; Prediction; Dairy powders
1. Introduction Food powders are often prone to sticking and caking problems. Since water is one factor responsible for such problems, moisture sorption isotherms are a useful tool for understanding the moisture relationship of a powder and consequently its stability problems. Moisture sorption isotherms for powders describe the equilibrium relationship between the moisture content of the powder and the relative humidity of the surrounding environment (Labuza, 1968). It is useful to know or be able to predict isotherms for dairy powders as, together with glass transition temperature profiles, they can provide important information about the stability of the powders. Understanding the moisture relationships of a powder allows the moisture content that the powder should be dried to, in order to prevent sticking problems Corresponding author. Tel.: +64-9-414-0800; fax: +64-9-4439640. E-mail address: [email protected] (K.D. Foster).
0958-6946/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.idairyj.2004.08.003
during storage, to be determined. Furthermore, it would be valuable to be able to understand the moisture relationships of a new powder during the product formulation stage. Several methods have been investigated in the literature for predicting isotherms for multicomponent powders. The most common method has used an additive isotherm model. Labuza (1968) suggested that it can be assumed that the amount of water sorbed at any given water activity can be predicted by the weighted addition of the moisture that the components would sorb alone, assuming no interactions between components occur (Eq. (1)). M pðaw Þ ¼
n X
xi M iðaw Þ ;
(1)
i¼1
where M pðaw Þ is the predicted moisture content at a given water activity (g 100 g1 dry solids), xi is the mass fraction of component i (dry basis) and M iðaw Þ is the moisture content of component i at a given water activity (g 100 g1 dry solids).
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This approach has been used to predict isotherms for milk powders (Berlin, Anderson, & Pallansch, 1968), beef products (Palnitkar & Heldman, 1971), a dried milk-orange product (Berlin, Anderson, & Pallansch, 1972), sugar beet root (Iglesias, Chirife, & Lombardi, 1975) and starch gel products (Iglesias, Chirife, & Boquet, 1980). Only in some cases was the agreement considered acceptable (Berlin et al., 1968, 1972; Iglesias et al., 1975). Recently, Bronlund and Paterson (2004) used this approach for predicting the isotherm of a crystalline lactose powder containing 9% amorphous lactose (amorphous lactose content quantified by Hargreaves (1995) using nuclear magnetic resonance). This method predicted the measured isotherm well up to the breakpoint in the isotherm, which was due to amorphous lactose crystallisation. It was suggested that this simple additive isotherm approach could be used for measuring the amorphous lactose content of lactose powders. Iglesias et al. (1980) stated that due to the reproducibility of equilibrium moisture content data of foods using the gravimetric method, a maximum permissible error of 710% is acceptable. It was further stated that where there was an unacceptable difference between the measured and predicted isotherms, the predicted isotherms were usually higher than the measured ones. It was suggested that interactions between components occur which results in a decrease in water sorption. These interactions were stated to probably consist of polymer–polymer hydrogen bonds, which compete with polymer–water hydrogen bonds, decreasing water sorption. Kamin´ski and Al–Bezweni (1994) considered the interactions between components when predicting isotherms by the introduction of an interaction coefficient for each component. While this worked well when predicting the isotherms for binary mixtures, it is unclear how well this method would work for multicomponent powders. It is likely that there would be too many interactions between components for interaction coefficients to be easily quantified in multicomponent powders. For general food powders, the amount of water held at a certain water activity decreases as temperature increases (Labuza, 1968) and has been shown to follow the Clausius–Clapeyron relationship (Bell & Labuza, 2000). With increasing temperature, an increase in water activity at a given moisture content occurs as the bond between the water molecule and the OH group of the food solid breaks. This allows the water to become free, which results in an increase in water activity (Jaya, Sughagar, & Das, 2002). This temperature effect has been seen with casein (Loncin, Bimbenet, & Lenges, 1968), whey protein concentrate (Hermansson, 1977), skim milk powder (Berlin, Anderson, & Pallansch, 1970), non-fat milk powder (Heldman, Hall, & Hedrick,
1965), amorphous sucrose (Iglesias et al., 1975), amorphous glucose (Loncin et al., 1968) and sugar beet root (Iglesias et al., 1975). Bronlund and Paterson (2004) found negligible influence of temperature on the isotherm of amorphous lactose over the temperature range of 20–38 1C and at 12 1C, the isotherm deviated downwards above 0.4 water activity. In some cases, amorphous maltose (Audu, Loncin, & Weisser, 1978) and a-lactose monohydrate (Audu et al., 1978; Bronlund & Paterson, 2004), no temperature effect was observed. The reverse temperature effect has been found to be true for some sugars and foods containing sugars, e.g., crystalline fructose (Audu et al., 1978). With sugars, when the powder is exposed to higher temperatures, the sugar dissolves in the newly formed free water. This results in a decrease in the water activity with an increase in temperature (or an increase in the amount of water held at a given water activity) (Jaya et al., 2002). This work investigates the applicability of the simple additive isotherm model for predicting isotherms for dairy powders, whose main components are lactose, milk fat, whey protein and casein. Since the accuracy of this method is strongly dependent on the accuracy of the isotherms for the components, considerable effort was made to assure the accuracy of the components’ isotherms. The effect of temperature on moisture sorption isotherms was also investigated.
2. Materials and methods 2.1. Powder samples Powders of varying compositions of lactose, whey protein and micellar casein were made in the proportions given in Table 1. Alpha-lactose monohydrate (USP grade, The Lactose Company of New Zealand, Hawera, New Zealand), a high micellar casein powder (HMCP) and a whey protein isolate powder (WPI: both supplied by the New Zealand Dairy Research Institute, Palmerston North, New Zealand and compositions given in Table 2) were used as the lactose, casein and whey Table 1 Composition of lactose, whey protein and micellar casein in freezedried powders Powdera
Amorphous lactose
Whey protein isolate
High micellar casein
L1W1C1 (ib, ii) L1W2b L2W1b L2C1 (i, ii, iii) W2C1
1/3 1/3 2/3 2/3 0
1/3 2/3 1/3 0 2/3
1/3 0 0 1/3 1/3
a
i, ii, iii denotes replicates of a given powder. Denotes 3 weeks as opposed to 2 weeks equilibration time.
b
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Table 2 Composition (% dry mass basis) of dairy powders Powder
Amorphous lactose
Whey protein
Casein
Fat
Othera
Whey protein isolate (WPI) High micellar casein powder (HMCP) Milk protein concentrate (MPC) Low fat cream powder (LFCP) High fat cream powder (HFCP) Skim milk powder (SMP) Dairy base powder (DBP)
0.1 0 1.4 22.9 13.1 50.4 48.0c
98.0 6.3 17.9 3.4b 2.3b 8.0b 3.0b
0 83.7 71.6 13.7b 9.4b 31.8b 11.9b
0.3 1.7 1.8 56.4 72.0 0.8 37.1c
1.6 8.3 7.4 3.6 3.3 9.0 —d
a
May include salts, soy phospholipids and free flow agent (for HFCP only). Estimated from the total protein content (80% casein and 20% whey protein). c Approximately 50% of the fat is coconut oil and the remaining 50% is milk fat. d Amorphous lactose content estimated by subtraction of the protein and fat contents. Salts content was not known and was assumed to be negligible. b
protein components, respectively. The powders were prepared by freeze-drying mixtures of the dissolved components using a freeze dryer (Virtis, Model 10–020, The Virtis Company Inc., Gardiner, New York, USA) which typically operated with a vacuum of 250 mTorr and condenser temperature of 58 1C. Due to solubility problems, micellar casein was dissolved in 0.05–0.1% sodium citrate. It is unknown what effect this would have on the micelles, however, it was thought that this would be minimal due to the low concentration of salt used. Isotherms were measured for these powders along with the isotherms for the WPI and HMCP, to use for prediction purposes. Isotherms were also measured for a milk protein concentrate powder (MPC: supplied by the New Zealand Dairy Research Institute, Palmerston North, New Zealand), low- and high-fat cream powders (LFCP, HFCP), skim milk powder (SMP) and a dairy base powder (DBP: all supplied by the New Zealand Dairy Board, Wellington, New Zealand). The compositions of these powders are given in Table 2.
Table 3 Equilibrium relative humidity (%) conditions for moisture sorption isotherm measurements Saturated salt solutiona
Lithium chloride Potassium acetate Potassium fluoride Magnesium chloride Potassium carbonate Magnesium nitrate Sodium bromide Potassium iodide Sodium chloride Potassium chloride Potassium nitrate a
Relative humidity 4 1C
20 1C
37 1C
50 1C
0.11 0.23 — 0.34 0.43 0.59 0.64 — 0.76 0.88 0.96
0.11 0.23 — 0.33 0.43 0.54 — — — — —
0.11 — 0.24 0.32 0.43 — 0.54 0.67 0.75 0.83 0.90
0.11 — 0.21 0.30 — 0.45 0.51 0.64 0.74 0.81 —
Equilibrium relative humidity values taken from Greenspan (1977).
2.3. Analysis of data 2.2. Isotherm measurement Working isotherms were measured gravimetrically by placing approximately 3 g of the powder samples in constant relative humidity environments for 2–3 weeks (Bell & Labuza, 2000). The resolution of the balance for moisture sorption was 0.1 mg. Constant relative humidity environments were obtained by placing saturated salt solutions in the bottom of desiccators. Table 3 outlines the salts used to provide the relative humidity environments at different temperatures as given by Greenspan (1977). The initial moisture contents of the powders were obtained by placing the powders over phosphorous pentoxide, which gives a relative humidity environment close to 0%, for 2–3 weeks at the desired isotherm temperature. Isotherms were measured at 20 1C for all powders, at 4 and 37 1C for whey powders, casein powders and cream powders and also at 50 1C for whey protein and casein powders.
The Guggenheim–Anderson–deBoer (GAB) equation (Eq. (2)) (van den Berg, 1985) was used to model water sorption. M¼
M o cf aw ; ð1 faw Þ ð1 þ ðc 1Þfaw Þ
(2)
where M is the moisture content (g 100 g1 dry powder), M o is the monolayer moisture content (g 100 g1 dry powder), aw is the water activity and c and f are constants. The GAB model was applied using non-linear regression (CurveExpert 1.3, version 1.38, 2003). The correlation coefficient, R2 ; was calculated to give an indication of the goodness of fit, that is, a measure of the proportion of variability attributed to the model. The standard error of the estimate, S, was calculated to give an indication of the precision of the estimation of the estimate.
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Table 4 GAB isotherm constants for dairy powder components and dairy powders Powder
Temperature (1C)
GAB constants 1
Mo (g 100 g Amorphous lactosea Whey protein isolate (WPI)
dry solids)
f
c
R2
S
12–38 4–37 4 20 37 50 4–37
6.27 8.36 8.63 6.82 8.33 6.56 7.53
1.01 0.77 0.79 0.94 0.75 0.84 0.74
2.81 9.63 8.96 13.25 9.58 7.63 10.12
0.9657 0.9828 0.9971 0.9995 0.9948 0.9960 0.9914
0.5459 1.0240 0.5295 0.1190 0.5770 0.4432 0.5670
Milk protein concentrate (MPC)
4 20 37 50 4–37
7.80 7.85 7.20 4.86 8.51
0.75 0.68 0.74 0.86 0.67
9.89 8.36 13.17 10.92 8.78
0.9998 0.9963 0.9976 0.9907 0.9958
0.0953 0.2785 0.3321 0.5310 0.3592
Micellar caseinb
4 20 37 50 4–37
7.28 7.83 7.68 7.01 8.91
0.79 0.75 0.71 0.74 0.69
9.85 9.12 11.47 7.48 9.47
0.9984 0.9996 0.9976 0.9970 0.9855
0.2317 0.0900 0.3274 0.3006 0.7373
High micellar casein powder (HMCP)
a
Constants taken from Brooks (2000). By calculation using the additive method.
3. Results and discussion Isotherms for the WPI, high micellar casein and MPC powders are given in Figs. 1, 3 and 4, respectively, and the constants for the prediction of their isotherms are given in Table 4. The GAB constants for the prediction of the isotherm for amorphous lactose were taken from Brooks (2000) and are included in Table 4. The isotherm data for the WPI powder (Fig. 1) measured at 4, 20, 37 and 50 1C do not show any obvious temperature dependence in the isotherms measured at 4, 20 and 37 1C up to a water activity of about 0.6. The isotherm at 50 1C is significantly lower. The GAB model was fitted to each isotherm and the constants are given in Table 4. From the moisture sorption isotherms at 4, 20, 37 and 50 1C, the water activity at a given moisture content was obtained and is presented in Fig. 2. Fig 2 illustrates the lack of temperature dependence over the temperature range of 4–37 1C. It also shows that the effect of temperature is greatest, when comparing data at 50 1C with 4, 20 and 37 1C, at lower to intermediate water activities. Due to the lack of temperature dependence from 4 to 37 1C, the GAB isotherm model was also fitted to the complete data obtained at 4, 20 and 37 1C (R2 ¼ 0:9828; S ¼ 1:0240) and the GAB constants are given in Table 4. This gives a good approximation of the isotherm for whey protein over the temperature range of 4–37 1C, up to a water activity of around 0.6. The isotherm data for the HMCP measured at 4, 20, 37 and 50 1C given in Fig. 3 show similar temperature
Moisture content (g 100 g-1 dry powder)
b
30
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C) R²=0.9828 S=1.0240
25 20 15 10
R²= 0.9960 S= 0.4432
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Water activity
Fig. 1. Effect of temperature on the moisture sorption isotherm of a WPI powder.
dependence. There is no obvious temperature dependence in the isotherms measured at 4, 20 and 37 1C and the isotherm measured at 50 1C is significantly lower above 0.2aw : The GAB model was fitted to the data measured at 4, 20 and 37 1C, individually and as a combined data set, and to the data measured at 50 1C. The GAB constants, correlation coefficients and standard error of estimates are given in Table 4. The decrease in moisture content at a given water activity with an increase in temperature, as seen with the data obtained for both the WPI and HMCP at 50 1C, is consistent with the observations of Loncin et al. (1968) and Hermansson (1977). MPC powder (Fig. 4) also shows similar temperature dependence. There is no
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0 Moisture content 20 g 100 g-1 15 g 100 g-1
-0.5
12 g 100 g-1 -1
10 g 100 g
ln(aw)
-1
8 g 100 g
-1
-1.5
-2
5 g 100 g
-2.5 0.003
0.0031
0.0032
0.0033
0.0034
0.0035
0.0036
-1
0.0037
1/T (K-1)
Moisture content (g 100 g-1 dry powder)
Fig. 2. Sorption isosteres of a WPI powder.
25
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C)
20 15
R2=0.9914 S=0.5670
10
R2=0.9907 S=0.5310
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Moisture content (g 100 g-1 dry powder)
Fig. 3. Effect of temperature on the moisture sorption isotherm of a HMCP.
25
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C)
20 15
R2=0.9958 S=0.3592
10 R2=0.9970 S=0.3006
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 4. Effect of temperature on the moisture sorption isotherm of a MPC powder.
apparent difference in the isotherms measured from 4–37 1C. The isotherm measured at 50 1C is slightly lower although this is not as obvious as it is for the WPI and HMCP. The GAB isotherm model was fitted to the
data measured at 4, 20 and 37 1C, individually and as a combined data set, and to the data measured at 50 1C and the constants are given in Table 4. The relationship between temperature and water activity, at a given moisture content, for high micellar casein and MPC powders was similar to that seen in Fig. 2 for the WPI powder. Using the isotherms for the HMCP and MPC powder measured at 4, 20 and 37 1C, along with their compositions given in Table 2, the isotherms for amorphous lactose and whey protein were subtracted (using Eq. (1)) to give an approximation of the isotherm for micellar casein. This was done to see whether the use of Eq. (1) could give an isotherm for micellar casein which was similar to the isotherm data given in literature (Berlin et al., 1968; Ru¨egg, Blanc, & Lu¨scher, 1979; Linko, Pollari, Harju, & Heikonen, 1981; Bandyopadhyay, Das, & Sharma, 1987). The effect of the fat was considered negligible since it was only present in very small amounts, i.e., no greater than 1.8%. The resulting isotherm data for micellar casein are given in Fig. 5 where it can be seen that there is very good agreement between predicted isotherm data for micellar casein and the literature data. The GAB isotherm model was fitted to the data (excluding the literature data) up to 0.86aw (R2 ¼ 0:9855; S ¼ 0:7373) and the resulting GAB coefficients are given in Table 4. The effect of milk fat on isotherm prediction can be investigated by examining the isotherms for the two powders containing high proportions of milk fat. The isotherms for a LFCP and HFCP, measured at 4, 20 and 37 1C, are given in Fig. 6. No obvious temperature dependence was observed for these powders. The isotherms for these powders were also predicted using the GAB isotherm models (Table 4) for amorphous
ARTICLE IN PRESS Moisture content (g 100 g-1 dry powder)
45
Berlin et al. 1968 Ruegg et al. 1979 Linko et al. 1981 Bandyopadhyay et al. 1987 MPC HMC GAB model
40 35 30 25
R2=0.9855 S=0.7373
20 15 10 5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Moisture content (g 100 g-1 dry powder)
Fig. 5. Comparison of the moisture sorption isotherm for micellar casein, predicted from the isotherms of a HMCP and a MPC, with literature data.
10 HFCP 4°C HFCP 20°C HFCP 37°C HFCP Predicted LFCP 4°C LFCP 20°C LFCP 37°C LFCP Predicted
9 8 7 6 5 4 3 2 1
Lactose Crystallisation
0 0
0.1
0.2
0.3
0.4 0.5 0.6 Water activity
0.7
0.8
0.9
1
Fig. 6. Prediction of the moisture sorption isotherms for a 56% fat cream powder (LFCP) and a 72% fat cream powder (HFCP).
lactose, WPI and micellar casein. It can be seen that there is a good agreement between measured and predicted isotherms, until the breakpoint, indicating that the milk fat does not have a significant effect on the isotherms for the powders even when it is present in a large amount (e.g., 56% and 72%). The breakpoint in the measured isotherms is due to amorphous lactose crystallisation (Berlin et al., 1968). It is noted that since only the percentage of total protein was known, the isotherms for whey protein and casein were added as a mass fraction of 0.2 and 0.8, respectively, as this is the proportion that the two proteins are present in milk. Isotherms for freeze-dried lactose/whey protein and lactose/casein powders are shown in Fig. 7. The isotherms were predicted from the isotherms of amorphous lactose, WPI and the isotherm for the HMCP. There is good agreement between the measured and predicted isotherms until the point where amorphous lactose crystallisation occurs. This can be seen for water activities above 0.43, where there is a drop in the measured moisture content. The drop in moisture content was not observed for mixed whey protein and amorphous lactose powders at 0.43aw, as it was for
Moisture content (g 100 g-1 dry powder)
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12
L2C1i L2C1ii L2C1iii L2C1 Predicted L2W1 L2W1 Predicted
10 8 6 4 2
outlier 0 0
0.1
0.2
0.3 0.4 Water activity
0.5
0.6
Fig. 7. Moisture sorption isotherms showing the presence of amorphous lactose crystallisation during equilibration.
mixed casein and amorphous lactose powders. It appears that whey protein may hinder the crystallisation of amorphous lactose. Delayed crystallisation has also been noted by Berlin et al. (1968) in isotherms for milk and whey powders. Amorphous lactose crystallisation occurred at higher water activities, which was attributed to a lowered concentration of lactose at the surface of the milk powder particles, with the initial sorption site being some component other than lactose (Berlin et al., 1968). It has also been noted that there is an overrepresentation of protein at the surface of mixed protein and lactose powders (Fa¨ldt & Bergensta˚hl, 1996). The proportion of protein relative to the other powder constituents is greater on the surfaces of the particles than in the powder in bulk. Referring to Fig. 7, the powder containing whey protein (L2W1) was equilibrated for 3 weeks and the powder containing casein (L2C1i, ii, iii) was equilibrated for 2 weeks. If the protein component did not affect amorphous lactose crystallisation, then it would be expected that the isotherms for both powders would show similar drops in moisture content above 0.43aw, since the lactose contents are similar. This was not the case, even when the powder containing the whey protein (L2W1) was equilibrated for longer, i.e., giving more time for lactose crystallisation to occur. This indicates that whey protein affects/delays the crystallisation of amorphous lactose. The implication of this is that it will require higher water activities to result in amorphous lactose crystallisation at a given temperature and period of time, when whey protein is present. This result may also indicate that interactions were established between whey protein and lactose but not between casein and lactose. Jouppila and Roos (1994) also observed delayed crystallisation in milk powders compared to pure lactose powder; milk fat was found to decrease the rate of lactose crystallisation. Fig. 8 shows an overall comparison between the measured and predicted moisture contents for the
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12 L1W1M1a L1W1M1b L1W2 L2W1 L2M1a L2M1b L2M1c W2M1 SMP DBP Keir (2001)
10 8 6 4
upper 15%
best fit lower 10%
2 0 0
2
4
6
8
10
12
Measured moisture content (g 100 g-1 dry powder) Fig. 8. Comparison of measured and predicted isotherms for freeze-dried lactose, whey protein, casein mixture powders, SMP, a DBP and a variety of dairy powders measured by Keir (2001).
powder mixtures detailed in Table 1, SMP and a DBP. Included are isotherm data from Keir (2001) for a variety of dairy powders containing only amorphous lactose, dairy protein and milk fat. For clarity, points where lactose crystallisation is likely to have occurred, as indicated by drops in the moisture content, have been omitted from Fig. 8. Relative error limits of 710 and 15% have also been included. It can be seen that there is good agreement between the measured and predicted moisture contents, with the difference mostly being less than 710%. In general, the predicted moisture contents are slightly greater than those measured. This indicates that there may be some interaction which decreases water sorption. As discussed previously, Iglesias et al. (1980) stated that the hydrogen bonding between components is likely to compete with hydrogen bonding between components and water. This would result in a decrease in water sorption. Since most of the data are within the 710% error limits, it can be concluded that the simple additive isotherm approach is acceptable for predicting the isotherms of dairy powders.
4. Conclusions Isotherms for a variety of freeze-dried dairy powders and commercial dairy powders were predicted using a simple additive isotherm model. There was good agreement between the measured and predicted isotherms with the average relative error being around 10%. Considering the errors involved in measuring isotherms gravimetrically, the simple additive isotherm model is a good method for predicting moisture sorption isotherms of dairy powders.
Acknowledgements The authors thank the New Zealand Dairy Board, Wellington, New Zealand for the funding of this work.
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Heldman, D. R., Hall, C. W., & Hedrick, T. I. (1965). Vapor equilibrium relationships of dry milk. Journal of Dairy Science, 48, 845. Hermansson, A. M. (1977). Functional properties of proteins for foods—water vapour sorption. Journal of Food Technology, 12, 177–187. Iglesias, H. A., Chirife, J., & Boquet, R. (1980). Prediction of water sorption isotherms of food models from knowledge of components sorption behaviour. Journal of Food Science, 45, 450–457. Iglesias, H. A., Chirife, J., & Lombardi, J. L. (1975). Comparison of water vapour sorption by sugar beet root components. Journal of Food Technology, 10, 385–391. Jaya, S., Sughagar, M., & Das, H. (2002). Stickiness of food powders and related physico-chemical properties of food components. Journal of Food Science & Technology—Mysore, 39, 1–7. Jouppila, K., & Roos, Y. H. (1994). Water sorption and timedependent phenomena of milk powders. Journal of Dairy Science, 77, 1798–1808. Kamin´ski, W., & Al-Bezweni, A. (1994). Calculation of water sorption isotherms for multicomponent protein-containing mixtures. International Journal of Food Science and Technology, 29, 129–136.
Keir, T. (2001). Milk powder stickiness: a preliminary study. Diploma in Dairy Science and Technology dissertation, New Zealand Dairy Research Institute, Palmerston North, New Zealand. Labuza, T. P. (1968). Sorption phenomena in foods. Food Technology, 22, 263–272. Linko, P., Pollari, T., Harju, M., & Heikonen, M. (1981). Water sorption properties and the effect of moisture on structure of dried milk products. Lebensmittel-Wissenschaft & Technologie, 15, 26–30. Loncin, M., Bimbenet, J. J., & Lenges, L. (1968). Influence of the activity of water on the spoilage of foodstuffs. Journal of Food Technology, 3, 131–142. Palnitkar, M. P., & Heldman, D. R. (1971). Equilibrium moisture characteristics of freeze-dried beef components. Journal of Food Science, 36, 1015–1018. Ru¨egg, M., Blanc, B., & Lu¨scher, M. (1979). Hydration of casein micelles: kinetics and isotherms of water sorption of micellar casein isolated from fresh and heat-treated milk. Journal of Dairy Research, 46, 325–328. van den Berg, C. (1985). Development of BET like models for sorption of water on foods, theory and relevance. In Simatos, D., & Multon, J. L. (Eds.), Properties of water in foods: in relation to quality and stability (pp. 119–131). Dordrecht: Martinus Nijhoff Publishing.
International Dairy Journal 15 (2005) 411–418 www.elsevier.com/locate/idairyj
The prediction of moisture sorption isotherms for dairy powders Kylie D. Fostera,, John E. Bronlundb, A.H.J. (Tony) Patersonb a
Institute of Food, Nutrition and Human Health, Massey University—Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand b Institute of Technology and Engineering, Massey University, Private Bag 11222, Palmerston North, New Zealand Received 7 March 2004; accepted 5 August 2004
Abstract Moisture sorption isotherms were measured for whey protein isolate, high micellar casein and a milk protein concentrate powder. No temperature dependence was observed over the temperature range of 4–37 1C. At 50 1C the powders absorbed less moisture than observed at the lower temperatures. These isotherms were used to predict the isotherms for freeze-dried amorphous lactose/casein/ whey protein powders. An isotherm for micellar casein was predicted using a simple additive isotherm model and was used along with isotherms for whey protein and amorphous lactose to predict moisture sorption isotherms for commercial dairy powders. Predicted isotherms compared well with measured isotherms indicating that this simple additive isotherm model is suitable for predicting moisture sorption isotherms of dairy powders. Delayed lactose crystallisation was observed in lactose/whey protein powders when compared to lactose/casein powders over the same water activity range. r 2004 Elsevier Ltd. All rights reserved. Keywords: Moisture sorption isotherms; Prediction; Dairy powders
1. Introduction Food powders are often prone to sticking and caking problems. Since water is one factor responsible for such problems, moisture sorption isotherms are a useful tool for understanding the moisture relationship of a powder and consequently its stability problems. Moisture sorption isotherms for powders describe the equilibrium relationship between the moisture content of the powder and the relative humidity of the surrounding environment (Labuza, 1968). It is useful to know or be able to predict isotherms for dairy powders as, together with glass transition temperature profiles, they can provide important information about the stability of the powders. Understanding the moisture relationships of a powder allows the moisture content that the powder should be dried to, in order to prevent sticking problems Corresponding author. Tel.: +64-9-414-0800; fax: +64-9-4439640. E-mail address: [email protected] (K.D. Foster).
0958-6946/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.idairyj.2004.08.003
during storage, to be determined. Furthermore, it would be valuable to be able to understand the moisture relationships of a new powder during the product formulation stage. Several methods have been investigated in the literature for predicting isotherms for multicomponent powders. The most common method has used an additive isotherm model. Labuza (1968) suggested that it can be assumed that the amount of water sorbed at any given water activity can be predicted by the weighted addition of the moisture that the components would sorb alone, assuming no interactions between components occur (Eq. (1)). M pðaw Þ ¼
n X
xi M iðaw Þ ;
(1)
i¼1
where M pðaw Þ is the predicted moisture content at a given water activity (g 100 g1 dry solids), xi is the mass fraction of component i (dry basis) and M iðaw Þ is the moisture content of component i at a given water activity (g 100 g1 dry solids).
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This approach has been used to predict isotherms for milk powders (Berlin, Anderson, & Pallansch, 1968), beef products (Palnitkar & Heldman, 1971), a dried milk-orange product (Berlin, Anderson, & Pallansch, 1972), sugar beet root (Iglesias, Chirife, & Lombardi, 1975) and starch gel products (Iglesias, Chirife, & Boquet, 1980). Only in some cases was the agreement considered acceptable (Berlin et al., 1968, 1972; Iglesias et al., 1975). Recently, Bronlund and Paterson (2004) used this approach for predicting the isotherm of a crystalline lactose powder containing 9% amorphous lactose (amorphous lactose content quantified by Hargreaves (1995) using nuclear magnetic resonance). This method predicted the measured isotherm well up to the breakpoint in the isotherm, which was due to amorphous lactose crystallisation. It was suggested that this simple additive isotherm approach could be used for measuring the amorphous lactose content of lactose powders. Iglesias et al. (1980) stated that due to the reproducibility of equilibrium moisture content data of foods using the gravimetric method, a maximum permissible error of 710% is acceptable. It was further stated that where there was an unacceptable difference between the measured and predicted isotherms, the predicted isotherms were usually higher than the measured ones. It was suggested that interactions between components occur which results in a decrease in water sorption. These interactions were stated to probably consist of polymer–polymer hydrogen bonds, which compete with polymer–water hydrogen bonds, decreasing water sorption. Kamin´ski and Al–Bezweni (1994) considered the interactions between components when predicting isotherms by the introduction of an interaction coefficient for each component. While this worked well when predicting the isotherms for binary mixtures, it is unclear how well this method would work for multicomponent powders. It is likely that there would be too many interactions between components for interaction coefficients to be easily quantified in multicomponent powders. For general food powders, the amount of water held at a certain water activity decreases as temperature increases (Labuza, 1968) and has been shown to follow the Clausius–Clapeyron relationship (Bell & Labuza, 2000). With increasing temperature, an increase in water activity at a given moisture content occurs as the bond between the water molecule and the OH group of the food solid breaks. This allows the water to become free, which results in an increase in water activity (Jaya, Sughagar, & Das, 2002). This temperature effect has been seen with casein (Loncin, Bimbenet, & Lenges, 1968), whey protein concentrate (Hermansson, 1977), skim milk powder (Berlin, Anderson, & Pallansch, 1970), non-fat milk powder (Heldman, Hall, & Hedrick,
1965), amorphous sucrose (Iglesias et al., 1975), amorphous glucose (Loncin et al., 1968) and sugar beet root (Iglesias et al., 1975). Bronlund and Paterson (2004) found negligible influence of temperature on the isotherm of amorphous lactose over the temperature range of 20–38 1C and at 12 1C, the isotherm deviated downwards above 0.4 water activity. In some cases, amorphous maltose (Audu, Loncin, & Weisser, 1978) and a-lactose monohydrate (Audu et al., 1978; Bronlund & Paterson, 2004), no temperature effect was observed. The reverse temperature effect has been found to be true for some sugars and foods containing sugars, e.g., crystalline fructose (Audu et al., 1978). With sugars, when the powder is exposed to higher temperatures, the sugar dissolves in the newly formed free water. This results in a decrease in the water activity with an increase in temperature (or an increase in the amount of water held at a given water activity) (Jaya et al., 2002). This work investigates the applicability of the simple additive isotherm model for predicting isotherms for dairy powders, whose main components are lactose, milk fat, whey protein and casein. Since the accuracy of this method is strongly dependent on the accuracy of the isotherms for the components, considerable effort was made to assure the accuracy of the components’ isotherms. The effect of temperature on moisture sorption isotherms was also investigated.
2. Materials and methods 2.1. Powder samples Powders of varying compositions of lactose, whey protein and micellar casein were made in the proportions given in Table 1. Alpha-lactose monohydrate (USP grade, The Lactose Company of New Zealand, Hawera, New Zealand), a high micellar casein powder (HMCP) and a whey protein isolate powder (WPI: both supplied by the New Zealand Dairy Research Institute, Palmerston North, New Zealand and compositions given in Table 2) were used as the lactose, casein and whey Table 1 Composition of lactose, whey protein and micellar casein in freezedried powders Powdera
Amorphous lactose
Whey protein isolate
High micellar casein
L1W1C1 (ib, ii) L1W2b L2W1b L2C1 (i, ii, iii) W2C1
1/3 1/3 2/3 2/3 0
1/3 2/3 1/3 0 2/3
1/3 0 0 1/3 1/3
a
i, ii, iii denotes replicates of a given powder. Denotes 3 weeks as opposed to 2 weeks equilibration time.
b
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Table 2 Composition (% dry mass basis) of dairy powders Powder
Amorphous lactose
Whey protein
Casein
Fat
Othera
Whey protein isolate (WPI) High micellar casein powder (HMCP) Milk protein concentrate (MPC) Low fat cream powder (LFCP) High fat cream powder (HFCP) Skim milk powder (SMP) Dairy base powder (DBP)
0.1 0 1.4 22.9 13.1 50.4 48.0c
98.0 6.3 17.9 3.4b 2.3b 8.0b 3.0b
0 83.7 71.6 13.7b 9.4b 31.8b 11.9b
0.3 1.7 1.8 56.4 72.0 0.8 37.1c
1.6 8.3 7.4 3.6 3.3 9.0 —d
a
May include salts, soy phospholipids and free flow agent (for HFCP only). Estimated from the total protein content (80% casein and 20% whey protein). c Approximately 50% of the fat is coconut oil and the remaining 50% is milk fat. d Amorphous lactose content estimated by subtraction of the protein and fat contents. Salts content was not known and was assumed to be negligible. b
protein components, respectively. The powders were prepared by freeze-drying mixtures of the dissolved components using a freeze dryer (Virtis, Model 10–020, The Virtis Company Inc., Gardiner, New York, USA) which typically operated with a vacuum of 250 mTorr and condenser temperature of 58 1C. Due to solubility problems, micellar casein was dissolved in 0.05–0.1% sodium citrate. It is unknown what effect this would have on the micelles, however, it was thought that this would be minimal due to the low concentration of salt used. Isotherms were measured for these powders along with the isotherms for the WPI and HMCP, to use for prediction purposes. Isotherms were also measured for a milk protein concentrate powder (MPC: supplied by the New Zealand Dairy Research Institute, Palmerston North, New Zealand), low- and high-fat cream powders (LFCP, HFCP), skim milk powder (SMP) and a dairy base powder (DBP: all supplied by the New Zealand Dairy Board, Wellington, New Zealand). The compositions of these powders are given in Table 2.
Table 3 Equilibrium relative humidity (%) conditions for moisture sorption isotherm measurements Saturated salt solutiona
Lithium chloride Potassium acetate Potassium fluoride Magnesium chloride Potassium carbonate Magnesium nitrate Sodium bromide Potassium iodide Sodium chloride Potassium chloride Potassium nitrate a
Relative humidity 4 1C
20 1C
37 1C
50 1C
0.11 0.23 — 0.34 0.43 0.59 0.64 — 0.76 0.88 0.96
0.11 0.23 — 0.33 0.43 0.54 — — — — —
0.11 — 0.24 0.32 0.43 — 0.54 0.67 0.75 0.83 0.90
0.11 — 0.21 0.30 — 0.45 0.51 0.64 0.74 0.81 —
Equilibrium relative humidity values taken from Greenspan (1977).
2.3. Analysis of data 2.2. Isotherm measurement Working isotherms were measured gravimetrically by placing approximately 3 g of the powder samples in constant relative humidity environments for 2–3 weeks (Bell & Labuza, 2000). The resolution of the balance for moisture sorption was 0.1 mg. Constant relative humidity environments were obtained by placing saturated salt solutions in the bottom of desiccators. Table 3 outlines the salts used to provide the relative humidity environments at different temperatures as given by Greenspan (1977). The initial moisture contents of the powders were obtained by placing the powders over phosphorous pentoxide, which gives a relative humidity environment close to 0%, for 2–3 weeks at the desired isotherm temperature. Isotherms were measured at 20 1C for all powders, at 4 and 37 1C for whey powders, casein powders and cream powders and also at 50 1C for whey protein and casein powders.
The Guggenheim–Anderson–deBoer (GAB) equation (Eq. (2)) (van den Berg, 1985) was used to model water sorption. M¼
M o cf aw ; ð1 faw Þ ð1 þ ðc 1Þfaw Þ
(2)
where M is the moisture content (g 100 g1 dry powder), M o is the monolayer moisture content (g 100 g1 dry powder), aw is the water activity and c and f are constants. The GAB model was applied using non-linear regression (CurveExpert 1.3, version 1.38, 2003). The correlation coefficient, R2 ; was calculated to give an indication of the goodness of fit, that is, a measure of the proportion of variability attributed to the model. The standard error of the estimate, S, was calculated to give an indication of the precision of the estimation of the estimate.
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Table 4 GAB isotherm constants for dairy powder components and dairy powders Powder
Temperature (1C)
GAB constants 1
Mo (g 100 g Amorphous lactosea Whey protein isolate (WPI)
dry solids)
f
c
R2
S
12–38 4–37 4 20 37 50 4–37
6.27 8.36 8.63 6.82 8.33 6.56 7.53
1.01 0.77 0.79 0.94 0.75 0.84 0.74
2.81 9.63 8.96 13.25 9.58 7.63 10.12
0.9657 0.9828 0.9971 0.9995 0.9948 0.9960 0.9914
0.5459 1.0240 0.5295 0.1190 0.5770 0.4432 0.5670
Milk protein concentrate (MPC)
4 20 37 50 4–37
7.80 7.85 7.20 4.86 8.51
0.75 0.68 0.74 0.86 0.67
9.89 8.36 13.17 10.92 8.78
0.9998 0.9963 0.9976 0.9907 0.9958
0.0953 0.2785 0.3321 0.5310 0.3592
Micellar caseinb
4 20 37 50 4–37
7.28 7.83 7.68 7.01 8.91
0.79 0.75 0.71 0.74 0.69
9.85 9.12 11.47 7.48 9.47
0.9984 0.9996 0.9976 0.9970 0.9855
0.2317 0.0900 0.3274 0.3006 0.7373
High micellar casein powder (HMCP)
a
Constants taken from Brooks (2000). By calculation using the additive method.
3. Results and discussion Isotherms for the WPI, high micellar casein and MPC powders are given in Figs. 1, 3 and 4, respectively, and the constants for the prediction of their isotherms are given in Table 4. The GAB constants for the prediction of the isotherm for amorphous lactose were taken from Brooks (2000) and are included in Table 4. The isotherm data for the WPI powder (Fig. 1) measured at 4, 20, 37 and 50 1C do not show any obvious temperature dependence in the isotherms measured at 4, 20 and 37 1C up to a water activity of about 0.6. The isotherm at 50 1C is significantly lower. The GAB model was fitted to each isotherm and the constants are given in Table 4. From the moisture sorption isotherms at 4, 20, 37 and 50 1C, the water activity at a given moisture content was obtained and is presented in Fig. 2. Fig 2 illustrates the lack of temperature dependence over the temperature range of 4–37 1C. It also shows that the effect of temperature is greatest, when comparing data at 50 1C with 4, 20 and 37 1C, at lower to intermediate water activities. Due to the lack of temperature dependence from 4 to 37 1C, the GAB isotherm model was also fitted to the complete data obtained at 4, 20 and 37 1C (R2 ¼ 0:9828; S ¼ 1:0240) and the GAB constants are given in Table 4. This gives a good approximation of the isotherm for whey protein over the temperature range of 4–37 1C, up to a water activity of around 0.6. The isotherm data for the HMCP measured at 4, 20, 37 and 50 1C given in Fig. 3 show similar temperature
Moisture content (g 100 g-1 dry powder)
b
30
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C) R²=0.9828 S=1.0240
25 20 15 10
R²= 0.9960 S= 0.4432
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Water activity
Fig. 1. Effect of temperature on the moisture sorption isotherm of a WPI powder.
dependence. There is no obvious temperature dependence in the isotherms measured at 4, 20 and 37 1C and the isotherm measured at 50 1C is significantly lower above 0.2aw : The GAB model was fitted to the data measured at 4, 20 and 37 1C, individually and as a combined data set, and to the data measured at 50 1C. The GAB constants, correlation coefficients and standard error of estimates are given in Table 4. The decrease in moisture content at a given water activity with an increase in temperature, as seen with the data obtained for both the WPI and HMCP at 50 1C, is consistent with the observations of Loncin et al. (1968) and Hermansson (1977). MPC powder (Fig. 4) also shows similar temperature dependence. There is no
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415
0 Moisture content 20 g 100 g-1 15 g 100 g-1
-0.5
12 g 100 g-1 -1
10 g 100 g
ln(aw)
-1
8 g 100 g
-1
-1.5
-2
5 g 100 g
-2.5 0.003
0.0031
0.0032
0.0033
0.0034
0.0035
0.0036
-1
0.0037
1/T (K-1)
Moisture content (g 100 g-1 dry powder)
Fig. 2. Sorption isosteres of a WPI powder.
25
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C)
20 15
R2=0.9914 S=0.5670
10
R2=0.9907 S=0.5310
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Moisture content (g 100 g-1 dry powder)
Fig. 3. Effect of temperature on the moisture sorption isotherm of a HMCP.
25
4 °C 20 °C 37 °C 50 °C GAB (4-37 °C) GAB (50 °C)
20 15
R2=0.9958 S=0.3592
10 R2=0.9970 S=0.3006
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 4. Effect of temperature on the moisture sorption isotherm of a MPC powder.
apparent difference in the isotherms measured from 4–37 1C. The isotherm measured at 50 1C is slightly lower although this is not as obvious as it is for the WPI and HMCP. The GAB isotherm model was fitted to the
data measured at 4, 20 and 37 1C, individually and as a combined data set, and to the data measured at 50 1C and the constants are given in Table 4. The relationship between temperature and water activity, at a given moisture content, for high micellar casein and MPC powders was similar to that seen in Fig. 2 for the WPI powder. Using the isotherms for the HMCP and MPC powder measured at 4, 20 and 37 1C, along with their compositions given in Table 2, the isotherms for amorphous lactose and whey protein were subtracted (using Eq. (1)) to give an approximation of the isotherm for micellar casein. This was done to see whether the use of Eq. (1) could give an isotherm for micellar casein which was similar to the isotherm data given in literature (Berlin et al., 1968; Ru¨egg, Blanc, & Lu¨scher, 1979; Linko, Pollari, Harju, & Heikonen, 1981; Bandyopadhyay, Das, & Sharma, 1987). The effect of the fat was considered negligible since it was only present in very small amounts, i.e., no greater than 1.8%. The resulting isotherm data for micellar casein are given in Fig. 5 where it can be seen that there is very good agreement between predicted isotherm data for micellar casein and the literature data. The GAB isotherm model was fitted to the data (excluding the literature data) up to 0.86aw (R2 ¼ 0:9855; S ¼ 0:7373) and the resulting GAB coefficients are given in Table 4. The effect of milk fat on isotherm prediction can be investigated by examining the isotherms for the two powders containing high proportions of milk fat. The isotherms for a LFCP and HFCP, measured at 4, 20 and 37 1C, are given in Fig. 6. No obvious temperature dependence was observed for these powders. The isotherms for these powders were also predicted using the GAB isotherm models (Table 4) for amorphous
ARTICLE IN PRESS Moisture content (g 100 g-1 dry powder)
45
Berlin et al. 1968 Ruegg et al. 1979 Linko et al. 1981 Bandyopadhyay et al. 1987 MPC HMC GAB model
40 35 30 25
R2=0.9855 S=0.7373
20 15 10 5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Moisture content (g 100 g-1 dry powder)
Fig. 5. Comparison of the moisture sorption isotherm for micellar casein, predicted from the isotherms of a HMCP and a MPC, with literature data.
10 HFCP 4°C HFCP 20°C HFCP 37°C HFCP Predicted LFCP 4°C LFCP 20°C LFCP 37°C LFCP Predicted
9 8 7 6 5 4 3 2 1
Lactose Crystallisation
0 0
0.1
0.2
0.3
0.4 0.5 0.6 Water activity
0.7
0.8
0.9
1
Fig. 6. Prediction of the moisture sorption isotherms for a 56% fat cream powder (LFCP) and a 72% fat cream powder (HFCP).
lactose, WPI and micellar casein. It can be seen that there is a good agreement between measured and predicted isotherms, until the breakpoint, indicating that the milk fat does not have a significant effect on the isotherms for the powders even when it is present in a large amount (e.g., 56% and 72%). The breakpoint in the measured isotherms is due to amorphous lactose crystallisation (Berlin et al., 1968). It is noted that since only the percentage of total protein was known, the isotherms for whey protein and casein were added as a mass fraction of 0.2 and 0.8, respectively, as this is the proportion that the two proteins are present in milk. Isotherms for freeze-dried lactose/whey protein and lactose/casein powders are shown in Fig. 7. The isotherms were predicted from the isotherms of amorphous lactose, WPI and the isotherm for the HMCP. There is good agreement between the measured and predicted isotherms until the point where amorphous lactose crystallisation occurs. This can be seen for water activities above 0.43, where there is a drop in the measured moisture content. The drop in moisture content was not observed for mixed whey protein and amorphous lactose powders at 0.43aw, as it was for
Moisture content (g 100 g-1 dry powder)
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416
12
L2C1i L2C1ii L2C1iii L2C1 Predicted L2W1 L2W1 Predicted
10 8 6 4 2
outlier 0 0
0.1
0.2
0.3 0.4 Water activity
0.5
0.6
Fig. 7. Moisture sorption isotherms showing the presence of amorphous lactose crystallisation during equilibration.
mixed casein and amorphous lactose powders. It appears that whey protein may hinder the crystallisation of amorphous lactose. Delayed crystallisation has also been noted by Berlin et al. (1968) in isotherms for milk and whey powders. Amorphous lactose crystallisation occurred at higher water activities, which was attributed to a lowered concentration of lactose at the surface of the milk powder particles, with the initial sorption site being some component other than lactose (Berlin et al., 1968). It has also been noted that there is an overrepresentation of protein at the surface of mixed protein and lactose powders (Fa¨ldt & Bergensta˚hl, 1996). The proportion of protein relative to the other powder constituents is greater on the surfaces of the particles than in the powder in bulk. Referring to Fig. 7, the powder containing whey protein (L2W1) was equilibrated for 3 weeks and the powder containing casein (L2C1i, ii, iii) was equilibrated for 2 weeks. If the protein component did not affect amorphous lactose crystallisation, then it would be expected that the isotherms for both powders would show similar drops in moisture content above 0.43aw, since the lactose contents are similar. This was not the case, even when the powder containing the whey protein (L2W1) was equilibrated for longer, i.e., giving more time for lactose crystallisation to occur. This indicates that whey protein affects/delays the crystallisation of amorphous lactose. The implication of this is that it will require higher water activities to result in amorphous lactose crystallisation at a given temperature and period of time, when whey protein is present. This result may also indicate that interactions were established between whey protein and lactose but not between casein and lactose. Jouppila and Roos (1994) also observed delayed crystallisation in milk powders compared to pure lactose powder; milk fat was found to decrease the rate of lactose crystallisation. Fig. 8 shows an overall comparison between the measured and predicted moisture contents for the
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12 L1W1M1a L1W1M1b L1W2 L2W1 L2M1a L2M1b L2M1c W2M1 SMP DBP Keir (2001)
10 8 6 4
upper 15%
best fit lower 10%
2 0 0
2
4
6
8
10
12
Measured moisture content (g 100 g-1 dry powder) Fig. 8. Comparison of measured and predicted isotherms for freeze-dried lactose, whey protein, casein mixture powders, SMP, a DBP and a variety of dairy powders measured by Keir (2001).
powder mixtures detailed in Table 1, SMP and a DBP. Included are isotherm data from Keir (2001) for a variety of dairy powders containing only amorphous lactose, dairy protein and milk fat. For clarity, points where lactose crystallisation is likely to have occurred, as indicated by drops in the moisture content, have been omitted from Fig. 8. Relative error limits of 710 and 15% have also been included. It can be seen that there is good agreement between the measured and predicted moisture contents, with the difference mostly being less than 710%. In general, the predicted moisture contents are slightly greater than those measured. This indicates that there may be some interaction which decreases water sorption. As discussed previously, Iglesias et al. (1980) stated that the hydrogen bonding between components is likely to compete with hydrogen bonding between components and water. This would result in a decrease in water sorption. Since most of the data are within the 710% error limits, it can be concluded that the simple additive isotherm approach is acceptable for predicting the isotherms of dairy powders.
4. Conclusions Isotherms for a variety of freeze-dried dairy powders and commercial dairy powders were predicted using a simple additive isotherm model. There was good agreement between the measured and predicted isotherms with the average relative error being around 10%. Considering the errors involved in measuring isotherms gravimetrically, the simple additive isotherm model is a good method for predicting moisture sorption isotherms of dairy powders.
Acknowledgements The authors thank the New Zealand Dairy Board, Wellington, New Zealand for the funding of this work.
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