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Moisture sorption isotherms and net isosteric heat of sorption for spray-dried pure orange juice powder
LWT - Food Science and Technology xxx (2014) 1e8
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Moisture sorption isotherms and net isosteric heat of sorption for spray-dried pure orange juice powder Mona Edrisi Sormoli*, Timothy A.G. Langrish Drying and Process Technology Group, School of Chemical & Biomolecular Engineering, Building J01, the University of Sydney, Darlington, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2014 Received in revised form 9 September 2014 Accepted 30 September 2014 Available online xxx
The aim of this study was to measure the moisture sorption isotherms of spray-dried pure orange-juice powders. These isotherms have been fitted using eleven different sorption equations. The GAB model was found to be the best fit. The GAB parameters were estimated both by direct and indirect regression methods. The net isosteric heat of sorption was also determined using the ClausiuseClapeyron equation and was successfully used as a limiting condition for estimating the six unknown parameters of the GAB equation using the direct regression method. The net isosteric heat of sorption decreased from 9.05 kJ/ mol at 0.05 kg/kg dry basis to approximately 0.0 kJ/mol at 0.7 kg/kg dry basis. These values, as expected, were comparable to the enthalpy difference between the monolayer and multilayer moisture (8.16 kJ/ mol), and the difference between the latent heat of condensation for pure water and the heat of sorption of multilayer moisture (¼ 0.88 ± 0.69 kJ/mol). © 2014 Elsevier Ltd. All rights reserved.
Keywords: Moisture sorption isotherm Orange juice powder Spray drying GAB equation Net isosteric heat of sorption
1. Introduction Moisture sorption isotherms describe how strongly water is bound to a solid (Van den Berg, 1981). They present valuable thermodynamic data about the material being studied. These thermodynamic data are useful for design calculations of the drying process, as well as the prediction of the final moisture content for rez, Ca rcel, Clemente, & the product at the end of drying (García-Pe Mulet, 2008; Langrish, 2009; Rizvi & Benado, 1983; Tsami, 1991). They can also be used in predicting the storage stability of food products (Tapia, Alzamora, & Chirife, 2007). Hence they have been the focus of many studies. A moisture sorption isotherm can be used to predict the amount of water that a material will hold if it is exposed to air at a certain relative humidity and a certain temperature. This moisture content is dependent on the temperature and the environmental relative humidity, as well as on the composition of the material (Garcíarez et al., 2008; Keey, 1978). Once the moisture sorption isoPe therms are determined for at least three temperatures, the net isosteric heat of sorption can be calculated from the sorption isotherms by using the ClausiuseClapeyron equation.
* Corresponding author. Tel.: þ61 2 9351 5660; fax: þ61 2 9351 2854. E-mail addresses: [email protected], [email protected] (M. Edrisi Sormoli).
The water molecules, when they are in the form of moisture in a solid, have a different enthalpy from the enthalpy of pure water. If the water is bound to the solid, this enthalpy is less than the enthalpy of pure water by the energy of this binding (Keey, 1978). Consequently the moisture in a solid has a higher heat of evaporation than for pure water. The difference between this actual heat of evaporation for the moisture in the solid and the latent heat of evaporation of pure water is called the net isosteric heat of sorption or the enthalpy of wetting (Basu, Shivhare, & Mujumdar, 2006; Keey, 1978). By knowing the net isosteric heat of sorption, the actual energy required for drying a product to a specific moisture content can be calculated. The moisture sorption isotherms and the net isosteric heat of sorption are unique for every material and must be evaluated experimentally. Fruit juices are challenging high-sugar content food products to dry. Fruit juice powders can be of more value in terms of transportation and handling, packaging and storage, and shelf life, compared with their liquid form (Goula & Adamopoulos, 2010). Spray drying is one of the techniques used for producing powders from liquid solutions and suspensions. The spray-drying technique is 30e50 times cheaper than freeze drying (Gharsallaoui, Roudaut, Chambin, Voilley, & Saurel, 2007). Orange juice is one of the most popular and more commonly consumed fruit juices. However, due to the presence of large amounts of sugars and acids in orange juice, significant product loss occurs during spray drying because of the stickiness of the powders (Shrestha, Ua-arak, Adhikari, Howes, &
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Please cite this article in press as: Edrisi Sormoli, M., & Langrish, T. A. G., Moisture sorption isotherms and net isosteric heat of sorption for spraydried pure orange juice powder, LWT - Food Science and Technology (2014), http://dx.doi.org/10.1016/j.lwt.2014.09.064
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
Bhandari, 2007). Hence, drying aids have been added to orange juice to overcome the stickiness issue during spray drying. As a result, there are just few studies on the moisture sorption isotherms for orange juice powders produced by spray drying which have used drying aids during the spray-drying process (Brennan, Herrera, & Jowitt, 1971). Brennan et al. (1971) used liquid glucose as a drying aid to spray dry orange juice and determined the moisture sorption isotherms for that mixture. There are also few studies on the sorption isotherms of pure orange juice powder produced with other techniques, such as freeze drying (Karel & Nickerson, 1964). Karel and Nickerson (1964) studied moisture sorption isotherms of pure dehydrated orange juice that had been produced by a company named Orange Crystals, Inc., Plant City, Florida. It is understood that the dehydrated juice had been produced by a vacuum-belt dryer and a freeze-drying technique. It has been reported in the literature that, for some food products, the drying method can affect the sorption isotherms of the final product significantly (Iglesias & Chirife, 1982). Hence there is a need to study the moisture sorption isotherms of pure spray-dried orange juice powders. Moisture-sorption isotherms are needed to predict the final moisture content of the spray-dried powders during the spraydrying process (Langrish, 2009). Combinations of temperature and moisture content in the final powders determine the glasstransition temperature of the product and the stickiness temperature that should be avoided during spray drying in order to reduce the product loss. Based on the knowledge obtained from the sorption isotherms, there may be some potential for spray drying the orange juice in its pure form. Therefore, the aim of this study has been to determine the moisture sorption isotherms and isosteric heat of sorption for pure spray-dried orange-juice powders. 2. Materials and methods 2.1. Materials Store-bought orange juice from Berri Pty Ltd, Australia was used for producing orange-juice powders. Laboratory-grade lithium chloride anhydrous, potassium acetate, magnesium nitrate, potassium iodide and potassium chloride from Chem-supply, Australia, magnesium chloride from, Unilab, Ajax Finechem, Australia and food-grade sodium chloride, SAXA, from Salpak Pty Ltd. Australia were used for salt solution preparation.
desiccator and was connected to a 6 V DC battery to enhance the rate of mass transfer and decrease the time required for equilibration. The batteries were connected through cables to the fans and were safely placed outside the desiccators and the oven. The temperatures at which the isotherms were measured were 20 C, 30 C, 40 C and 50 C. The desiccators were placed in a fanforced oven to maintain a constant temperature during all experiments, except for the 20 C isotherms where they were put in a low-temperature incubator (Shanghai Farui Instrument Co. Ltd, China). Two grams of freshly spray-dried orange juice powders were spread on a Petri dish and were put in each desiccator. The lid of the desiccators were double sealed using three layers of a thin polythene film to ensure a sealed environment in the desiccators. The samples were taken out of the desiccators every two days to measure their weight using a four-figure (±0.0001 g) analytical balance (Mettler Toledo AB204-S, Switzerland) until the mass change of the sample was less than 0.001 g. After a constant weight was observed, the equilibrium moisture content of the samples was determined by oven drying at 85 C for 24 h using a fan-forced drying oven and was reported on a dry basis (Thermoline TD 150F) (Islam, Edrisi, & Langrish, 2013). The whole procedure was repeated three times for each temperature.
2.3. Data analysis 2.3.1. Analysis of sorption data The equilibrium moisture content of the powders for each temperature was plotted against the corresponding water activity to produce the sorption isotherms. The water activity is equal to the relative humidity divided by 100 (Seinfeld & Pandis, 2006). Eleven different mathematical models (Kammoun Bejar, Boudhrioua Mihoubi, & Kechaou, 2012), among many in the literature, were used to fit to the experimental data using regression analysis. The curve fitting and regression analysis were performed using MATLAB R2013b. Inc, MathWorks Natick, Massachusetts, U.S.A. The best fit was chosen according to the minimum sum of squares due to error for the fit, abbreviated to SSE, minimum standard error of the fit RMSE, minimum mean absolute percentage error (P), and the maximum degrees of freedom adjusted R-square, R2Adj (R2Adj > 0.98 is considered here to be a reasonable fit).
SSE ¼
n X
wi ðyi b yiÞ
2
(1)
i¼1
2.1.1. Orange juice powder The orange juice was spray dried using a Buchi-B290 spray dryer (Buchi, Switzerland) at an inlet air temperature of 150 C, a pump rate of 4.9 ml/min, an aspirator flow rate of approximately 35 m3/h, and an atomizing air flow rate of 536 Nl/h. All experiments were performed in triplicate. The powders were placed in air-tight plastic bags and were used for the experiments immediately. 2.2. Determination of sorption isotherms In order to produce and maintain a range of relative humidities from 11% to 82%, saturated salt solutions of LiCl, CH3COOK, MgCl2, Mg (NO3)2, KI, NaCl and KCl were prepared by dissolving sufficient amounts of the dry salts into 60 C de-ionized water according to the technique used by Nyqvist (1983). These saturated solutions were placed in seven separate glass desiccators and were equilibrated at the respective experimental temperatures, for at least 24 h prior to each set of experiments. A fan with dimensions of 40 40 20 mm (model 412 DC axial compact) from ebm-papst A&NZ Pty Ltd, was placed in each
Where yi are the experimental data, b y i are the predicted data from the fit, and wi is the weighting applied to each data point, which was set to unity in these analyses.
R2Adj ¼ 1 SST ¼
SSEðn 1Þ SSTðvÞ
Xn i¼1
wi ðyi yi Þ2
v¼nm RMSE ¼
P¼
rffiffiffiffiffiffiffiffi SSE v
100XN yi b y i i¼1 y N i
(2)
(3) (4)
(5)
(6)
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Table 1 The models used for fitting the sorption isotherms for orange juice powders. Name of the model
Equation
GAB (GuggenheimeAndersenede Boer)
Xe ¼
BET
Xe ¼
Reference
Xm $c$k$aw ð1k$aw Þð1k$aw þc$k$aw Þ Xm $c$aw ½ð1aw Þþðc1Þ$ð1aw Þ$aw
1 B Xe ¼ lnAa
Halsey
Maroulis et al. (1988) Kaymak-Ertekin and Gedik (2004) Iglesias and Chirife (1982)
w
Xe ¼ A$aBw þ C$aD w B aw Xe ¼ A$ 1a w
Kammoun Bejar et al. (2012)
Oswin Caurie Iglesias and Chirife
Xe ¼ expðA þ B$aw Þ aw Xe ¼ A þ B$ 1a w
Kammoun Bejar et al. (2012) Kammoun Bejar et al. (2012)
Smith White and Eiring
Xe ¼ A B$ðlnð1 aw ÞÞ
Kammoun Bejar et al. (2012) Kammoun Bejar et al. (2012)
Henderson
aw ¼ 1 expððB$XeA ÞÞ
Iglesias and Chirife (1982)
Kuhn
Xe ¼ lnAa þ B
Iglesias and Chirife (1982)
Peleg
1 Xe ¼ ðAþB$a wÞ
Iglesias and Chirife (1982)
w
Where SST is the total sum of squares, yi is the mean of experimental data, n is the number of experimental data points, and m is the number of coefficients in each equation. Eleven different models were used to fit the sorption isotherms to the experimental data for orange-juice powders (Table 1). There are many models in the literature for moisture sorption isotherms of food products. However, some models have been used more often by researchers.
2.3.2. Determination of net isosteric heat of sorption The net isosteric heat of sorption has been determined from the ClausiuseClapeyron equation by many researchers (Basu et al., 2006; Kammoun Bejar et al., 2012; Kaymak-Ertekin & Gedik, 2004; Maleki Majd, Karparvarfard, Farahnaky, & Jafarpour, 2013; Reid, 2007; Rizvi & Benado, 1983; Tsami, 1991), as follows:
0
1
qst;n ¼ qst DHvap
(8)
Where aw ¼ water activity, T ¼ temperature (K), qst;n ¼ net isosteric heat of sorption (kJ/mol water), qst ¼ isosteric heat of sorption, DHvap ¼ heat of vaporization of pure water (kJ/mol water), R ¼ 8.314 (kJ/kmol K). To determine the net isosteric heat of sorption, at a certain moisture content, the natural logarithm of the water activity was plotted against the inverse of the corresponding absolute temperature, and the regression line was plotted. The net isosteric heat of sorption was determined from the slope of the straight line. This process was repeated for different moisture contents to determine the net isosteric heat of sorption at different moisture contents (Tsami, 1991). 3. Results and discussion 3.1. Sorption isotherm models
Bd ln aw C B C ¼ qst;n @ A R d T1
(7)
Fig. 1 illustrates the moisture sorption behavior of spray-dried pure orange juice powder at four different temperatures, as fitted by the GAB equation.
and
Fig. 1. Sorption isotherms of spray-dried pure orange juice powders and the fitted GAB model at the four different temperatures. Each data point is the average of the three experimental replicates. Pure orange juice powders kept at (-) 20 C, ( ) 30 C, (△) 40 C and () 50 C.
▫
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A sharp increase in the equilibrium moisture content was observed at higher water activities (aw > 0.45 at 50 C, aw > 0.48 at 40 C, aw > 0.51 at 30 C) (Fig. 1). This behavior has been reported in the literature for many high-sugar content foods, such as raisins, figs, apricots, prunes (Maroulis, Tsami, Marinos-Kouris, & Saravacos, 1988), grapes, apples (Kaymak-Ertekin & Gedik, 2004) and orange peels (Kammoun Bejar et al., 2012). It has been related to the dissolution of the fruit sugars in the sorbed water vapor (Kammoun Bejar et al., 2012; Kaymak-Ertekin & Gedik, 2004; Maroulis et al., 1988). It is well known from the literature that the composition of food products affects the moisture sorption capacity and the drying behavior of the food products (Iglesias & Chirife, 1982; Labuza & Altunakar, 2007). The dry solids in orange juice consist of more than 80% sugars with a sugar content ratio of 2:1:1 sucrose: glucose: fructose, respectively (Kelebek, Selli, Canbas, & Cabaroglu, 2009; Lee & Coates, 2000), which may explain the similarity in the sorption behavior of the orange juice powders with high-sugar content foods. The results of the regression analysis for fitting the experimental data to the eleven equations are summarized in Table 2. The models were sorted based on the minimum sum of squares due to error (SSE) except for the BET equation. In terms of the mean absolute percentage error (P) of the fits, those with less than 10% error can be considered acceptable (Foster, Bronlund, & Paterson, 2005; Kaymak-Ertekin & Gedik, 2004) and an R-square of >0.98 may also indicate a good fit. Regarding the BET equation, since only the data over the range of aw ¼ 0.1e0.5 were fitted into the equation, the SSE cannot be used for comparison and therefore the adjusted R-square was considered for comparison. By comparing the SSE and the adjusted R-square of the fits, it may be concluded that most of these equations can fit the sorption behavior of the spray-dried orange juice powders. As shown in Table 2 GAB model, has the minimum values for SSE and P and the maximum adjusted R-square when used to predict the moisture sorption isotherm of orange juice powder at 30 C, 40 C and 50 C, respectively. At 20 C (Table 2), the Peleg model, followed by the GAB model, has the minimum SSE and P. This trend suggests that both GAB and Peleg models fit the sorption isotherms of spray-dried pure orange juice over the range of temperatures from 20 C to 50 C better than the other studied models. The Peleg equation has been suggested by Kammoun Bejar et al. (2012) to best fit the moisture sorption isotherms for orange leaves and peels. However, in this study there is just one temperature at which the Peleg equation fits the moisture sorption data better than the GAB equation. Fig. 1 illustrates the moisture sorption behavior of spray-dried pure orange juice powder at four different temperatures, as fitted by the GAB equation. GAB model has been used by many researchers to predict the sorption isotherms of food products (Lewicki, 1997; Maroulis et al., 1988; Quirijns, van Boxtel, van Loon, & van Straten, 2005b; Timmermann, Chirife, & Iglesias, 2001) such as dried-onions and green beans (Samaniego-Esguerra, Boag, & Robertson, 1991), apple, black currant and sour cherries (Klewicki et al., 2009), apricots (Djendoubi Mrad, Bonazzi, Boudhrioua, ^a, Kechaou, & Courtois, 2012) and coffee fruit (Goneli, Corre Oliveira, & Afonso Júnior, 2013). The shape of the isotherms (Fig. 1) and the value for parameter c > 1 of the BET equation (Table 2) suggest that the moisture sorption isotherms for spray-dried pure orange juice powders are sigmoid and based on the classification of isotherms suggested by Brunauer, Deming, Deming, and Teller (1940) belong to type 2 class of isotherms. As discussed by Labuza and Altunakar (2007) at the water activity range of 0.2e0.3, the monolayer moisture content represents the optimal moisture content at which the dehydrated food products will have the maximum shelf-life. At this moisture content,
chemical reactions that require presence of water will begin, and above this moisture content, lipid oxidation (if any) will start. At a water activity range of (0.35e0.5), physical changes in food products such as loss of crispiness, caking and stickiness of powders occur. These changes are also related to the glass-transition temperature of the materials that should be taken into account. However, the critical moisture content in terms of microbial growth for food products has been suggested to be 0.6 (Labuza & Altunakar, 2007). Therefore, the safest water activity for orange juice powders and corresponding moisture contents at 20, 30 40 and 50 C will be at aw « 0.25 and moisture contents of 12.6, 10.9, 10.2 and 9.8% (w/w). The GAB equation and the definition of its three parameters are shown in equations (9)e(12).
Xe ¼
Xm $c$k$aw ð1 k$aw Þð1 k$aw þ c$k$aw Þ
(9)
DH1 Hm Hn ¼ C0 exp C ¼ C0 exp RT RT
(10)
DH2 H Hn k ¼ k0 exp ¼ k0 exp l RT RT
(11)
DHx Xm ¼ Xm0 exp RT
(12)
Where DH1 ¼ the difference between the heat of sorption for monolayer of water (Hm) and the heat of sorption for multilayer water (Hn), and DH2 ¼ the difference between the latent heat of condensation of pure water (Hl) and the heat of sorption for multilayer water (Hn) (Maroulis et al., 1988; Quirijns et al., 2005b). Equation (12) expresses the dependence of the monolayer moisture content (Xm) on the temperature. DHx is a constant parameter to express the temperature dependence of the monolayer moisture (Quirijns et al., 2005b). Xm is the amount of water that is adsorbed in a monolayer on the surface of the adsorbent (monolayer moisture content) and is a measure of the availability of active sorption sites (Quirijns et al., 2005b). The parameter c (Eqs. (9) and (10)) represents the strength of binding for water molecules to the primary binding sites on the product surface. The larger the value of c, the stronger the bonds between water molecules in the monolayer and the binding sites on the surface of the sorbent (Quirijns et al., 2005b). The parameter k (Eqs. (9) and (11)) is a correction factor for multilayer molecules relative to the bulk liquid; when k ¼ 1 the molecules beyond the monolayer have the same characteristics as pure water (Quirijns et al., 2005b). Hence when k ¼ 1, the heat of evaporation for the multilayer molecules is the same as that for pure water, and the GAB equation reduces to the BET equation (Samaniego-Esguerra et al., 1991). This physical meaning, the ability of the GAB equation to fit the moisture sorption data better than the other equations at three consecutive temperatures and the ability of the GAB equation to predict the moisture sorption isotherms of food products over a wide range (0.05 < aw < 0.8e0.9) (Timmermann, 2003), suggests that the GAB model is the preferred model to fit the moisture sorption behavior of the spray-dried pure orange juice powders in this study. 3.2. Heat of sorption As shown in Fig. 2, the net isosteric heat of sorption for orange juice powders increases sharply at lower moisture contents,
Please cite this article in press as: Edrisi Sormoli, M., & Langrish, T. A. G., Moisture sorption isotherms and net isosteric heat of sorption for spraydried pure orange juice powder, LWT - Food Science and Technology (2014), http://dx.doi.org/10.1016/j.lwt.2014.09.064
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Table 2 Predicted parameters of the fitted models to the experimental data for the moisture sorption isotherm of spray-dried pure orange juice powder at 20, 30, 40 and 50 C. Goodness of fit parameters
Model coefficients
Model type
Temperature ( C)
SSE*
Adj-R-sq
RMSE**
P (%)
A
B
C
D
GAB
20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50
0.003 0.005 0.0023 0.0044 0.0022 0.0058 0.0103 0.0065 0.0032 0.0085 0.0112 0.0075 0.0035 0.0087 0.0111 0.0072 0.0086 0.0107 0.0126 0.0082 0.0009 0.0011 0.0011 0.0004 0.0104 0.0123 0.0031 0.0091 0.013 0.0158 0.0159 0.0102 0.013 0.0175 0.0179 0.0146 0.0153 0.0154 0.0142 0.0107 0.0308 0.0454 0.0287 0.0243
0.99 0.99 0.99 0.99 0.99 0.99 0.97 0.98 0.99 0.99 0.97 0.98 0.99 0.99 0.97 0.98 0.99 0.98 0.97 0.98 0.98 0.96 0.95 0.97 0.98 0.98 0.99 0.98 0.98 0.98 0.96 0.97 0.98 0.97 0.96 0.96 0.98 0.98 0.97 0.97 0.98 0.97 0.97 0.98
0.014 0.0164 0.012 0.0167 0.0124 0.0179 0.0262 0.0209 0.0142 0.0206 0.0257 0.0209 0.0148 0.0208 0.0255 0.0206 0.0232 0.0231 0.0273 0.0219 0.0113 0.0098 0.0108 0.0069 0.0256 0.0248 0.0138 0.0231 0.0285 0.0281 0.0306 0.0245 0.0285 0.0296 0.0324 0.0293 0.0309 0.0277 0.0289 0.0251 0.0439 0.0477 0.0423 0.0378
3.6 5.8 7.0 6.2 6.3 5.2 7.3 6.3 6.4 7.9 7.9 7.9 7.1 9.1 8.7 7.4 9.8 10.2 7.9 7.0 8.0 6.1 8.6 6.2 11.9 11.1 9.1 9.6 13.8 13.0 13.1 11.6 16.5 16.5 17.2 18.4 11.6 13.0 10.2 10.7 7.0 14.4 12.0 11.5
7.613, c 8.956, c 9.485, c 6.885, c 0.279 0.2293 0.253 0.2295 0.09431 0.08495 0.08181 0.08675 0.2119 0.1966 0.1905 0.1763 3.289 3.192 3.139 3.286 9.755, c 12.85, c 8.806, c 7.274, c 0.1002 0.0932 0.0991 0.0946 0.08946 0.07881 0.07425 0.0595 9.644 10.88 11.45 12.78 0.01256 0.0157 0.01933 0.0086 1.171 1.15 1.162 1.096
0.953, k 0.969, k 0.9867, k 0.994, k 0.6321 0.5571 0.6499 0.6733 1.265 1.257 1.252 1.163 0.6357 0.6241 0.615 0.6589 3.31 3.064 2.92 3.054 0.1134, Xm 0.0981, xm 0.1031, Xm 0.09624, xm 0.05083 0.04306 0.0304 0.02359 0.1025 0.09543 0.0943 0.09728 9.546 10.87 11.51 13.15 0.3113 0.2804 0.262 0.2613 3.835 4.146 4.391 4.294
0.126, xm 0.109, xm 0.102, xm 0.098, xm 0.9557 0.8103 0.7472 0.7581 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e
e e e e 5.508 4.878 5.225 5.052 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e
Peleg
Halsey
Oswin
Caurie
BET
Kuhn
Iglesias and Chirife
White and Eiring
Smith
Henderson
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
reaching a maximum. This behavior has been previously observed for other food products (Kammoun Bejar et al., 2012; KaymakErtekin & Gedik, 2004; Quirijns et al., 2005b; Tsami, Maroulis, Marinos-Kouris, & Saravacos, 1990). The same trend was observed for spray-dried pure orange juice powders (Fig. 2). It has been reported that the enthalpy difference between the monolayer and multilayer moisture (DH1), calculated from the GAB equation for dried fruits, is approximately equal to the net isosteric heat of sorption at low moisture contents calculated using the ClausiuseClapeyron equation. Similarly, the difference between the latent heat of condensation of water and the enthalpy of sorption of the multilayer moisture (DH2) has been also reported to be approximately equal to the net isosteric heat of sorption at higher moisture contents (Quirijns et al., 2005b; Tsami et al., 1990). Quirijns et al. (2005b) stated the relationship between the net isosteric heat of sorption and the enthalpy components of the GAB equation using the following equation (13):
9.05 kJ/mol for 0.05 g/g dry solids to approximately 0.0 kJ/mol for 0.7 g/g dry solids moisture content. The maximum isosteric heat of sorption for spray-dried pure orange juice powders calculated in this study is comparable with the value for orange peels (8.00 kJ/ mol) calculated by Kammoun Bejar et al. (2012) and also falls within the range of the values reported in the literature for dried fruits and vegetables (Tsami et al., 1990). The decreasing trend of the isosteric heat of sorption suggests that the heat of sorption approaches the heat of vaporization of pure water at higher moisture contents. As the moisture content decreases and only the monolayer moisture is left, the water molecules become tightly bound to the surface of the powders and to the sorption sites with high interaction energies. At the same time, the heat of sorption increases above the heat of vaporization of pure water, making it difficult to remove water from the surface of the powders. Hence evaporating the water from orange juice is easier at higher moisture contents.
qst;n ¼ DH1 DH2
3.3. Parameters of the GAB equation
(13)
The net isosteric heat of sorption, calculated using the ClausiuseClapeyron, decreases with increasing moisture content from
It has been suggested by Maroulis et al. (1988) that a direct nonlinear regression analysis and curve fitting of the data were more
Please cite this article in press as: Edrisi Sormoli, M., & Langrish, T. A. G., Moisture sorption isotherms and net isosteric heat of sorption for spraydried pure orange juice powder, LWT - Food Science and Technology (2014), http://dx.doi.org/10.1016/j.lwt.2014.09.064
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
Fig. 2. Variation in the net isosteric heat of sorption of spray-dried pure orange juice powders as a function of moisture content. (DH1): enthalpy difference between the monolayer and multilayer moisture, (DH2): the difference between the latent heat of condensation of pure water and the enthalpy of sorption of the multilayer moisture.
accurate for fitting the GAB parameters. There are three methods to determine the parameters of GAB equation. In the first method, the GAB equation is rearranged, and a polynomial regression analysis is performed. This method has been suggested to have two disadvantages. Firstly the transformation results in incorrect weighing of data and secondly the confidence intervals for the GAB parameters cannot be determined directly (Samaniego-Esguerra et al., 1991). Hence this method will not be discussed in this paper. In the second method, non-linear regression analysis of the standard threeparameter GAB equation (Eq. (9)) is performed, and the three parameters of the GAB equation (Xm, c and k) are determined at each temperature. Then the parameters DH1, DH2, c0, k0 are estimated by using a successive regression of equations (10) and (11). This second method is referred to here as the indirect regression method. In the third method, the definition of the parameters of the GAB equation c, k and Xm, (Eqs (10)e(12)) are substituted into the standard GAB equation (Eq. (9)). This substitution results in a form of GAB equation where the unknown parameters to be determined are DH1, DH2, DHx, c0, k0 and Xm0. A non-linear regression has been performed for this six-parameter GAB equation (Maroulis et al., 1988; Samaniego-Esguerra et al., 1991). This third method has been described as direct regression and has been recommended for predicting the GAB parameters (Samaniego-Esguerra et al., 1991). Direct regression considers and incorporates the temperature as a variable in the GAB equation. Hence, once these six unknowns are calculated, it is possible to calculate and predict the parameters of the GAB equation and consequently the moisture sorption behavior at other temperatures. However, the determination of six unknown parameters using regression analysis is quite challenging. Quirijns, van Boxtel, van Loon, and van Straten (2005a) argued that the Table 3 Parameters for GAB equation calculated from the indirect regression method. Temperature ( C) 20
30
GAB parameters ± 95% confidence bounds c 7.61 ± 3.56 8.956 ± 5.35 k 0.95 ± 0.02 0.97 ± 0.03 Xm (g/g) 0.126 ± 0.011 0.110 ± 0.013 Goodness of fit: *SSE: 0.003 0.005 R-square: 0.996 0.996 Adjusted 0.996 0.995 R-square: **RMSE: 0.0130 0.014 P (%) 3.59 5.76
40
50
9.48 ± 7.51 6.89 ± 5.06 0.99 ± 0.03 0.99 ± 0.04 0.102 ± 0.016 0.098 ± 0.017 0.005 0.992 0.992
0.004 0.989 0.987
0.016 6.96
0.018 6.15
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
physical meaning of the parameters of the GAB equation may get lost during the direct regression process, and these parameters are difficult to determine with high precision and within a narrow confidence interval. Both direct and indirect regression methods were used in this study to fit the experimental data to the GAB equation. Table 3 shows the calculated parameters for the GAB equation using the indirect regression methods. As found for the indirect regression method, the values of the monolayer moisture contents (Xm) decreased slightly as the temperature increased, whereas the parameter k slightly increased, and the parameter c also increased up to 40 C. A slight decrease in parameter c was observed at 50 C. The same increasing and decreasing trend for the parameter c has been reported in the literature for onions, apricots and green beans (Djendoubi Mrad et al., 2012; Samaniego-Esguerra et al., 1991) using the indirect regression method. All the calculated parameters in this study fall within the range found for c, k and Xm values for food products. It has been suggested that, in order to represent a sigmoid type of sorption isotherm, the parameters of the GAB equations should be kept in the following ranges: c > 5.67 and 0 < k < 1 (Lewicki, 1997). The monolayer moisture content has also been found to be comparable with the data found in the literature for similar fruits such as 12% (w/w) for dried apple, 17% (w/w) for dried sour cherry and 12% (w/w) for dried black currants (Klewicki et al., 2009).
Table 4 GAB parameters calculated using direct regression method. Coefficients ± 95% confidence bounds
GAB parameters calculated at different temperatures using the direct regression results
Temperatures ( C)
DH1, J/mol
8158 C0 0.329 ± 0.086 DH2, J/mol 883.5 ± 686.5 k0 1.375 ± 0.376 Xm0 0.0119 ± 0.0115 DHx, J/mol 5676 ± 2414 Goodness of the fit parameters SSE: 0.014 R-square: 0.99 Adjusted R-square: 0.99 RMSE: 0.014 P (%) 6.33
20
30
40
50
C
9.36
8.38
7.56
6.86
K
0.96
0.97
0.98
0.99
Xm
0.122
0.113
0.105
0.098
4.75
6.54
7.72
6.21
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
However, in the direct regression method, a slightly decreasing trend was observed for parameters c and Xm, and the same increasing trend as found from the indirect regression method was observed for parameter k (Table 4). When performing the regression analysis, the physical meaning of the parameters can be used to narrow down the estimation criteria for the unknown parameters. This helps to determine the values for the parameters within narrow confidence intervals. By using equation (13) as a limiting condition, and estimating the parameter DH1, the values for the parameters of the GAB equation were determined (Table 4). In other words the initial guessing value for DH1 was chosen to be approximately equal to the maximum net isosteric heat of sorption (qst,n). As shown in Table 4 the only parameter which could not be determined with high precision was the value of Xm0. A positive value for DH1 was expected as a result of the exothermic interaction of the water molecules with the sorption sites on the surfaces of the powders. A negative value is usually expected for DH2 due to the weaker bonding of the multilayer molecules (Gabas, Menegalli, & Telis-Romero, 2000; Maroulis et al., 1988; SamaniegoEsguerra et al., 1991; Tsami et al., 1990) which has been the case here. However, a positive value of the DH2 has been also reported for fruits at high water activities and has been related to the endothermic dissolution of fruit sugars in the absorbed water (Maroulis et al., 1988; Quirijns et al., 2005b). By substituting the results of the direct regression analysis into equations (10)e(12), the parameters of the GAB equations have been recalculated. As shown in Table 4, these parameters follow a reasonable trend and can predict the moisture sorption isotherms of the orange-juice powders with less than 8% mean absolute error. Therefore these parameters can be used with confidence to predict the moisture sorption behavior of orange-juice powders at different temperatures. Considering the explanation of the physical meaning for the GAB parameter c given previously and the data shown in Table 4, water molecules appear to be bound to spray-dried pure orange juice powders more strongly at lower temperatures than at higher temperatures. This binding between the water molecules and the powders becomes weaker at higher temperatures, and the monolayer moisture content of the powders also decreases. Values of c [ 1 and k ~ 1 indicate that the monolayer and multilayer moisture have significantly different binding strengths, and the heat of sorption of the multilayer moisture is the same as the latent heat of vaporization of pure water (Quirijns et al., 2005b). Considering this background, the GAB parameters for spray-dried pure orange juice suggest that the monolayer moisture is strongly bound to the surface of the powders; however, the multilayer moisture molecules are not structured and are almost the same as bulk liquid (pure water) molecules. This means that evaporation of water molecules from the orange-juice solids, at high moisture contents, needs the same heat of evaporation for pure water until the moisture content of the powders is nearly reduced to the value of the monolayer moisture content. After this point, much more energy must be used to evaporate the strongly bound water molecules from the surface of the solids. 4. Conclusions The moisture sorption isotherms for spray-dried pure orange juice have been studied at four different temperatures; 20 C, 30 C, 40 C and 50 C. Eleven different sorption models have been fitted to the experimental data. The GAB model fitted the experimental data well over a wider range of temperatures. Therefore the GAB model was chosen as the preferred model for predicting the moisture sorption isotherms of pure spray-dried orange juice powders. The GAB parameters were also determined using direct
7
regression technique. The net isosteric heats of sorption of spraydried pure orange juice powders were determined using the ClausiuseClapeyron equation, decreasing at greater moisture contents and ranging from 9.05 kJ/mol for 0.05 g/g dry solids to approximately 0.0 kJ/mol for 0.7 g/g dry solids. These values for the net isosteric heat of sorption were successfully used as limiting conditions to predict the six parameters of the GAB equation during the direct regression method. The differential enthalpy between the monolayer and multilayer moisture (DH1 ¼ 8.16 kJ/mol), and the difference between the latent heat of condensation for water and the heat of multilayer sorption for water (DH2 ¼ 0.88 ± 0.69 kJ/ mol), were estimated from direct regression analysis of the GAB equation to be comparable with the values calculated using the ClausiuseClapeyron equation. Acknowledgments Financial support from the Australian Research Council under the Linkage Grants Program (LP120200585) and LangTech International Pty Ltd is gratefully acknowledged. References Basu, S., Shivhare, U. S., & Mujumdar, A. S. (2006). Models for sorption isotherms for foods: a review. Drying Technology, 24(8), 917e930. Brennan, J. G., Herrera, J., & Jowitt, R. (1971). A study of some of the factors affecting the spray drying of concentrated orange juice, on a laboratory scale. International Journal of Food Science & Technology, 6(3), 295e307. Brunauer, S., Deming, L. S., Deming, W. E., & Teller, E. (1940). On a theory of the van der Waals adsorption of gases. Journal of the American Chemical Society, 62(7), 1723e1732. Djendoubi Mrad, N., Bonazzi, C., Boudhrioua, N., Kechaou, N., & Courtois, F. (2012). Influence of sugar composition on water sorption isotherms and on glass transition in apricots. Journal of Food Engineering, 111(2), 403e411. Foster, K. D., Bronlund, J. E., & Paterson, A. H. J. (2005). The prediction of moisture sorption isotherms for dairy powders. International Dairy Journal, 15(4), 411e418. Gabas, A. L., Menegalli, F. C., & Telis-Romero, J. (2000). Water sorption enthalpyentropy compensation based on isotherms of plum skin and pulp. Journal of Food Science, 65(4), 680. rez, J. V., Ca rcel, J. A., Clemente, G., & Mulet, A. (2008). Water sorption García-Pe isotherms for lemon peel at different temperatures and isosteric heats. LWT Food Science and Technology, 41(1), 18e25. Gharsallaoui, A., Roudaut, G., Chambin, O., Voilley, A., & Saurel, R. (2007). Applications of spray-drying in microencapsulation of food ingredients: an overview. Food Research International, 40(9), 1107e1121. ^a, P. C., Oliveira, G. H. H., & Afonso Júnior, P. C. (2013). Water Goneli, A. L. D., Corre sorption properties of coffee fruits, pulped and green coffee. LWT - Food Science and Technology, 50(2), 386e391. Goula, A. M., & Adamopoulos, K. G. (2010). A new technique for spray drying orange juice concentrate. Innovative Food Science & Emerging Technologies, 11(2), 342e351. Iglesias, H., & Chirife, J. (1982). Handbook of food Isotherms: Water sorption parameters for food and food components. New York: Academic Press Inc. Islam, M. I.-U., Edrisi, M., & Langrish, T. (2013). Improving process yield by adding WPI to lactose during crystallization and spray drying under high-humidity conditions. Drying Technology, 31(4), 393e404. Kammoun Bejar, A., Boudhrioua Mihoubi, N., & Kechaou, N. (2012). Moisture sorption isotherms e experimental and mathematical investigations of orange (Citrus sinensis) peel and leaves. Food Chemistry, 132(4), 1728e1735. Karel, M., & Nickerson, I. T. R. (1964). Effects of relative humidity, air, and vacuum on browning of dehydrated orange juice. Food Technology. (Chicago, IL, U. S.), 18(8), 104e108. Kaymak-Ertekin, F., & Gedik, A. (2004). Sorption isotherms and isosteric heat of sorption for grapes, apricots, apples and potatoes. LWT - Food Science and Technology, 37(4), 429e438. Keey, R. B. (1978). Introduction to industrial drying operations. Oxford; New York: Pergamon: Pergamon Press. Kelebek, H., Selli, S., Canbas, A., & Cabaroglu, T. (2009). HPLC determination of organic acids, sugars, phenolic compositions and antioxidant capacity of orange juice and orange wine made from a Turkish cv. Kozan. Microchemical Journal, 91(2), 187e192. Klewicki, R., Konopack, D., Uczciwek, M., Irzyniec, Z., Piasecka, E., & Bonazzi, C. (2009). Sorption isotherms for osmo-convectively-dried and osmo-freezedried apple, sour cherry, and blackcurrant. Journal of Horticultural Science & Biotechnology (ISAFRUIT Special Issue), 75e79. Labuza, T. P., & Altunakar, B. (2007). Water activity prediction and moisture sorption novas, A. J. Fontana, Jr., S. J. Schmidt, & T. P. Labuza isotherms. In G. V. Barbosa-Ca
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(Eds.), Water activity in foods - Fundamentals and applications (pp. 109e131). John Wiley & Sons. Langrish, T. A. G. (2009). Multi-scale mathematical modelling of spray dryers. Journal of Food Engineering, 93(2), 218e228. Lee, H. S., & Coates, G. A. (2000). Quantitative study of free sugars and myo-inositol in citrus juices by HPLC and a literature compilation. Journal of Liquid Chromatography & Related Technologies, 23(14), 2123e2141. Lewicki, P. P. (1997). The applicability of the GAB model to food water sorption isotherms. International Journal of Food Science & Technology, 32(6), 553e557. Maleki Majd, K., Karparvarfard, S., Farahnaky, A., & Jafarpour, K. (2013). Thermodynamic of water sorption of grape seed: temperature effect of sorption isotherms and thermodynamic characteristics. Food Biophysics, 8(1), 1e11. Maroulis, Z. B., Tsami, E., Marinos-Kouris, D., & Saravacos, G. D. (1988). Application of the GAB model to the moisture sorption isotherms for dried fruits. Journal of Food Engineering, 7(1), 63e78. Nyqvist, H. (1983). Saturated salt solutions for maintaining specified relative humidities. International Journal of Pharmaceutical Technology and Product Manufacture, 4(2), 47e48. Quirijns, E. J., van Boxtel, A. J. B., van Loon, W. K. P., & van Straten, G. (2005a). An improved experimental and regression methodology for sorption isotherms. Journal of the Science of Food and Agriculture, 85(2), 175e185. Quirijns, E. J., van Boxtel, A. J. B., van Loon, W. K. P., & van Straten, G. (2005b). Sorption isotherms, GAB parameters and isosteric heat of sorption. Journal of the Science of Food and Agriculture, 85(11), 1805e1814. Reid, D. S. (2007). Water activity: fundamentals and relationships. In G. V. Barbosanovas, A. J. Fontana, Jr., S. J. Schmidt, & T. P. Labuza (Eds.), Water activity in Ca foods - Fundamentals and applications (pp. 15e28). John Wiley & Sons. Rizvi, S. S. H., & Benado, A. L. (1983). Thermodynamic analysis of drying foods. Drying Technology, 2(4), 471e502.
Samaniego-Esguerra, C. M., Boag, I. F., & Robertson, G. L. (1991). Comparison of regression methods for fitting the GAB model to the moisture isotherms of some dried fruit and vegetables. Journal of Food Engineering, 13(2), 115e133. Seinfeld, J. H., & Pandis, S. N. (2006). Thermodynamics of aerosols. In J. H. Seinfeld, & S. N. Pandis (Eds.), Atmospheric chemistry and physics - From air pollution to climate change (2nd ed.). (pp. 434e460). John Wiley & Sons. Shrestha, A. K., Ua-arak, T., Adhikari, B. P., Howes, T., & Bhandari, B. R. (2007). Glass transition behavior of Spray dried orange juice powder measured by differential scanning calorimetry (DSC) and thermal mechanical compression test (TMCT). International Journal of Food Properties, 10(3), 661e673. Tapia, M. S., Alzamora, S. M., & Chirife, J. (2007). Effects of water activity (aw) on microbial stability: as a hurdle in food preservation. In G. V. Barbosa-C anovas, A. J. Fontana, Jr., S. J. Schmidt, & T. P. Labuza (Eds.), Water activity in foods Fundamentals and applications (pp. 239e255). John Wiley & Sons. Timmermann, E. O. (2003). Multilayer sorption parameters: BET or GAB values? Colloids and Surfaces A: Physicochemical and Engineering Aspects, 220(1e3), 235e260. Timmermann, E. O., Chirife, J., & Iglesias, H. A. (2001). Water sorption isotherms of foods and foodstuffs: BET or GAB parameters? Journal of Food Engineering, 48(1), 19e31. Tsami, E. (1991). Net isosteric heat of sorption in dried fruits. Journal of Food Engineering, 14(4), 327e335. Tsami, E., Maroulis, Z. B., Marinos-Kouris, D., & Saravacos, G. D. (1990). Heat of sorption of water in dried fruits. International Journal of Food Science & Technology, 25(3), 350e359. Van den Berg, C. (1981). Vapour sorption equilibria and other water-starch interactions : A physico-chemical approach (PhD thesis). Wageningen, Netherlands: Agricultural University (864).
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Moisture sorption isotherms and net isosteric heat of sorption for spray-dried pure orange juice powder Mona Edrisi Sormoli*, Timothy A.G. Langrish Drying and Process Technology Group, School of Chemical & Biomolecular Engineering, Building J01, the University of Sydney, Darlington, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2014 Received in revised form 9 September 2014 Accepted 30 September 2014 Available online xxx
The aim of this study was to measure the moisture sorption isotherms of spray-dried pure orange-juice powders. These isotherms have been fitted using eleven different sorption equations. The GAB model was found to be the best fit. The GAB parameters were estimated both by direct and indirect regression methods. The net isosteric heat of sorption was also determined using the ClausiuseClapeyron equation and was successfully used as a limiting condition for estimating the six unknown parameters of the GAB equation using the direct regression method. The net isosteric heat of sorption decreased from 9.05 kJ/ mol at 0.05 kg/kg dry basis to approximately 0.0 kJ/mol at 0.7 kg/kg dry basis. These values, as expected, were comparable to the enthalpy difference between the monolayer and multilayer moisture (8.16 kJ/ mol), and the difference between the latent heat of condensation for pure water and the heat of sorption of multilayer moisture (¼ 0.88 ± 0.69 kJ/mol). © 2014 Elsevier Ltd. All rights reserved.
Keywords: Moisture sorption isotherm Orange juice powder Spray drying GAB equation Net isosteric heat of sorption
1. Introduction Moisture sorption isotherms describe how strongly water is bound to a solid (Van den Berg, 1981). They present valuable thermodynamic data about the material being studied. These thermodynamic data are useful for design calculations of the drying process, as well as the prediction of the final moisture content for rez, Ca rcel, Clemente, & the product at the end of drying (García-Pe Mulet, 2008; Langrish, 2009; Rizvi & Benado, 1983; Tsami, 1991). They can also be used in predicting the storage stability of food products (Tapia, Alzamora, & Chirife, 2007). Hence they have been the focus of many studies. A moisture sorption isotherm can be used to predict the amount of water that a material will hold if it is exposed to air at a certain relative humidity and a certain temperature. This moisture content is dependent on the temperature and the environmental relative humidity, as well as on the composition of the material (Garcíarez et al., 2008; Keey, 1978). Once the moisture sorption isoPe therms are determined for at least three temperatures, the net isosteric heat of sorption can be calculated from the sorption isotherms by using the ClausiuseClapeyron equation.
* Corresponding author. Tel.: þ61 2 9351 5660; fax: þ61 2 9351 2854. E-mail addresses: [email protected], [email protected] (M. Edrisi Sormoli).
The water molecules, when they are in the form of moisture in a solid, have a different enthalpy from the enthalpy of pure water. If the water is bound to the solid, this enthalpy is less than the enthalpy of pure water by the energy of this binding (Keey, 1978). Consequently the moisture in a solid has a higher heat of evaporation than for pure water. The difference between this actual heat of evaporation for the moisture in the solid and the latent heat of evaporation of pure water is called the net isosteric heat of sorption or the enthalpy of wetting (Basu, Shivhare, & Mujumdar, 2006; Keey, 1978). By knowing the net isosteric heat of sorption, the actual energy required for drying a product to a specific moisture content can be calculated. The moisture sorption isotherms and the net isosteric heat of sorption are unique for every material and must be evaluated experimentally. Fruit juices are challenging high-sugar content food products to dry. Fruit juice powders can be of more value in terms of transportation and handling, packaging and storage, and shelf life, compared with their liquid form (Goula & Adamopoulos, 2010). Spray drying is one of the techniques used for producing powders from liquid solutions and suspensions. The spray-drying technique is 30e50 times cheaper than freeze drying (Gharsallaoui, Roudaut, Chambin, Voilley, & Saurel, 2007). Orange juice is one of the most popular and more commonly consumed fruit juices. However, due to the presence of large amounts of sugars and acids in orange juice, significant product loss occurs during spray drying because of the stickiness of the powders (Shrestha, Ua-arak, Adhikari, Howes, &
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
Bhandari, 2007). Hence, drying aids have been added to orange juice to overcome the stickiness issue during spray drying. As a result, there are just few studies on the moisture sorption isotherms for orange juice powders produced by spray drying which have used drying aids during the spray-drying process (Brennan, Herrera, & Jowitt, 1971). Brennan et al. (1971) used liquid glucose as a drying aid to spray dry orange juice and determined the moisture sorption isotherms for that mixture. There are also few studies on the sorption isotherms of pure orange juice powder produced with other techniques, such as freeze drying (Karel & Nickerson, 1964). Karel and Nickerson (1964) studied moisture sorption isotherms of pure dehydrated orange juice that had been produced by a company named Orange Crystals, Inc., Plant City, Florida. It is understood that the dehydrated juice had been produced by a vacuum-belt dryer and a freeze-drying technique. It has been reported in the literature that, for some food products, the drying method can affect the sorption isotherms of the final product significantly (Iglesias & Chirife, 1982). Hence there is a need to study the moisture sorption isotherms of pure spray-dried orange juice powders. Moisture-sorption isotherms are needed to predict the final moisture content of the spray-dried powders during the spraydrying process (Langrish, 2009). Combinations of temperature and moisture content in the final powders determine the glasstransition temperature of the product and the stickiness temperature that should be avoided during spray drying in order to reduce the product loss. Based on the knowledge obtained from the sorption isotherms, there may be some potential for spray drying the orange juice in its pure form. Therefore, the aim of this study has been to determine the moisture sorption isotherms and isosteric heat of sorption for pure spray-dried orange-juice powders. 2. Materials and methods 2.1. Materials Store-bought orange juice from Berri Pty Ltd, Australia was used for producing orange-juice powders. Laboratory-grade lithium chloride anhydrous, potassium acetate, magnesium nitrate, potassium iodide and potassium chloride from Chem-supply, Australia, magnesium chloride from, Unilab, Ajax Finechem, Australia and food-grade sodium chloride, SAXA, from Salpak Pty Ltd. Australia were used for salt solution preparation.
desiccator and was connected to a 6 V DC battery to enhance the rate of mass transfer and decrease the time required for equilibration. The batteries were connected through cables to the fans and were safely placed outside the desiccators and the oven. The temperatures at which the isotherms were measured were 20 C, 30 C, 40 C and 50 C. The desiccators were placed in a fanforced oven to maintain a constant temperature during all experiments, except for the 20 C isotherms where they were put in a low-temperature incubator (Shanghai Farui Instrument Co. Ltd, China). Two grams of freshly spray-dried orange juice powders were spread on a Petri dish and were put in each desiccator. The lid of the desiccators were double sealed using three layers of a thin polythene film to ensure a sealed environment in the desiccators. The samples were taken out of the desiccators every two days to measure their weight using a four-figure (±0.0001 g) analytical balance (Mettler Toledo AB204-S, Switzerland) until the mass change of the sample was less than 0.001 g. After a constant weight was observed, the equilibrium moisture content of the samples was determined by oven drying at 85 C for 24 h using a fan-forced drying oven and was reported on a dry basis (Thermoline TD 150F) (Islam, Edrisi, & Langrish, 2013). The whole procedure was repeated three times for each temperature.
2.3. Data analysis 2.3.1. Analysis of sorption data The equilibrium moisture content of the powders for each temperature was plotted against the corresponding water activity to produce the sorption isotherms. The water activity is equal to the relative humidity divided by 100 (Seinfeld & Pandis, 2006). Eleven different mathematical models (Kammoun Bejar, Boudhrioua Mihoubi, & Kechaou, 2012), among many in the literature, were used to fit to the experimental data using regression analysis. The curve fitting and regression analysis were performed using MATLAB R2013b. Inc, MathWorks Natick, Massachusetts, U.S.A. The best fit was chosen according to the minimum sum of squares due to error for the fit, abbreviated to SSE, minimum standard error of the fit RMSE, minimum mean absolute percentage error (P), and the maximum degrees of freedom adjusted R-square, R2Adj (R2Adj > 0.98 is considered here to be a reasonable fit).
SSE ¼
n X
wi ðyi b yiÞ
2
(1)
i¼1
2.1.1. Orange juice powder The orange juice was spray dried using a Buchi-B290 spray dryer (Buchi, Switzerland) at an inlet air temperature of 150 C, a pump rate of 4.9 ml/min, an aspirator flow rate of approximately 35 m3/h, and an atomizing air flow rate of 536 Nl/h. All experiments were performed in triplicate. The powders were placed in air-tight plastic bags and were used for the experiments immediately. 2.2. Determination of sorption isotherms In order to produce and maintain a range of relative humidities from 11% to 82%, saturated salt solutions of LiCl, CH3COOK, MgCl2, Mg (NO3)2, KI, NaCl and KCl were prepared by dissolving sufficient amounts of the dry salts into 60 C de-ionized water according to the technique used by Nyqvist (1983). These saturated solutions were placed in seven separate glass desiccators and were equilibrated at the respective experimental temperatures, for at least 24 h prior to each set of experiments. A fan with dimensions of 40 40 20 mm (model 412 DC axial compact) from ebm-papst A&NZ Pty Ltd, was placed in each
Where yi are the experimental data, b y i are the predicted data from the fit, and wi is the weighting applied to each data point, which was set to unity in these analyses.
R2Adj ¼ 1 SST ¼
SSEðn 1Þ SSTðvÞ
Xn i¼1
wi ðyi yi Þ2
v¼nm RMSE ¼
P¼
rffiffiffiffiffiffiffiffi SSE v
100XN yi b y i i¼1 y N i
(2)
(3) (4)
(5)
(6)
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
3
Table 1 The models used for fitting the sorption isotherms for orange juice powders. Name of the model
Equation
GAB (GuggenheimeAndersenede Boer)
Xe ¼
BET
Xe ¼
Reference
Xm $c$k$aw ð1k$aw Þð1k$aw þc$k$aw Þ Xm $c$aw ½ð1aw Þþðc1Þ$ð1aw Þ$aw
1 B Xe ¼ lnAa
Halsey
Maroulis et al. (1988) Kaymak-Ertekin and Gedik (2004) Iglesias and Chirife (1982)
w
Xe ¼ A$aBw þ C$aD w B aw Xe ¼ A$ 1a w
Kammoun Bejar et al. (2012)
Oswin Caurie Iglesias and Chirife
Xe ¼ expðA þ B$aw Þ aw Xe ¼ A þ B$ 1a w
Kammoun Bejar et al. (2012) Kammoun Bejar et al. (2012)
Smith White and Eiring
Xe ¼ A B$ðlnð1 aw ÞÞ
Kammoun Bejar et al. (2012) Kammoun Bejar et al. (2012)
Henderson
aw ¼ 1 expððB$XeA ÞÞ
Iglesias and Chirife (1982)
Kuhn
Xe ¼ lnAa þ B
Iglesias and Chirife (1982)
Peleg
1 Xe ¼ ðAþB$a wÞ
Iglesias and Chirife (1982)
w
Where SST is the total sum of squares, yi is the mean of experimental data, n is the number of experimental data points, and m is the number of coefficients in each equation. Eleven different models were used to fit the sorption isotherms to the experimental data for orange-juice powders (Table 1). There are many models in the literature for moisture sorption isotherms of food products. However, some models have been used more often by researchers.
2.3.2. Determination of net isosteric heat of sorption The net isosteric heat of sorption has been determined from the ClausiuseClapeyron equation by many researchers (Basu et al., 2006; Kammoun Bejar et al., 2012; Kaymak-Ertekin & Gedik, 2004; Maleki Majd, Karparvarfard, Farahnaky, & Jafarpour, 2013; Reid, 2007; Rizvi & Benado, 1983; Tsami, 1991), as follows:
0
1
qst;n ¼ qst DHvap
(8)
Where aw ¼ water activity, T ¼ temperature (K), qst;n ¼ net isosteric heat of sorption (kJ/mol water), qst ¼ isosteric heat of sorption, DHvap ¼ heat of vaporization of pure water (kJ/mol water), R ¼ 8.314 (kJ/kmol K). To determine the net isosteric heat of sorption, at a certain moisture content, the natural logarithm of the water activity was plotted against the inverse of the corresponding absolute temperature, and the regression line was plotted. The net isosteric heat of sorption was determined from the slope of the straight line. This process was repeated for different moisture contents to determine the net isosteric heat of sorption at different moisture contents (Tsami, 1991). 3. Results and discussion 3.1. Sorption isotherm models
Bd ln aw C B C ¼ qst;n @ A R d T1
(7)
Fig. 1 illustrates the moisture sorption behavior of spray-dried pure orange juice powder at four different temperatures, as fitted by the GAB equation.
and
Fig. 1. Sorption isotherms of spray-dried pure orange juice powders and the fitted GAB model at the four different temperatures. Each data point is the average of the three experimental replicates. Pure orange juice powders kept at (-) 20 C, ( ) 30 C, (△) 40 C and () 50 C.
▫
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
A sharp increase in the equilibrium moisture content was observed at higher water activities (aw > 0.45 at 50 C, aw > 0.48 at 40 C, aw > 0.51 at 30 C) (Fig. 1). This behavior has been reported in the literature for many high-sugar content foods, such as raisins, figs, apricots, prunes (Maroulis, Tsami, Marinos-Kouris, & Saravacos, 1988), grapes, apples (Kaymak-Ertekin & Gedik, 2004) and orange peels (Kammoun Bejar et al., 2012). It has been related to the dissolution of the fruit sugars in the sorbed water vapor (Kammoun Bejar et al., 2012; Kaymak-Ertekin & Gedik, 2004; Maroulis et al., 1988). It is well known from the literature that the composition of food products affects the moisture sorption capacity and the drying behavior of the food products (Iglesias & Chirife, 1982; Labuza & Altunakar, 2007). The dry solids in orange juice consist of more than 80% sugars with a sugar content ratio of 2:1:1 sucrose: glucose: fructose, respectively (Kelebek, Selli, Canbas, & Cabaroglu, 2009; Lee & Coates, 2000), which may explain the similarity in the sorption behavior of the orange juice powders with high-sugar content foods. The results of the regression analysis for fitting the experimental data to the eleven equations are summarized in Table 2. The models were sorted based on the minimum sum of squares due to error (SSE) except for the BET equation. In terms of the mean absolute percentage error (P) of the fits, those with less than 10% error can be considered acceptable (Foster, Bronlund, & Paterson, 2005; Kaymak-Ertekin & Gedik, 2004) and an R-square of >0.98 may also indicate a good fit. Regarding the BET equation, since only the data over the range of aw ¼ 0.1e0.5 were fitted into the equation, the SSE cannot be used for comparison and therefore the adjusted R-square was considered for comparison. By comparing the SSE and the adjusted R-square of the fits, it may be concluded that most of these equations can fit the sorption behavior of the spray-dried orange juice powders. As shown in Table 2 GAB model, has the minimum values for SSE and P and the maximum adjusted R-square when used to predict the moisture sorption isotherm of orange juice powder at 30 C, 40 C and 50 C, respectively. At 20 C (Table 2), the Peleg model, followed by the GAB model, has the minimum SSE and P. This trend suggests that both GAB and Peleg models fit the sorption isotherms of spray-dried pure orange juice over the range of temperatures from 20 C to 50 C better than the other studied models. The Peleg equation has been suggested by Kammoun Bejar et al. (2012) to best fit the moisture sorption isotherms for orange leaves and peels. However, in this study there is just one temperature at which the Peleg equation fits the moisture sorption data better than the GAB equation. Fig. 1 illustrates the moisture sorption behavior of spray-dried pure orange juice powder at four different temperatures, as fitted by the GAB equation. GAB model has been used by many researchers to predict the sorption isotherms of food products (Lewicki, 1997; Maroulis et al., 1988; Quirijns, van Boxtel, van Loon, & van Straten, 2005b; Timmermann, Chirife, & Iglesias, 2001) such as dried-onions and green beans (Samaniego-Esguerra, Boag, & Robertson, 1991), apple, black currant and sour cherries (Klewicki et al., 2009), apricots (Djendoubi Mrad, Bonazzi, Boudhrioua, ^a, Kechaou, & Courtois, 2012) and coffee fruit (Goneli, Corre Oliveira, & Afonso Júnior, 2013). The shape of the isotherms (Fig. 1) and the value for parameter c > 1 of the BET equation (Table 2) suggest that the moisture sorption isotherms for spray-dried pure orange juice powders are sigmoid and based on the classification of isotherms suggested by Brunauer, Deming, Deming, and Teller (1940) belong to type 2 class of isotherms. As discussed by Labuza and Altunakar (2007) at the water activity range of 0.2e0.3, the monolayer moisture content represents the optimal moisture content at which the dehydrated food products will have the maximum shelf-life. At this moisture content,
chemical reactions that require presence of water will begin, and above this moisture content, lipid oxidation (if any) will start. At a water activity range of (0.35e0.5), physical changes in food products such as loss of crispiness, caking and stickiness of powders occur. These changes are also related to the glass-transition temperature of the materials that should be taken into account. However, the critical moisture content in terms of microbial growth for food products has been suggested to be 0.6 (Labuza & Altunakar, 2007). Therefore, the safest water activity for orange juice powders and corresponding moisture contents at 20, 30 40 and 50 C will be at aw « 0.25 and moisture contents of 12.6, 10.9, 10.2 and 9.8% (w/w). The GAB equation and the definition of its three parameters are shown in equations (9)e(12).
Xe ¼
Xm $c$k$aw ð1 k$aw Þð1 k$aw þ c$k$aw Þ
(9)
DH1 Hm Hn ¼ C0 exp C ¼ C0 exp RT RT
(10)
DH2 H Hn k ¼ k0 exp ¼ k0 exp l RT RT
(11)
DHx Xm ¼ Xm0 exp RT
(12)
Where DH1 ¼ the difference between the heat of sorption for monolayer of water (Hm) and the heat of sorption for multilayer water (Hn), and DH2 ¼ the difference between the latent heat of condensation of pure water (Hl) and the heat of sorption for multilayer water (Hn) (Maroulis et al., 1988; Quirijns et al., 2005b). Equation (12) expresses the dependence of the monolayer moisture content (Xm) on the temperature. DHx is a constant parameter to express the temperature dependence of the monolayer moisture (Quirijns et al., 2005b). Xm is the amount of water that is adsorbed in a monolayer on the surface of the adsorbent (monolayer moisture content) and is a measure of the availability of active sorption sites (Quirijns et al., 2005b). The parameter c (Eqs. (9) and (10)) represents the strength of binding for water molecules to the primary binding sites on the product surface. The larger the value of c, the stronger the bonds between water molecules in the monolayer and the binding sites on the surface of the sorbent (Quirijns et al., 2005b). The parameter k (Eqs. (9) and (11)) is a correction factor for multilayer molecules relative to the bulk liquid; when k ¼ 1 the molecules beyond the monolayer have the same characteristics as pure water (Quirijns et al., 2005b). Hence when k ¼ 1, the heat of evaporation for the multilayer molecules is the same as that for pure water, and the GAB equation reduces to the BET equation (Samaniego-Esguerra et al., 1991). This physical meaning, the ability of the GAB equation to fit the moisture sorption data better than the other equations at three consecutive temperatures and the ability of the GAB equation to predict the moisture sorption isotherms of food products over a wide range (0.05 < aw < 0.8e0.9) (Timmermann, 2003), suggests that the GAB model is the preferred model to fit the moisture sorption behavior of the spray-dried pure orange juice powders in this study. 3.2. Heat of sorption As shown in Fig. 2, the net isosteric heat of sorption for orange juice powders increases sharply at lower moisture contents,
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5
Table 2 Predicted parameters of the fitted models to the experimental data for the moisture sorption isotherm of spray-dried pure orange juice powder at 20, 30, 40 and 50 C. Goodness of fit parameters
Model coefficients
Model type
Temperature ( C)
SSE*
Adj-R-sq
RMSE**
P (%)
A
B
C
D
GAB
20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50
0.003 0.005 0.0023 0.0044 0.0022 0.0058 0.0103 0.0065 0.0032 0.0085 0.0112 0.0075 0.0035 0.0087 0.0111 0.0072 0.0086 0.0107 0.0126 0.0082 0.0009 0.0011 0.0011 0.0004 0.0104 0.0123 0.0031 0.0091 0.013 0.0158 0.0159 0.0102 0.013 0.0175 0.0179 0.0146 0.0153 0.0154 0.0142 0.0107 0.0308 0.0454 0.0287 0.0243
0.99 0.99 0.99 0.99 0.99 0.99 0.97 0.98 0.99 0.99 0.97 0.98 0.99 0.99 0.97 0.98 0.99 0.98 0.97 0.98 0.98 0.96 0.95 0.97 0.98 0.98 0.99 0.98 0.98 0.98 0.96 0.97 0.98 0.97 0.96 0.96 0.98 0.98 0.97 0.97 0.98 0.97 0.97 0.98
0.014 0.0164 0.012 0.0167 0.0124 0.0179 0.0262 0.0209 0.0142 0.0206 0.0257 0.0209 0.0148 0.0208 0.0255 0.0206 0.0232 0.0231 0.0273 0.0219 0.0113 0.0098 0.0108 0.0069 0.0256 0.0248 0.0138 0.0231 0.0285 0.0281 0.0306 0.0245 0.0285 0.0296 0.0324 0.0293 0.0309 0.0277 0.0289 0.0251 0.0439 0.0477 0.0423 0.0378
3.6 5.8 7.0 6.2 6.3 5.2 7.3 6.3 6.4 7.9 7.9 7.9 7.1 9.1 8.7 7.4 9.8 10.2 7.9 7.0 8.0 6.1 8.6 6.2 11.9 11.1 9.1 9.6 13.8 13.0 13.1 11.6 16.5 16.5 17.2 18.4 11.6 13.0 10.2 10.7 7.0 14.4 12.0 11.5
7.613, c 8.956, c 9.485, c 6.885, c 0.279 0.2293 0.253 0.2295 0.09431 0.08495 0.08181 0.08675 0.2119 0.1966 0.1905 0.1763 3.289 3.192 3.139 3.286 9.755, c 12.85, c 8.806, c 7.274, c 0.1002 0.0932 0.0991 0.0946 0.08946 0.07881 0.07425 0.0595 9.644 10.88 11.45 12.78 0.01256 0.0157 0.01933 0.0086 1.171 1.15 1.162 1.096
0.953, k 0.969, k 0.9867, k 0.994, k 0.6321 0.5571 0.6499 0.6733 1.265 1.257 1.252 1.163 0.6357 0.6241 0.615 0.6589 3.31 3.064 2.92 3.054 0.1134, Xm 0.0981, xm 0.1031, Xm 0.09624, xm 0.05083 0.04306 0.0304 0.02359 0.1025 0.09543 0.0943 0.09728 9.546 10.87 11.51 13.15 0.3113 0.2804 0.262 0.2613 3.835 4.146 4.391 4.294
0.126, xm 0.109, xm 0.102, xm 0.098, xm 0.9557 0.8103 0.7472 0.7581 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e
e e e e 5.508 4.878 5.225 5.052 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e
Peleg
Halsey
Oswin
Caurie
BET
Kuhn
Iglesias and Chirife
White and Eiring
Smith
Henderson
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
reaching a maximum. This behavior has been previously observed for other food products (Kammoun Bejar et al., 2012; KaymakErtekin & Gedik, 2004; Quirijns et al., 2005b; Tsami, Maroulis, Marinos-Kouris, & Saravacos, 1990). The same trend was observed for spray-dried pure orange juice powders (Fig. 2). It has been reported that the enthalpy difference between the monolayer and multilayer moisture (DH1), calculated from the GAB equation for dried fruits, is approximately equal to the net isosteric heat of sorption at low moisture contents calculated using the ClausiuseClapeyron equation. Similarly, the difference between the latent heat of condensation of water and the enthalpy of sorption of the multilayer moisture (DH2) has been also reported to be approximately equal to the net isosteric heat of sorption at higher moisture contents (Quirijns et al., 2005b; Tsami et al., 1990). Quirijns et al. (2005b) stated the relationship between the net isosteric heat of sorption and the enthalpy components of the GAB equation using the following equation (13):
9.05 kJ/mol for 0.05 g/g dry solids to approximately 0.0 kJ/mol for 0.7 g/g dry solids moisture content. The maximum isosteric heat of sorption for spray-dried pure orange juice powders calculated in this study is comparable with the value for orange peels (8.00 kJ/ mol) calculated by Kammoun Bejar et al. (2012) and also falls within the range of the values reported in the literature for dried fruits and vegetables (Tsami et al., 1990). The decreasing trend of the isosteric heat of sorption suggests that the heat of sorption approaches the heat of vaporization of pure water at higher moisture contents. As the moisture content decreases and only the monolayer moisture is left, the water molecules become tightly bound to the surface of the powders and to the sorption sites with high interaction energies. At the same time, the heat of sorption increases above the heat of vaporization of pure water, making it difficult to remove water from the surface of the powders. Hence evaporating the water from orange juice is easier at higher moisture contents.
qst;n ¼ DH1 DH2
3.3. Parameters of the GAB equation
(13)
The net isosteric heat of sorption, calculated using the ClausiuseClapeyron, decreases with increasing moisture content from
It has been suggested by Maroulis et al. (1988) that a direct nonlinear regression analysis and curve fitting of the data were more
Please cite this article in press as: Edrisi Sormoli, M., & Langrish, T. A. G., Moisture sorption isotherms and net isosteric heat of sorption for spraydried pure orange juice powder, LWT - Food Science and Technology (2014), http://dx.doi.org/10.1016/j.lwt.2014.09.064
6
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Fig. 2. Variation in the net isosteric heat of sorption of spray-dried pure orange juice powders as a function of moisture content. (DH1): enthalpy difference between the monolayer and multilayer moisture, (DH2): the difference between the latent heat of condensation of pure water and the enthalpy of sorption of the multilayer moisture.
accurate for fitting the GAB parameters. There are three methods to determine the parameters of GAB equation. In the first method, the GAB equation is rearranged, and a polynomial regression analysis is performed. This method has been suggested to have two disadvantages. Firstly the transformation results in incorrect weighing of data and secondly the confidence intervals for the GAB parameters cannot be determined directly (Samaniego-Esguerra et al., 1991). Hence this method will not be discussed in this paper. In the second method, non-linear regression analysis of the standard threeparameter GAB equation (Eq. (9)) is performed, and the three parameters of the GAB equation (Xm, c and k) are determined at each temperature. Then the parameters DH1, DH2, c0, k0 are estimated by using a successive regression of equations (10) and (11). This second method is referred to here as the indirect regression method. In the third method, the definition of the parameters of the GAB equation c, k and Xm, (Eqs (10)e(12)) are substituted into the standard GAB equation (Eq. (9)). This substitution results in a form of GAB equation where the unknown parameters to be determined are DH1, DH2, DHx, c0, k0 and Xm0. A non-linear regression has been performed for this six-parameter GAB equation (Maroulis et al., 1988; Samaniego-Esguerra et al., 1991). This third method has been described as direct regression and has been recommended for predicting the GAB parameters (Samaniego-Esguerra et al., 1991). Direct regression considers and incorporates the temperature as a variable in the GAB equation. Hence, once these six unknowns are calculated, it is possible to calculate and predict the parameters of the GAB equation and consequently the moisture sorption behavior at other temperatures. However, the determination of six unknown parameters using regression analysis is quite challenging. Quirijns, van Boxtel, van Loon, and van Straten (2005a) argued that the Table 3 Parameters for GAB equation calculated from the indirect regression method. Temperature ( C) 20
30
GAB parameters ± 95% confidence bounds c 7.61 ± 3.56 8.956 ± 5.35 k 0.95 ± 0.02 0.97 ± 0.03 Xm (g/g) 0.126 ± 0.011 0.110 ± 0.013 Goodness of fit: *SSE: 0.003 0.005 R-square: 0.996 0.996 Adjusted 0.996 0.995 R-square: **RMSE: 0.0130 0.014 P (%) 3.59 5.76
40
50
9.48 ± 7.51 6.89 ± 5.06 0.99 ± 0.03 0.99 ± 0.04 0.102 ± 0.016 0.098 ± 0.017 0.005 0.992 0.992
0.004 0.989 0.987
0.016 6.96
0.018 6.15
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
physical meaning of the parameters of the GAB equation may get lost during the direct regression process, and these parameters are difficult to determine with high precision and within a narrow confidence interval. Both direct and indirect regression methods were used in this study to fit the experimental data to the GAB equation. Table 3 shows the calculated parameters for the GAB equation using the indirect regression methods. As found for the indirect regression method, the values of the monolayer moisture contents (Xm) decreased slightly as the temperature increased, whereas the parameter k slightly increased, and the parameter c also increased up to 40 C. A slight decrease in parameter c was observed at 50 C. The same increasing and decreasing trend for the parameter c has been reported in the literature for onions, apricots and green beans (Djendoubi Mrad et al., 2012; Samaniego-Esguerra et al., 1991) using the indirect regression method. All the calculated parameters in this study fall within the range found for c, k and Xm values for food products. It has been suggested that, in order to represent a sigmoid type of sorption isotherm, the parameters of the GAB equations should be kept in the following ranges: c > 5.67 and 0 < k < 1 (Lewicki, 1997). The monolayer moisture content has also been found to be comparable with the data found in the literature for similar fruits such as 12% (w/w) for dried apple, 17% (w/w) for dried sour cherry and 12% (w/w) for dried black currants (Klewicki et al., 2009).
Table 4 GAB parameters calculated using direct regression method. Coefficients ± 95% confidence bounds
GAB parameters calculated at different temperatures using the direct regression results
Temperatures ( C)
DH1, J/mol
8158 C0 0.329 ± 0.086 DH2, J/mol 883.5 ± 686.5 k0 1.375 ± 0.376 Xm0 0.0119 ± 0.0115 DHx, J/mol 5676 ± 2414 Goodness of the fit parameters SSE: 0.014 R-square: 0.99 Adjusted R-square: 0.99 RMSE: 0.014 P (%) 6.33
20
30
40
50
C
9.36
8.38
7.56
6.86
K
0.96
0.97
0.98
0.99
Xm
0.122
0.113
0.105
0.098
4.75
6.54
7.72
6.21
* Sum of squares due to error of the fit, ** root mean squared error (standard error), P: mean absolute percentage error.
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M. Edrisi Sormoli, T.A.G. Langrish / LWT - Food Science and Technology xxx (2014) 1e8
However, in the direct regression method, a slightly decreasing trend was observed for parameters c and Xm, and the same increasing trend as found from the indirect regression method was observed for parameter k (Table 4). When performing the regression analysis, the physical meaning of the parameters can be used to narrow down the estimation criteria for the unknown parameters. This helps to determine the values for the parameters within narrow confidence intervals. By using equation (13) as a limiting condition, and estimating the parameter DH1, the values for the parameters of the GAB equation were determined (Table 4). In other words the initial guessing value for DH1 was chosen to be approximately equal to the maximum net isosteric heat of sorption (qst,n). As shown in Table 4 the only parameter which could not be determined with high precision was the value of Xm0. A positive value for DH1 was expected as a result of the exothermic interaction of the water molecules with the sorption sites on the surfaces of the powders. A negative value is usually expected for DH2 due to the weaker bonding of the multilayer molecules (Gabas, Menegalli, & Telis-Romero, 2000; Maroulis et al., 1988; SamaniegoEsguerra et al., 1991; Tsami et al., 1990) which has been the case here. However, a positive value of the DH2 has been also reported for fruits at high water activities and has been related to the endothermic dissolution of fruit sugars in the absorbed water (Maroulis et al., 1988; Quirijns et al., 2005b). By substituting the results of the direct regression analysis into equations (10)e(12), the parameters of the GAB equations have been recalculated. As shown in Table 4, these parameters follow a reasonable trend and can predict the moisture sorption isotherms of the orange-juice powders with less than 8% mean absolute error. Therefore these parameters can be used with confidence to predict the moisture sorption behavior of orange-juice powders at different temperatures. Considering the explanation of the physical meaning for the GAB parameter c given previously and the data shown in Table 4, water molecules appear to be bound to spray-dried pure orange juice powders more strongly at lower temperatures than at higher temperatures. This binding between the water molecules and the powders becomes weaker at higher temperatures, and the monolayer moisture content of the powders also decreases. Values of c [ 1 and k ~ 1 indicate that the monolayer and multilayer moisture have significantly different binding strengths, and the heat of sorption of the multilayer moisture is the same as the latent heat of vaporization of pure water (Quirijns et al., 2005b). Considering this background, the GAB parameters for spray-dried pure orange juice suggest that the monolayer moisture is strongly bound to the surface of the powders; however, the multilayer moisture molecules are not structured and are almost the same as bulk liquid (pure water) molecules. This means that evaporation of water molecules from the orange-juice solids, at high moisture contents, needs the same heat of evaporation for pure water until the moisture content of the powders is nearly reduced to the value of the monolayer moisture content. After this point, much more energy must be used to evaporate the strongly bound water molecules from the surface of the solids. 4. Conclusions The moisture sorption isotherms for spray-dried pure orange juice have been studied at four different temperatures; 20 C, 30 C, 40 C and 50 C. Eleven different sorption models have been fitted to the experimental data. The GAB model fitted the experimental data well over a wider range of temperatures. Therefore the GAB model was chosen as the preferred model for predicting the moisture sorption isotherms of pure spray-dried orange juice powders. The GAB parameters were also determined using direct
7
regression technique. The net isosteric heats of sorption of spraydried pure orange juice powders were determined using the ClausiuseClapeyron equation, decreasing at greater moisture contents and ranging from 9.05 kJ/mol for 0.05 g/g dry solids to approximately 0.0 kJ/mol for 0.7 g/g dry solids. These values for the net isosteric heat of sorption were successfully used as limiting conditions to predict the six parameters of the GAB equation during the direct regression method. The differential enthalpy between the monolayer and multilayer moisture (DH1 ¼ 8.16 kJ/mol), and the difference between the latent heat of condensation for water and the heat of multilayer sorption for water (DH2 ¼ 0.88 ± 0.69 kJ/ mol), were estimated from direct regression analysis of the GAB equation to be comparable with the values calculated using the ClausiuseClapeyron equation. Acknowledgments Financial support from the Australian Research Council under the Linkage Grants Program (LP120200585) and LangTech International Pty Ltd is gratefully acknowledged. References Basu, S., Shivhare, U. S., & Mujumdar, A. S. (2006). Models for sorption isotherms for foods: a review. Drying Technology, 24(8), 917e930. Brennan, J. G., Herrera, J., & Jowitt, R. (1971). A study of some of the factors affecting the spray drying of concentrated orange juice, on a laboratory scale. International Journal of Food Science & Technology, 6(3), 295e307. Brunauer, S., Deming, L. S., Deming, W. E., & Teller, E. (1940). On a theory of the van der Waals adsorption of gases. Journal of the American Chemical Society, 62(7), 1723e1732. Djendoubi Mrad, N., Bonazzi, C., Boudhrioua, N., Kechaou, N., & Courtois, F. (2012). Influence of sugar composition on water sorption isotherms and on glass transition in apricots. Journal of Food Engineering, 111(2), 403e411. Foster, K. D., Bronlund, J. E., & Paterson, A. H. J. (2005). The prediction of moisture sorption isotherms for dairy powders. International Dairy Journal, 15(4), 411e418. Gabas, A. L., Menegalli, F. C., & Telis-Romero, J. (2000). Water sorption enthalpyentropy compensation based on isotherms of plum skin and pulp. Journal of Food Science, 65(4), 680. rez, J. V., Ca rcel, J. A., Clemente, G., & Mulet, A. (2008). Water sorption García-Pe isotherms for lemon peel at different temperatures and isosteric heats. LWT Food Science and Technology, 41(1), 18e25. Gharsallaoui, A., Roudaut, G., Chambin, O., Voilley, A., & Saurel, R. (2007). Applications of spray-drying in microencapsulation of food ingredients: an overview. Food Research International, 40(9), 1107e1121. ^a, P. C., Oliveira, G. H. H., & Afonso Júnior, P. C. (2013). Water Goneli, A. L. D., Corre sorption properties of coffee fruits, pulped and green coffee. LWT - Food Science and Technology, 50(2), 386e391. Goula, A. M., & Adamopoulos, K. G. (2010). A new technique for spray drying orange juice concentrate. Innovative Food Science & Emerging Technologies, 11(2), 342e351. Iglesias, H., & Chirife, J. (1982). Handbook of food Isotherms: Water sorption parameters for food and food components. New York: Academic Press Inc. Islam, M. I.-U., Edrisi, M., & Langrish, T. (2013). Improving process yield by adding WPI to lactose during crystallization and spray drying under high-humidity conditions. Drying Technology, 31(4), 393e404. Kammoun Bejar, A., Boudhrioua Mihoubi, N., & Kechaou, N. (2012). Moisture sorption isotherms e experimental and mathematical investigations of orange (Citrus sinensis) peel and leaves. Food Chemistry, 132(4), 1728e1735. Karel, M., & Nickerson, I. T. R. (1964). Effects of relative humidity, air, and vacuum on browning of dehydrated orange juice. Food Technology. (Chicago, IL, U. S.), 18(8), 104e108. Kaymak-Ertekin, F., & Gedik, A. (2004). Sorption isotherms and isosteric heat of sorption for grapes, apricots, apples and potatoes. LWT - Food Science and Technology, 37(4), 429e438. Keey, R. B. (1978). Introduction to industrial drying operations. Oxford; New York: Pergamon: Pergamon Press. Kelebek, H., Selli, S., Canbas, A., & Cabaroglu, T. (2009). HPLC determination of organic acids, sugars, phenolic compositions and antioxidant capacity of orange juice and orange wine made from a Turkish cv. Kozan. Microchemical Journal, 91(2), 187e192. Klewicki, R., Konopack, D., Uczciwek, M., Irzyniec, Z., Piasecka, E., & Bonazzi, C. (2009). Sorption isotherms for osmo-convectively-dried and osmo-freezedried apple, sour cherry, and blackcurrant. Journal of Horticultural Science & Biotechnology (ISAFRUIT Special Issue), 75e79. Labuza, T. P., & Altunakar, B. (2007). Water activity prediction and moisture sorption novas, A. J. Fontana, Jr., S. J. Schmidt, & T. P. Labuza isotherms. In G. V. Barbosa-Ca
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Please cite this article in press as: Edrisi Sormoli, M., & Langrish, T. A. G., Moisture sorption isotherms and net isosteric heat of sorption for spraydried pure orange juice powder, LWT - Food Science and Technology (2014), http://dx.doi.org/10.1016/j.lwt.2014.09.064