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Drying of garlic slices: Kinetics and nonlinearity measures for selecting the best equilibrium moisture content equation
Journal of Food Engineering 107 (2011) 347–352
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Drying of garlic slices: Kinetics and nonlinearity measures for selecting the best equilibrium moisture content equation A.C. Babetto a, F.B. Freire a, M.A.S. Barrozo b,⇑, J.T. Freire a a b
Department of Chemical Engineering, Federal University of São Carlos, C.P. 676, 13565-905 São Carlos, SP, Brazil School of Chemical Engineering, Federal University of Uberlândia, C.P. 593, 38400-902 Uberlândia, MG, Brazil
a r t i c l e
i n f o
Article history: Received 25 April 2011 Received in revised form 5 July 2011 Accepted 7 July 2011 Available online 18 July 2011 Keywords: Drying kinetics Sorption isotherms Nonlinearity measures Garlic slices
a b s t r a c t The objective of this work was to analyze the drying process of garlic slices based on an experimental study involving its equilibrium moisture content and drying kinetics. The equilibrium data were obtained by the static method using saturated salt solutions. The main equilibrium equations for biological materials were discriminated using some measures of nonlinearity. The drying kinetics was studied in a forced convection dryer, and the influence of three types of slices was analyzed. The results showed that the modified Halsey equation was the most suitable to represent the equilibrium data for garlic slices. The Page equation adequately represented the drying kinetics data. The highest drying rates of sliced garlic were obtained with crosswise cut. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Like other biological crops (Duarte et al., 2004), garlic (Allium sativum L.) is subject to waste due to respiration and microbial spoilage during storage. In fact, an estimated loss of 30% of fresh garlic crops is attributed to inadequate transportation and storage (Aware and Thorat, 2010). Dehydration of foods is one of the most common processes used to improve food stability, since it decreases considerably the microbiological activity and minimizes physical and chemical changes during it storage (Barrozo et al., 2001). Also, it extends the shelf-life with sensorial characteristics similar to those of fresh products (Sacilik and Unai, 2005). Besides the importance the drying garlic to preserve its properties, the demand for dried garlic has increased due to its widespread use as an ingredient in precooked foods and instant convenience foods (Figiel, 2009). The drying time by the convective technique can be shortened by using higher temperatures, which increase moisture diffusivity, and by cutting the material into small pieces. Thus, garlic can be dehydrated into different products such as flakes, slices, and powders. In the case of garlic slices, the cutting direction can affect the behavior of its drying kinetics. Knowledge of the drying kinetics and equilibrium moisture of biological materials in processing conditions is extremely important both for dryer design and for modeling drying processes. From a drying standpoint, the equilibrium sorption isotherms are also ⇑ Corresponding author. E-mail addresses: [email protected] (F.B. Freire), [email protected] (M.A.S. Barrozo). 0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.07.007
required to evaluate the driving force and to define the end point of the process. Sorption isotherms are also an extremely valuable tool for scientists because they can be used to predict potential changes in the stability of biological products. The available information on sorption equilibrium of garlic slices is rather scarce and does not cover the entire range of practical interest (Pezzutti and Crapiste, 1997). Besides, previous studies on drying kinetics of garlic do not provide information on the effect of type of cutting. Hence, experimental studies and application of simplified models to represent the drying behavior are still required (Pezzutti and Crapiste, 1997). Several equations have been proposed to correlate the equilibrium moisture content, Meq, of agricultural and food products as a function of the relative humidity of air, RH, and the temperature of solid material, Ts. Among these theoretical equations are several based on well-known theories of sorption kinetics such as those of Kelvin, Langmuir and BET (Dabrowski, 2001). However, in practical applications, these theoretical equations cannot accurately predict the equilibrium moisture content of biological materials over a wide range of temperatures and relative humidities. This has led some researchers to develop empirical or semi-empirical models in order to improve the accuracy of predicted Meq values. Table 1 presents several equations reported in the literature for estimating the Meq = f(RH,Ts) of biological materials. The coefficients a, b, c and d are the models’ parameters to be fitted to experimental data. These models have been tested and their parameters evaluated for many agricultural crops (Barrozo et al., 2008; Cordeiro et al., 2006; Ribeiro et al., 2005; Pagano and Mascheroni, 2005; Tolaba et al., 2004; Chen, 2003; Arnosti et al., 1999).
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A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Nomenclature a, b, n F K M Meq M0
MR R RH t T
parameters of the Eq. (6) Fisher’s statistics, dimensionless drying constant, Tn garlic moisture, dry base equilibrium moisture, dry base initial moisture, dry base
moisture, dimensionless correlation coefficient, dimensionless relative humidity of air, dimensionless time, T temperature, h
2.1. Experimental methodology
vessels contained a different saturated salt solution, corresponding to a range of relative humidities of 11–84% (Table 2). The amount of salt used was that corresponding to saturation at a high temperature. The garlic slices were placed on a perforated tray, positioned 30 mm above the base of the vessel to prevent any contact between the saturated salt solutions and the garlic samples. The vessels were then placed in an oven at controlled temperatures of 25, 30, 40, 45 and 50 °C (maximum variation of 0.5 °C), and kept under constant thermodynamic conditions. Equilibrium was considered to be attained when three subsequent measurements of the mass sample yielded identical results. Measurements were taken at intervals of 48 h. Each sample was weighed on an analytical balance with a precision of 1 mg. The dry weight of each sample was determined by the oven-drying method at 105 °C for 24 h. The assays were performed in three receptacles containing the same salt solution to check the reliability of the experimental procedure.
2.1.1. Equilibrium moisture content The garlic used in the experiments was of the purple variety. The equilibrium data were obtained by the static method, using saturated salt solutions, as proposed by Greenspan (1977). Salt was chosen in order to obtain a wider range of relative humidities. Table 2 describes the saturated salt solutions used here and the respective relative humidity at the five temperature levels employed in the experimental work. The samples were sealed in small cylindrical glass vessels with a base diameter of 40 mm and a height of 60 mm. Each of these
2.1.2. Drying kinetics To analyze how the type of cutting of the material influences the drying kinetics, the peeled garlic cloves were sliced in three different ways (halfwise, crosswise and lengthwise), as illustrated in Fig. 1. Each garlic slice was approximately of 2 mm thick. The experimental setup used here is illustrated schematically in Fig. 2. In this apparatus, the air impelled by a blower circulated in a closed circuit. The air was heated by electric resistances before the material entered the drying chamber. The humid air exiting the chamber was dried on a silica bed (relative humidity near 0%) be-
Since the majority of the sorption equilibrium equations in the literature are nonlinear, care should be taken when estimating their parameters from experimental data. In some situations, the estimators (especially, confidence intervals) may not be appropriate. Thus some procedures are available in the literature to validate the statistical properties of the least squares (LS) estimators of nonlinear models (Box, 1971; Bates and Watts, 1980). The present work focuses on to identify the best equilibrium moisture content equation for sliced garlic based on the bias measures proposed by Box (1971) and curvature measures (Bates and Watts, 1980). A forced convection dryer operating at different temperature is utilized to analyze the influence of the cutting direction of garlic slices on its drying kinetics. 2. Materials and methods
Table 1 Equilibrium moisture equations. Name
Equation
Henderson
Meq ¼
Henderson–Thompson
Meq ¼
Chung–Pfost
Meq ¼
Chen–Clayton
Meq ¼
Halsey modified
Meq ¼
Reference
1=b lnð1 RHÞ a Ts
lnð1 RHÞ a ðTs þ cÞ
ð1Þ
Henderson (1952)
ð2Þ
Thompson et al. (1968)
1=b
1 ðT s þ cÞ lnðRHÞ ln ð3Þ b a
1 cT ds
ln
lnðRHÞ
Chung and Pfost (1967)
!
aT bs
1=b expðaT s þ cÞ lnðRHÞ
ð4Þ
Chen and Clayton (1971)
ð5Þ
Osborn et al. (1989)
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352 Table 2 Relative humidity of air over saturated aqueous salt solutions at different temperatures (Greenspan, 1977). Salt solution
Temperature (C)
Lithium chloride Potassium acetate Magnesium chloride Potassium carbonate Sodium nitrite Sodium chloride Potassium chloride
25
30
40
45
50
0.113 0.225 0.328 0.432 0.645 0.753 0.843
0.113 0.216 0.324 0.432 0.635 0.750 0.834
0.112 0.204 0.318 0.432 0.616 0.748 0.818
0.111 0.198 0.315 0.433 0.606 0.747 0.809
0.111 0.192 0.312 0.433 0.597 0.746 0.802
cut 1
cut 2
halfwise
crosswise
cut 3 lenghtwise
Fig. 1. Garlic cutting directions.
fore restarting each cycle. The dryer had a glass viewing window, a pair of gloves for accessing the interior, a set of four trays and a digital analytical balance with a precision of 1 105 kg. After defining the operating conditions, the system was turned on and left empty until the air temperature stabilized at the desired level. The garlic slices were placed in the drying chamber only when this temperature became stable. The samples were weighed periodically using the analytical balance inside the unit. A typical time interval for weighing the sliced garlic was 15 s, while the whole experiment took 36,000 s. The temperature was monitored using copper-constantan thermocouples located in each tray and the air velocity was close to 1 m/s. At the end of each experiment, the samples were placed in an oven to determine their dry mass and then calculate their moisture content.
3. Calculation
like equilibrium sorption isotherms equations (Conceição Filho et al., 1998). Other properties are desirable for nonlinear models such as the least squares (LS) estimators, whose parameters are almost unbiased, normally distributed, and whose variances are close to the minimum variance (Lira et al., 2010). In this work we used the measures of nonlinearity developed by Bates and Watts (1980) and the bias measure proposed by Box (1971) to discriminate the equilibrium sorption isotherms equations presented in Table 1. Bates and Watts (1980) showed that the nonlinearity of a model can be separated into two components: an ‘‘intrinsic’’ nonlinearity (IN) and a ‘‘parameter-effects’’ nonlinearity (PE). The statistical significance of these measures pffiffiffi can be evaluated by comparing the IN and PE values with 1=2 F , where F = F(a, n p, p) is the inverse of Fisher’s probability distribution obtained at the significance level a. Such models should have both a low intrinsic nonlinearity (IN) and low parameter-effects (PE) nonlinearity. A negligible intrinsic nonlinearity (IN) will mean a negligible bias in the predicted values of response. If, at the same time, the parameter-effects (PE) nonlinearity is also negligible, the statistical tests of the consistency of the fitted parameters will be all the more valid. If the parameter-effects (PE) nonlinearity is significant, the bias of Box, expressed as a percentage of the LS estimate, is useful to identify the parameter(s) responsible by the nonlinearity. An absolute value in excess of 1% appears to be a good rule of thumb for indicating nonlinear behavior of the respective parameter (Ratkowsky, 1983). Details about the development, procedure and equations for determining intrinsic nonlinearity (IN), parameter-effects (PE) nonlinearity and bias of box are found in Bates and Watts (1980) and Box (1971), respectively. 3.2. Drying kinetic equation Empirical equations for drying kinetics have been widely used. The main justification for the empirical approach is the satisfactory fit to the experimental data. Eq. (6) is known as Page’s equation (Page, 1949) and is quite used in modeling of drying of biological products.
MR ¼ expðKt n Þ
3.1. Statistical analysis of the sorption isotherms
349
ð6Þ
where
2
Comparisons of the R values and residuals analysis may be insufficient to discriminate between nonlinear regression models
A – Dryer B – Silica Bed C – Blower D- Venturi
Fig. 2. Schematic diagram of the experimental apparatus.
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A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Table 3 Results of least square estimation and of the curvature and bias measures. R2 and F ratio
Equation Henderson (1)
a
2
R = 0.739 F = 416 R2 = 0.917 F = 932
IN = 0.082 PE = 2.71 IN = 0.064 PE = 124.27
Chung–Pfost (3)b
R2 = 0.843 F = 476
IN = 0.045 PE = 11.95
Chen–Clayton (4)c
R2 = 0.846 F = 361
IN = 0.135 PE = 33.30
Halsey modified (5)b
R2 = 0.949 F = 1536
IN = 0.038 PE = 0.102
b
Henderson–Thompson (2)
a b c
Curvature
Parameter
Estimated value 4
a b a b c a b c a b c d a b c
8.14 10 1.215 2.07 104 0.844 471.00 1806.1 0.0836 833.52 5.50 0.244 0.197 0.236 3.16 103 1.040 1.968
%Bias Box 2.57 0.42 0.68 0.11 51.86 959.1 0.21 916.6 43.56 2.43 22.52 1.08 0.318 0.056 0.058
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð2;92;0:95Þ ¼ 0:284. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð3;91;0:95Þ ¼ 0:304. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð4;90;0:95Þ ¼ 0:318.
MR ¼
M M eq M 0 M eq
ð7Þ
The relationship between the drying constant (K) and the temperature is usually represented by the Arrhenius equation (Barrozo et al., 2006):
K ¼ a exp
b T
ð8Þ
4. Results and discussion 4.1. Equilibrium sorption isotherms – parameters and nonlinearity measures Table 3 presents the results obtained by the least squares parameter estimation for the five model listed in Table 1. These results include the estimated parameter values (for Meq expressed in dry basis percentage, temperature in °C and RH in the decimal fraction), as well as the respective values of the quadratic regression coefficient (R2), the intrinsic curvature measure (IN), the parameter-effects (PE) measure and the bias percentage. As mentioned previously, the higher R2 value for the Halsey equation does not suffice to ensure the statistical validity of the parameters obtained in a nonlinear regression. In Table 3, it can be observed that all the calculated values of the pffiffiffi intrinsic curvature measures (IN) are not significant (IN < 1=2 F ), revealing only a small deviation of the model solution locus from linearity (Ratkowsky, 1983). On the other hand, the calculated values of PE (the parameters-effects pffiffiffi curvature measure) are significant for Eqs. (1)–(4) (PE > 1=2 F ), meaning that at least one parameter of these equations has a strong nonlinear behavior. The best results are obpffiffiffi tained with the modified Halsey model (Eq. (5)), since PE < 1=2 F for all the three parameters. Therefore, among the five equations, this modified Halsey equation behaves closest to the LS linear model approach, meaning valid inference results based on asymptotic approximations assumed in the LS nonlinear estimates. Since Eqs. (1)–(4) present significant nonlinear parameter-effects (PE), the bias measures should be used to identify parameters that are responsible for the nonlinear behavior (% bias > 1%). The largest bias is given by Eq. (3) (Chung–Pfost). Another important result is that the inclusion of a third parameter (c) in the Henderson equation, which originated the Henderson–Thompson equation, implies significant nonlinear behavior. Since this parameter is empirical, a reparameterization could be considered in order to
Table 4 Regression results of kinetic model (Eq. (15)). Parameter
Cut 1
Cut 2
Cut 3
a b n
32.2 103 4.25 103 0.78
8.4 103 3.71 103 0.70
9.7 102 3.42 103 0.87
R2
0.991
0.983
0.986
improve this nonlinear behavior. As predicted by the parameter-effects (PE) curvature measure, the first four equations presented at least one parameter with a percentage bias higher than 1%. It was also observed that only the Halsey equation presented a negligible bias for all parameters.
4.2. Drying kinetics The parameters of drying kinetic equation were estimated using the experimental results of each type of cut as a data set. The results of the regression are presented in Table 4. Figs. 3–5 present typical results of comparisons between the experimental data and the response from Eq. (6) for cuts 1, 2 and 3, respectively. These figures show a good agreement between the experimental results and the Page model. Fig. 6 shows the drying kinetics curves of the three types of cuts in the temperature of 25 °C. It can be see in this figure that the way that cut is made affects the drying kinetic. The drying rate obtained with cut in crosswise slices (cut 2) is higher than those obtained with halfwise and lengthwise cuts. The values of the drying constant (K) at 25 °C were 2.03 102, 3.28 102 and 1.00 102 minn, respectively for the cuts 1, 2 and 3. There are some works in literature that show that the thickness of sample food strongly influences the drying rate (Ertekin and Yaldiz, 2004; Condori et al., 2001), indicating that internal resistance to water migration in food material during drying is very important. In the present work the three different cutting directions of garlic slices had the same thickness: 2 mm. Thus, the results of this study show that not only the thickness but also the form the cut is made can influence the characteristics of drying. Moisture movement in food material during drying is due to a combination of different mechanisms, mainly liquid diffusion, capillary flow and vapor diffusion. The type of cut can influence significantly these moisture movement mechanisms.
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Fig. 3. Drying curves for cut 1 (halfwise).
351
Fig. 6. Drying curves for the three types of cuts in the temperature of 25 °C.
5. Conclusions The following conclusions can be drawn based on the results obtained in this work:
Fig. 4. Drying curves for cut 2 (crosswise).
In this work a deep statistic analysis on non-linear models used for to describe sorption isotherms is performed. The best model equation to describe the experimental sorption equilibrium data of garlic slices can be selected by using the discrimination approach based on nonlinearity measures. Among five models analyzed in this work, the modified Halsey equation is the only one for which curvature measures and bias were not significant. Thus, for this model, it is possible assume a negligible bias in the predicted values of the equilibrium moisture content of the garlic slices, and the statistical tests of the consistency of the fitted parameters will be all the more valid than the others equilibrium sorption equations. The Page equation used to describe the drying kinetics represented the experimental data adequately. The drying kinetics curves have been obtained with three different cutting directions of garlic slices with the same thickness: 2 mm. The highest drying rates of sliced garlic were obtained with cut 2 (crosswise cut). Thus, not only the thickness but also the form the cut is made can significantly influence the characteristics of garlic drying.
References
Fig. 5. Drying curves for cut 3 (lengthwise).
Arnosti Jr., S., Freire, J.T., Sartori, D.J.M., Barrozo, M.A.S., 1999. Equilibrium moisture content of Brachiaria brizantha. Seed Science and Technology 27, 273–282. Aware, R.S., Thorat, B.N., 2010. Garlic drying by various methods and its impact onallicin retention. In: Proceedings of the 17th International Drying Symposium, Magdeburg, Germany, pp. 1587–1585. Barrozo, M.A.S., Souza, A.M., Costa, S.M., Murata, V.V., 2001. Simultaneous heat and mass transfer between air and soybean seeds in a concurrent moving bed. International Journal of Food Science and Technology 36 (4), 393–399. Barrozo, M.A.S., Henrique, H.M., Sartori, D.J.M., Freire, J.T., 2006. The use of the orthogonal collocation method on the study of the drying kinetics of soybean seeds. Journal of Stored Products Research 42, 348–356. Barrozo, M.A.S., Silva, A.A.M., Oliveira, D.T., 2008. The use of curvature and bias measures to discriminate among equilibrium moisture equations for mustard seeds. Journal of Stored Products Research 44 (1), 65–70. Bates, D.M., Watts, D.G., 1980. Relative curvature measures of non-linearity. Journal of the Royal Statistical Society Series B 42, 1–25. Box, M.J., 1971. Bias in nonlinear estimation. Journal of the Royal Statistical Society Series B 33, 171–201.
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Chen, C., 2003. Moisture sorption isotherms of pea seeds. Journal of Food Engineering 58, 45–51. Chen, C.S., Clayton, J.T., 1971. The effect of temperature on sorption isotherms of biological materials. Transactions of the ASAE 14 (5), 927–929. Chung, D.S., Pfost, H.B., 1967. Adsorption and desorption of water vapour by cereal grains and their products part II. Transactions of the ASAE 10 (4), 549–551. Conceição Filho, R.S., Barrozo, M.A.S., Limaverde, J.R., Ataíde, C.H., 1998. The use of spouted bed in fertilizer coating over soybean seeds. Drying Technology 16 (9), 2049–2064. Condori, M., Echazu, R., Saravia, L., 2001. Solar drying of sweet pepper and garlic using the tunnel greenhouse drier. Renewable Energy 22 (4), 447–460. Cordeiro, D.S., Raghavan, G.S.V., Oliveira, W.P., 2006. Equilibrium moisture content models for Maytenus ilicifolia leaves. Biosystems Engineering 94, 221–228. Dabrowski, A., 2001. Adsorption – from theory to practice. Advances in Colloid and Interface Science 93, 135–224. Duarte, C.R., Vieira Neto, J.L., Lisboa, M.H., Murata, V.V., Barrozo, M.A.S., 2004. Experimental study and simulation of mass distribution of covering layer of soybean seeds coated in a spouted bed. Brazilian Journal of Chemical Engineering 21 (1), 59–67. Ertekin, C., Yaldiz, O., 2004. Drying of eggplant and selection of a suitable thin layer drying model. Journal of Food Engineering 63 (3), 349–359. Figiel, A., 2009. Drying kinetics and quality of vacuum-microwave dehydrated garlic cloves and slices. Journal of Food Engineering 94, 98–104. Greenspan, L., 1977. Humidity fixed points of binary saturated aqueous solutions. Journal of Research of the National Bureau of Standards 81, 89–93.
Henderson, S.M., 1952. A basic concept of equilibrium moisture content. Agricultural Engineering 33 (2), 29–31. Lira, T.S., Santos, K.G., Murata, V.V., Gianesella, M., Barrozo, M.A.S., 2010. The use of nonlinearity measures in the estimation of kinetic parameters of sugarcane bagasse pyrolysis. Chemical Engineering and Technology 33 (10), 1699–1705. Osborn, G.S., White, G.M., Sulaiman, A.H., Welton, L.R., 1989. Predicting equilibrium moisture proportions of soybeans. Transactions of the ASAE 32 (6), 2109– 2113. Pagano, A.M., Mascheroni, R.H., 2005. Sorption isotherms for amaranth grains. Journal of Food Engineering 67, 441–450. Page, G.E., 1949. Factors Influencing the Maximum Rates of Air Drying Shelled Corn in Thin-Layer. M.Sc. Purdue University, Indiana-USA. Pezzutti, A., Crapiste, G.H., 1997. Sorptional equilibrium and drying characteristics of garlic. Journal of Food Engineering 31, 113–123. Ratkowsky, D.A., 1983. Nonlinear Regression Analysis. Marcel Decker Inc., New York. Ribeiro, J.A., Oliveira, D.T., Passos, M.L., Barrozo, M.A.S., 2005. The use of nonlinearity measures to discriminate the equilibrium moisture equations for Bixa orellana seeds. Journal of Food Engineering 66, 63–68. Sacilik, K., Unai, G., 2005. Dehydration characteristics of Kastamonu garlic slices. Biosystems Engineering 92 (2), 201–215. Thompson, T.L., Peart, R.M., Foster, G.H., 1968. Mathematical simulation of corn drying – a new model. Transactions of the ASAE 11, 582–586. Tolaba, M.P., Peltzer, M., Enriquez, N., Pollio, M.L., 2004. Grain sorption equilibria of quinoa grains. Journal of Food Engineering 61, 365–371.
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Drying of garlic slices: Kinetics and nonlinearity measures for selecting the best equilibrium moisture content equation A.C. Babetto a, F.B. Freire a, M.A.S. Barrozo b,⇑, J.T. Freire a a b
Department of Chemical Engineering, Federal University of São Carlos, C.P. 676, 13565-905 São Carlos, SP, Brazil School of Chemical Engineering, Federal University of Uberlândia, C.P. 593, 38400-902 Uberlândia, MG, Brazil
a r t i c l e
i n f o
Article history: Received 25 April 2011 Received in revised form 5 July 2011 Accepted 7 July 2011 Available online 18 July 2011 Keywords: Drying kinetics Sorption isotherms Nonlinearity measures Garlic slices
a b s t r a c t The objective of this work was to analyze the drying process of garlic slices based on an experimental study involving its equilibrium moisture content and drying kinetics. The equilibrium data were obtained by the static method using saturated salt solutions. The main equilibrium equations for biological materials were discriminated using some measures of nonlinearity. The drying kinetics was studied in a forced convection dryer, and the influence of three types of slices was analyzed. The results showed that the modified Halsey equation was the most suitable to represent the equilibrium data for garlic slices. The Page equation adequately represented the drying kinetics data. The highest drying rates of sliced garlic were obtained with crosswise cut. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Like other biological crops (Duarte et al., 2004), garlic (Allium sativum L.) is subject to waste due to respiration and microbial spoilage during storage. In fact, an estimated loss of 30% of fresh garlic crops is attributed to inadequate transportation and storage (Aware and Thorat, 2010). Dehydration of foods is one of the most common processes used to improve food stability, since it decreases considerably the microbiological activity and minimizes physical and chemical changes during it storage (Barrozo et al., 2001). Also, it extends the shelf-life with sensorial characteristics similar to those of fresh products (Sacilik and Unai, 2005). Besides the importance the drying garlic to preserve its properties, the demand for dried garlic has increased due to its widespread use as an ingredient in precooked foods and instant convenience foods (Figiel, 2009). The drying time by the convective technique can be shortened by using higher temperatures, which increase moisture diffusivity, and by cutting the material into small pieces. Thus, garlic can be dehydrated into different products such as flakes, slices, and powders. In the case of garlic slices, the cutting direction can affect the behavior of its drying kinetics. Knowledge of the drying kinetics and equilibrium moisture of biological materials in processing conditions is extremely important both for dryer design and for modeling drying processes. From a drying standpoint, the equilibrium sorption isotherms are also ⇑ Corresponding author. E-mail addresses: [email protected] (F.B. Freire), [email protected] (M.A.S. Barrozo). 0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.07.007
required to evaluate the driving force and to define the end point of the process. Sorption isotherms are also an extremely valuable tool for scientists because they can be used to predict potential changes in the stability of biological products. The available information on sorption equilibrium of garlic slices is rather scarce and does not cover the entire range of practical interest (Pezzutti and Crapiste, 1997). Besides, previous studies on drying kinetics of garlic do not provide information on the effect of type of cutting. Hence, experimental studies and application of simplified models to represent the drying behavior are still required (Pezzutti and Crapiste, 1997). Several equations have been proposed to correlate the equilibrium moisture content, Meq, of agricultural and food products as a function of the relative humidity of air, RH, and the temperature of solid material, Ts. Among these theoretical equations are several based on well-known theories of sorption kinetics such as those of Kelvin, Langmuir and BET (Dabrowski, 2001). However, in practical applications, these theoretical equations cannot accurately predict the equilibrium moisture content of biological materials over a wide range of temperatures and relative humidities. This has led some researchers to develop empirical or semi-empirical models in order to improve the accuracy of predicted Meq values. Table 1 presents several equations reported in the literature for estimating the Meq = f(RH,Ts) of biological materials. The coefficients a, b, c and d are the models’ parameters to be fitted to experimental data. These models have been tested and their parameters evaluated for many agricultural crops (Barrozo et al., 2008; Cordeiro et al., 2006; Ribeiro et al., 2005; Pagano and Mascheroni, 2005; Tolaba et al., 2004; Chen, 2003; Arnosti et al., 1999).
348
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Nomenclature a, b, n F K M Meq M0
MR R RH t T
parameters of the Eq. (6) Fisher’s statistics, dimensionless drying constant, Tn garlic moisture, dry base equilibrium moisture, dry base initial moisture, dry base
moisture, dimensionless correlation coefficient, dimensionless relative humidity of air, dimensionless time, T temperature, h
2.1. Experimental methodology
vessels contained a different saturated salt solution, corresponding to a range of relative humidities of 11–84% (Table 2). The amount of salt used was that corresponding to saturation at a high temperature. The garlic slices were placed on a perforated tray, positioned 30 mm above the base of the vessel to prevent any contact between the saturated salt solutions and the garlic samples. The vessels were then placed in an oven at controlled temperatures of 25, 30, 40, 45 and 50 °C (maximum variation of 0.5 °C), and kept under constant thermodynamic conditions. Equilibrium was considered to be attained when three subsequent measurements of the mass sample yielded identical results. Measurements were taken at intervals of 48 h. Each sample was weighed on an analytical balance with a precision of 1 mg. The dry weight of each sample was determined by the oven-drying method at 105 °C for 24 h. The assays were performed in three receptacles containing the same salt solution to check the reliability of the experimental procedure.
2.1.1. Equilibrium moisture content The garlic used in the experiments was of the purple variety. The equilibrium data were obtained by the static method, using saturated salt solutions, as proposed by Greenspan (1977). Salt was chosen in order to obtain a wider range of relative humidities. Table 2 describes the saturated salt solutions used here and the respective relative humidity at the five temperature levels employed in the experimental work. The samples were sealed in small cylindrical glass vessels with a base diameter of 40 mm and a height of 60 mm. Each of these
2.1.2. Drying kinetics To analyze how the type of cutting of the material influences the drying kinetics, the peeled garlic cloves were sliced in three different ways (halfwise, crosswise and lengthwise), as illustrated in Fig. 1. Each garlic slice was approximately of 2 mm thick. The experimental setup used here is illustrated schematically in Fig. 2. In this apparatus, the air impelled by a blower circulated in a closed circuit. The air was heated by electric resistances before the material entered the drying chamber. The humid air exiting the chamber was dried on a silica bed (relative humidity near 0%) be-
Since the majority of the sorption equilibrium equations in the literature are nonlinear, care should be taken when estimating their parameters from experimental data. In some situations, the estimators (especially, confidence intervals) may not be appropriate. Thus some procedures are available in the literature to validate the statistical properties of the least squares (LS) estimators of nonlinear models (Box, 1971; Bates and Watts, 1980). The present work focuses on to identify the best equilibrium moisture content equation for sliced garlic based on the bias measures proposed by Box (1971) and curvature measures (Bates and Watts, 1980). A forced convection dryer operating at different temperature is utilized to analyze the influence of the cutting direction of garlic slices on its drying kinetics. 2. Materials and methods
Table 1 Equilibrium moisture equations. Name
Equation
Henderson
Meq ¼
Henderson–Thompson
Meq ¼
Chung–Pfost
Meq ¼
Chen–Clayton
Meq ¼
Halsey modified
Meq ¼
Reference
1=b lnð1 RHÞ a Ts
lnð1 RHÞ a ðTs þ cÞ
ð1Þ
Henderson (1952)
ð2Þ
Thompson et al. (1968)
1=b
1 ðT s þ cÞ lnðRHÞ ln ð3Þ b a
1 cT ds
ln
lnðRHÞ
Chung and Pfost (1967)
!
aT bs
1=b expðaT s þ cÞ lnðRHÞ
ð4Þ
Chen and Clayton (1971)
ð5Þ
Osborn et al. (1989)
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352 Table 2 Relative humidity of air over saturated aqueous salt solutions at different temperatures (Greenspan, 1977). Salt solution
Temperature (C)
Lithium chloride Potassium acetate Magnesium chloride Potassium carbonate Sodium nitrite Sodium chloride Potassium chloride
25
30
40
45
50
0.113 0.225 0.328 0.432 0.645 0.753 0.843
0.113 0.216 0.324 0.432 0.635 0.750 0.834
0.112 0.204 0.318 0.432 0.616 0.748 0.818
0.111 0.198 0.315 0.433 0.606 0.747 0.809
0.111 0.192 0.312 0.433 0.597 0.746 0.802
cut 1
cut 2
halfwise
crosswise
cut 3 lenghtwise
Fig. 1. Garlic cutting directions.
fore restarting each cycle. The dryer had a glass viewing window, a pair of gloves for accessing the interior, a set of four trays and a digital analytical balance with a precision of 1 105 kg. After defining the operating conditions, the system was turned on and left empty until the air temperature stabilized at the desired level. The garlic slices were placed in the drying chamber only when this temperature became stable. The samples were weighed periodically using the analytical balance inside the unit. A typical time interval for weighing the sliced garlic was 15 s, while the whole experiment took 36,000 s. The temperature was monitored using copper-constantan thermocouples located in each tray and the air velocity was close to 1 m/s. At the end of each experiment, the samples were placed in an oven to determine their dry mass and then calculate their moisture content.
3. Calculation
like equilibrium sorption isotherms equations (Conceição Filho et al., 1998). Other properties are desirable for nonlinear models such as the least squares (LS) estimators, whose parameters are almost unbiased, normally distributed, and whose variances are close to the minimum variance (Lira et al., 2010). In this work we used the measures of nonlinearity developed by Bates and Watts (1980) and the bias measure proposed by Box (1971) to discriminate the equilibrium sorption isotherms equations presented in Table 1. Bates and Watts (1980) showed that the nonlinearity of a model can be separated into two components: an ‘‘intrinsic’’ nonlinearity (IN) and a ‘‘parameter-effects’’ nonlinearity (PE). The statistical significance of these measures pffiffiffi can be evaluated by comparing the IN and PE values with 1=2 F , where F = F(a, n p, p) is the inverse of Fisher’s probability distribution obtained at the significance level a. Such models should have both a low intrinsic nonlinearity (IN) and low parameter-effects (PE) nonlinearity. A negligible intrinsic nonlinearity (IN) will mean a negligible bias in the predicted values of response. If, at the same time, the parameter-effects (PE) nonlinearity is also negligible, the statistical tests of the consistency of the fitted parameters will be all the more valid. If the parameter-effects (PE) nonlinearity is significant, the bias of Box, expressed as a percentage of the LS estimate, is useful to identify the parameter(s) responsible by the nonlinearity. An absolute value in excess of 1% appears to be a good rule of thumb for indicating nonlinear behavior of the respective parameter (Ratkowsky, 1983). Details about the development, procedure and equations for determining intrinsic nonlinearity (IN), parameter-effects (PE) nonlinearity and bias of box are found in Bates and Watts (1980) and Box (1971), respectively. 3.2. Drying kinetic equation Empirical equations for drying kinetics have been widely used. The main justification for the empirical approach is the satisfactory fit to the experimental data. Eq. (6) is known as Page’s equation (Page, 1949) and is quite used in modeling of drying of biological products.
MR ¼ expðKt n Þ
3.1. Statistical analysis of the sorption isotherms
349
ð6Þ
where
2
Comparisons of the R values and residuals analysis may be insufficient to discriminate between nonlinear regression models
A – Dryer B – Silica Bed C – Blower D- Venturi
Fig. 2. Schematic diagram of the experimental apparatus.
350
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Table 3 Results of least square estimation and of the curvature and bias measures. R2 and F ratio
Equation Henderson (1)
a
2
R = 0.739 F = 416 R2 = 0.917 F = 932
IN = 0.082 PE = 2.71 IN = 0.064 PE = 124.27
Chung–Pfost (3)b
R2 = 0.843 F = 476
IN = 0.045 PE = 11.95
Chen–Clayton (4)c
R2 = 0.846 F = 361
IN = 0.135 PE = 33.30
Halsey modified (5)b
R2 = 0.949 F = 1536
IN = 0.038 PE = 0.102
b
Henderson–Thompson (2)
a b c
Curvature
Parameter
Estimated value 4
a b a b c a b c a b c d a b c
8.14 10 1.215 2.07 104 0.844 471.00 1806.1 0.0836 833.52 5.50 0.244 0.197 0.236 3.16 103 1.040 1.968
%Bias Box 2.57 0.42 0.68 0.11 51.86 959.1 0.21 916.6 43.56 2.43 22.52 1.08 0.318 0.056 0.058
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð2;92;0:95Þ ¼ 0:284. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð3;91;0:95Þ ¼ 0:304. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 F ð4;90;0:95Þ ¼ 0:318.
MR ¼
M M eq M 0 M eq
ð7Þ
The relationship between the drying constant (K) and the temperature is usually represented by the Arrhenius equation (Barrozo et al., 2006):
K ¼ a exp
b T
ð8Þ
4. Results and discussion 4.1. Equilibrium sorption isotherms – parameters and nonlinearity measures Table 3 presents the results obtained by the least squares parameter estimation for the five model listed in Table 1. These results include the estimated parameter values (for Meq expressed in dry basis percentage, temperature in °C and RH in the decimal fraction), as well as the respective values of the quadratic regression coefficient (R2), the intrinsic curvature measure (IN), the parameter-effects (PE) measure and the bias percentage. As mentioned previously, the higher R2 value for the Halsey equation does not suffice to ensure the statistical validity of the parameters obtained in a nonlinear regression. In Table 3, it can be observed that all the calculated values of the pffiffiffi intrinsic curvature measures (IN) are not significant (IN < 1=2 F ), revealing only a small deviation of the model solution locus from linearity (Ratkowsky, 1983). On the other hand, the calculated values of PE (the parameters-effects pffiffiffi curvature measure) are significant for Eqs. (1)–(4) (PE > 1=2 F ), meaning that at least one parameter of these equations has a strong nonlinear behavior. The best results are obpffiffiffi tained with the modified Halsey model (Eq. (5)), since PE < 1=2 F for all the three parameters. Therefore, among the five equations, this modified Halsey equation behaves closest to the LS linear model approach, meaning valid inference results based on asymptotic approximations assumed in the LS nonlinear estimates. Since Eqs. (1)–(4) present significant nonlinear parameter-effects (PE), the bias measures should be used to identify parameters that are responsible for the nonlinear behavior (% bias > 1%). The largest bias is given by Eq. (3) (Chung–Pfost). Another important result is that the inclusion of a third parameter (c) in the Henderson equation, which originated the Henderson–Thompson equation, implies significant nonlinear behavior. Since this parameter is empirical, a reparameterization could be considered in order to
Table 4 Regression results of kinetic model (Eq. (15)). Parameter
Cut 1
Cut 2
Cut 3
a b n
32.2 103 4.25 103 0.78
8.4 103 3.71 103 0.70
9.7 102 3.42 103 0.87
R2
0.991
0.983
0.986
improve this nonlinear behavior. As predicted by the parameter-effects (PE) curvature measure, the first four equations presented at least one parameter with a percentage bias higher than 1%. It was also observed that only the Halsey equation presented a negligible bias for all parameters.
4.2. Drying kinetics The parameters of drying kinetic equation were estimated using the experimental results of each type of cut as a data set. The results of the regression are presented in Table 4. Figs. 3–5 present typical results of comparisons between the experimental data and the response from Eq. (6) for cuts 1, 2 and 3, respectively. These figures show a good agreement between the experimental results and the Page model. Fig. 6 shows the drying kinetics curves of the three types of cuts in the temperature of 25 °C. It can be see in this figure that the way that cut is made affects the drying kinetic. The drying rate obtained with cut in crosswise slices (cut 2) is higher than those obtained with halfwise and lengthwise cuts. The values of the drying constant (K) at 25 °C were 2.03 102, 3.28 102 and 1.00 102 minn, respectively for the cuts 1, 2 and 3. There are some works in literature that show that the thickness of sample food strongly influences the drying rate (Ertekin and Yaldiz, 2004; Condori et al., 2001), indicating that internal resistance to water migration in food material during drying is very important. In the present work the three different cutting directions of garlic slices had the same thickness: 2 mm. Thus, the results of this study show that not only the thickness but also the form the cut is made can influence the characteristics of drying. Moisture movement in food material during drying is due to a combination of different mechanisms, mainly liquid diffusion, capillary flow and vapor diffusion. The type of cut can influence significantly these moisture movement mechanisms.
A.C. Babetto et al. / Journal of Food Engineering 107 (2011) 347–352
Fig. 3. Drying curves for cut 1 (halfwise).
351
Fig. 6. Drying curves for the three types of cuts in the temperature of 25 °C.
5. Conclusions The following conclusions can be drawn based on the results obtained in this work:
Fig. 4. Drying curves for cut 2 (crosswise).
In this work a deep statistic analysis on non-linear models used for to describe sorption isotherms is performed. The best model equation to describe the experimental sorption equilibrium data of garlic slices can be selected by using the discrimination approach based on nonlinearity measures. Among five models analyzed in this work, the modified Halsey equation is the only one for which curvature measures and bias were not significant. Thus, for this model, it is possible assume a negligible bias in the predicted values of the equilibrium moisture content of the garlic slices, and the statistical tests of the consistency of the fitted parameters will be all the more valid than the others equilibrium sorption equations. The Page equation used to describe the drying kinetics represented the experimental data adequately. The drying kinetics curves have been obtained with three different cutting directions of garlic slices with the same thickness: 2 mm. The highest drying rates of sliced garlic were obtained with cut 2 (crosswise cut). Thus, not only the thickness but also the form the cut is made can significantly influence the characteristics of garlic drying.
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