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Effects of far-infrared radiation on the freeze-drying of sweet potato
Journal of Food Engineering 68 (2005) 249–255 www.elsevier.com/locate/jfoodeng
Effects of far-infrared radiation on the freeze-drying of sweet potato Yeu-Pyng Lin
a,b
, Jen-Horng Tsen c, V. An-Erl King
b,*
a
b
Department of Food Science and Technology, Tung-Fang Institute of Technology, 110 Tung-Fang Road, Hu-Nei Hsiang, Kaohsiung 829, Taiwan, ROC Department of Food Science, National Chung-Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan, ROC c Department of Nutrition, China Medical University, 91 Hsueh-Shih Road, Taichung 404, Taiwan, ROC Received 2 January 2004; accepted 31 May 2004
Abstract An experimental dryer was developed to determine the drying characteristics of sweet potato during freeze-drying with far-infrared radiation. The experimental drying time of sweet potato cubes dehydrated by three drying methods, i.e., air-drying, freeze-drying, and freeze-drying with far-infrared radiation, were compared, and freeze-drying with far-infrared radiation was found to be able to reduce the drying time of sweet potato. Both constant and falling rate drying periods were observed, and empirical equations were developed to study the behavior of drying rate in falling rate period. On the other hand, four mathematical models were used to describe the drying characteristics of sweet potato during freeze-drying with far-infrared radiation. The coefficients of determination (R2) in the exponential, Page, and approximate diffusion model were found to be above 0.98, and that of diffusion model was above 0.92. The rank of fitness of those models was Page, approximate diffusion, exponential and diffusion model. The choice of Page model was evident because of the lowest residual as well as RMSE. The Page model described the far-infrared freeze-drying characteristics of sweet potato properly. 2004 Elsevier Ltd. All rights reserved. Keywords: Far-infrared radiation; Freeze-drying; Sweet potato; Model
1. Introduction Sweet potato (Ipomoea batatas Lam.) is an important agricultural product in Taiwan, and applied in both fresh and dried forms. Since its root part is rich in b-carotene, food fiber, and potassium ion, etc., sweet potato is used widely in ready-to-eat foods such as noodles, Chinese style French fries, canned foods, etc. The technique of dehydration is probably the oldest method of food preservation practiced by mankind. The use of artificial drying to preserve agricultural products has been expanding, creating a need for more rapid and efficient drying techniques and methods that reduce energy consumption and cost in drying processes (Afzal, Abe, *
Corresponding author. Tel.: +886 4 22873192; fax: +886 4 22876211. E-mail address: [email protected] (V. An-Erl King). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.05.037
& Hikida, 1999). Innovative techniques that increase drying rates and enhance product quality have acquired considerable attention. Freeze-drying is an expensive process, and the cost might be reduced if processing time could be effectively shortened. This would require an increase in the rate of either mass transfer or heat transfer, whichever acting as the limiting factors. The heat transfer of traditional freeze-drying depends on temperature difference between frozen sample and ambient air as well as thermal conductivity of heating plate. Far-infrared radiation creates internal heating with molecular vibration of material, i.e., molecules absorb the radiation of certain wavelengths and energy, and cause vibration excitedly. Moreover, the mechanism of far-infrared drying is different from hot air drying (Mongpraneet, Abe, & Tsurusaki, 2002), and the electromagnetic wave energy is absorbed directly by the dried food with less energy loss.
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Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
Nomenclature t MR M M0 Me k K N n
drying time, h moisture ratio, dimensionless moisture content at any time, decimal dry basis initial moisture content, decimal dry basis equilibrium moisture content, decimal dry basis drying parameter in Eq. (1), h1 drying parameter in Eq. (2), h1 drying exponent in Eq. (2), dimensionless integer
At present, various driers have been developed by using far-infrared radiators. The utilization of far-infrared is a novel process that could increase the drying efficiency, save working space, and result in a clean working environment, etc. (Ratti & Mujumdar, 1995; Yamazaki, Hashimoto, Honda, & Shimizu, 1992). Ginzburg (1969) and Yagi and Kunii (1951) attempted to apply far-infrared to the drying of agricultural materials and improved results were reported. Combination of far-infrared radiation with convection or vacuum drying had also been tested (Abe & Afzal, 1997; Dontigny, Angers, & Supino, 1992; Hasatani, Arai, Itaya, & Onoda, 1983; Mongpraneet et al., 2002). Far-infrared drying of potato had attained high drying rates by using infrared heaters of high emissive power (Masamura et al., 1988). Although significant product value increases would occur if vacuum- or freeze-drying methods were combined with far-infrared treatment, only studies combining far-infrared and vacuum operation has been studied (Itoh & Chung, 1995; Mongpraneet et al., 2002). Similarly, combination of far-infrared radiation and freeze-drying could increase drying efficiency and enhance product quality. Since freeze-drying operation have to keep samples under low temperature to avoid thawing, temperature control by using far-infrared radiation could not be neglected. The objective of this study is to examine the drying behavior by the combination of freeze-drying and far-infrared radiation on sweet potato, estimating parameters of four drying models, and the accuracy of the prediction of those drying models were investigated. The outcome of this study would provide an innovative approach for further research development.
2. Materials and methods
L D A B W W0 a b R2 RMSE p
thickness of cube, mm diffusion coefficient, m2/h drying parameter in Eq. (6) drying parameter in Eq. (6) weight of sample, g initial weight of sample, g drying parameter in Eqs. (7) and (8), g/h drying parameter in Eqs. (7) and (8) coefficient of determination, dimensionless root mean square error, dimensionless absolute pressure, mm Hg
540, Eyela Co., Japan) and a far-infrared ceramic radiator, was used in this study. The far-infrared ceramic radiator (110 V) possesses a maximum power of 200 W, and emits thermal radiation in a wavelength range of 4–50 lm. The setting temperature of far-infrared ceramic radiator was 35 ± 0.5 C, and temperature was controlled by a micro-processor temperature controller (Model MC2838, Maxthermo Co., Japan). The far-infrared ceramic heater temperature was measured using type K thermocouples. Wire-equipped tray which contained the materials to be dried was fitted in the interior of a stainless drying chamber. The tray was placed under the far-infrared ceramic radiator and the distance between heater and sample was maintained constant at 2 cm through the experiments. The freeze-drying was operated under vacuum at an absolute pressure of 2 mm Hg. 2.2. Experimental procedure Sweet potato (Ipomoea batatas Lam.) was obtained from a local market at Taichung (Taiwan) in August 2003 and stored in a refrigerator at 4 ± 0.5 C for 48 h. Prior to freeze-drying, sweet potato was cut into cubes of 10, 17.5 and 25 mm, respectively. After blanching in 90 C hot water for 3 min, samples were frozen in a refrigerator at 60 ± 0.5 C. The drying system was run at least 1 h to obtain steady conditions before sample loading. Water loss from samples was tracked by a top-loading electronic scale fitted within the drying chamber. The accuracy of the weighing system was 0.01 g. 2.3. Models Four models were used to describe the behavior of freeze-drying with far-infrared radiation during drying process.
2.1. Experimental equipment A bench scale experimental FIR freeze-dryer (Fig. 1), constructed by combining a freeze-dryer (Model FDU-
2.3.1. The exponential model Many empirical equations describing thin layer drying of foods have been proposed in the literatures
Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
251
Fig. 1. Schematic view of experimental freeze-dryer with far-infrared radiation.
(Abe & Afzal, 1997; Bruce, 1985; Lahsasni, Kouhila, Mahrouz, & Jaouhari, 2004; Panchariya, Popovic, & Sharma, 2002), and Eq. (1) was proposed by Lewis (1921) and is known as the exponential model: MR ¼ expðktÞ:
ð1Þ
2.3.2. The Page model An empirical modification of the exponential model was made by Page (1949) , and an additional exponent (N) was involved in the exponential model as follows: MR ¼ expðKtN Þ:
ð2Þ
The Page model has been widely used in thin layer drying studies (Diamante & Munro, 1993; Madamba, Driscoll, & Buckle, 1996). Several researchers have successfully applied both the simple exponential and Page model to describe their results (Dandamrongrak, Young, & Mason, 2002; Lahsasni et al., 2004; Panchariya et al., 2002). 2.3.3. The diffusion model The most widely investigated theoretical model in the thin layer drying of different foods is given by the solution of FickÕs second law, using FickÕs diffusion model oM o2 M ¼D : ot oX 2
ð3Þ
Assuming uniform initial moisture distribution and negligible external resistance, the solution is
1 M Me 8 X 1 Dt 2 exp ð2n þ 1Þ p2 2 : ¼ 2 M 0 M e p n¼0 ð2n þ 1Þ L ð4Þ Simplifying this by taking the first term of the series solution and by assuming that Me = 0, gives M 8 2 Dt MR ¼ ¼ exp p 2 : ð5Þ M 0 p2 L This model was used by Maskan, Kaya, and Maskan (2002) to estimate the effective moisture diffusivity in the drying of grape leather (pestil). 2.3.4. Approximation of the diffusion model Various approximations and variations of the diffusion model have been used. The approximation of the diffusion model is the solution of the first term of the infinite series of FickÕs second law: MR ¼ A expðBtÞ:
ð6Þ
A and B are constants to be determined by the experimental data. Eq. (6) has been used in black tea drying studies (Panchariya et al., 2002). 2.4. Statistical analysis Drying rates of constant rate period and falling rate period were determined using Sigmaplot software (Scientific Graph System, version 7.00, SPSS Inc., 2001, USA). Estimation of parameters in those four models was conducted by using nonlinear regression
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drying rate of sweet potato under freeze-drying with far-infrared radiation could not be found in former literatures, both constant and falling rate drying period were observed in this study, and the constant drying rate were found to be 0.4344, 0.6633 and 1.259 g/h for 10, 17.5, and 25 mm of sweet potato cube, respectively. Samples should be kept under low temperature during freeze-drying to avoid thawing. Far-infrared radia-
analysis and fitness of models were evaluated (SPSS, version 8.0.1C, SPSS Inc., 1998, USA).
3. Results and discussion The experimental drying time of sweet potato cubes with various sizes dehydrated by using different methods was shown in Table 1. Far-infrared freeze-drying used less drying time, less than half the time required by freeze-drying. The size of sweet potato cube was found to be an important influence factor to drying time. Since the penetration of far-infrared radiation decreased with the thickness of sample, the effect of drying time reduction was not significant for 25 mm sweet potato cube. In this study, air drying method was found to spend more drying time. The utilization of far-infrared combined with freeze-drying provides an improved result, and the drying behavior of sweet potato with far-infrared freeze-drying deserves further investigation. 3.1. Analysis of drying rate Drying rate was determined according to the curve representing the variation, i.e., the slope of the weight of sample versus drying time. Since information about
Fig. 2. The change of moisture ratio of sweet potato cubes during freeze-drying with far-infrared treatment.
Table 1 The experimental drying time (h) of sweet potato cubes dried by various drying methodsa Methods
Length of cube (mm)
Freeze-drying with far infrared Freeze-drying (p = 2 mmHg) Air drying (50 C)
10
17.5
25
5.167 12.353 9.966
13.382 23.063 24.105
25.891 30.936 49.147
Table 2 Parameters of falling rate drying obtained in the freeze-drying of sweet potato cubes with far-infrared Falling rate drying equation (W = W0 + a · exp(bt))
Length of cube (mm)
10 17.5 25
W0
a (g/h)
b
R2
0.402 1.425 4.781
0.537 2.999 7.671
0.725 0.252 0.151
0.9946 0.9991 0.9998
Table 3 Coefficients of various models obtained in the freeze-drying of sweet potato cubes with far-infrared Length of cube (mm)
10 17.5 25
Exponential model (MR = exp(kt))
Page model (MR = exp(KtN))
Diffusion model (MR = (8/ p2) exp[(p2/L2) · Dt])
Approximation of the diffusion model (MR = A exp(Bt))
k
R2
K
N
R2
D (m2/h) · 106
R2
A
B
R2
0.544 0.225 0.135
0.9861 0.9872 0.9910
0.430 0.151 0.092
1.286 1.237 1.176
0.9995 0.9984 0.9980
4.606 5.815 7.065
0.9338 0.9281 0.9344
1.109 1.112 1.098
0.597 0.249 0.148
0.9935 0.9958 0.9978
Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
tion provided efficient heat transfer, and the temperature of far-infrared ceramic radiator was controlled at 35 C to avoid thawing of the frozen sample in this study. Water removing in freeze-drying is based on sublimation
253
of ice. On the other hand, nonexistence of a constant rate period either at high temperature or thin samples might be because of the quick drying on the surface of products at high temperature and a partial barrier is generated to resist the free movement of moisture (Maskan et al., 2002). Therefore, constant drying rate period was clearly observed in this study. Results of falling rate drying were shown in Table 2. Nonlinear regression was used to analyze the falling rate drying curve, and the falling rate drying equation was shown as Eq. (7), in which a and b represent drying parameters. Eq. (8) is the derivative of Eq. (7), and the drying rate of falling rate period could be calculated using a, b values. Falling rate drying equation W ¼ W 0 þ a expðbtÞ:
ð7Þ
Drying rate of falling rate period
dW ¼ a b expðbtÞ: dt
ð8Þ
Table 2 showed that the coefficient of determination (R2) of falling rate drying equation was all above 0.99. It indicated that drying rate of falling rate period could be predicted adequately by using the values of a and b. 3.2. Modelling of drying curves Since the initial moisture content of samples were not identical, the data of percentage dry basis moisture content versus time were transformed to dimensionless parameter as moisture ratio versus time. Fig. 2 shows the drying curve of sweet potato cubes with various sizes during freeze-drying with far-infrared radiation. Drying data obtained were fitted to four drying models, i.e. exponential, Page, diffusion, and approximate diffusion. Nonlinear regression analysis in the SPSS software was used to estimate the parameters of those four models. Coefficients of those four models obtained are listed in Table 3. The coefficients of determination (R2) for exponential, Page, and approximate diffusion model were all above 0.98, and that for diffusion model was lower, but still above 0.92. Largest coefficient of
Table 4 DuncanÕs multiple range test for comparison of mean RMSE values between the experimental and predicted moisture ratiosa
Fig. 3. Plots of moisture ratio residuals versus time of sweet potato cubes with different sizes during freeze-drying with far-infrared treatment.
Model
Mean RMSE
Groupingb
Exponential Page Diffusion Approximate diffusion
0.029137 0.009047 0.069927 0.017100
B D A C
a
5% Significant level. Means of RMSE with the same letter are not different significantly. b
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Table 5 Experimental and predicted drying time (h) of various models obtained in the freeze-drying of sweet potato cubes with far-infrareda Length of cube (mm)
Experimental drying time (h)
Predicted drying time (h) Exponential model (MR = exp(kt))
Page model (MR = exp(KtN))
Diffusion model (MR = (8/p2)exp[(p2/L2) · Dt])
Approximation of the diffusion model (MR = A exp(Bt))
10 17.5 25
5.167 13.382 25.891
7.288 17.620 29.367
5.626 14.038 24.536
8.259 20.007 33.635
6.814 16.348 27.419
a
Final moisture content: 5% (wet basis).
determination (R2) could be found in Page and approximate diffusion model. The larger values of coefficients k, K and B indicated that less drying time was used. Constant N values could be obtained in Page model. Evaluation of the goodness of fit of the tested models to the experimental data was not only determined by the coefficient of determination (R2) but also need other statistical data. Therefore, additional statistical analysis was processed to examine the accuracy of those four drying models. 3.3. Prediction accuracy of the drying models The residual plots and RMSE value were examined to assess the adequacy of each model. Plots of the residuals of moisture ratio against the independent variable of time are shown in Fig. 3. Residual is the difference between experimental results and predicted values obtained from a particular model. The residuals of the Page model were all found to be within 0.05, whereas the residuals of the exponential model and the approximate diffusion model were scattered within the range of 0.1. The residuals of the diffusion model raised up to 0.24 at early stages, and this indicated that it could not describe drying behavior accurately. Means of RMSE of those four models are presented in Table 4. DuncanÕs multiple range test was used for the comparison of the mean RMSE values between the experimental and predicted moisture ratios. The analysis indicated that those four models were significantly different among one another, and the rank of the fitness of models is Page, approximate diffusion, exponential, and diffusion. The choice of Page model was evident because of the smaller residual as well as RMSE. Abe and Afzal (1997) applied those four models to describe the thin-layer infrared radiation drying of rough rice, and Page model showed higher prediction accuracy of the drying model. Their results indicated significant difference between diffusion model and other models, and Page model also possessed smaller residual and RMSE. Based on a drying limit of the moisture content of sweet potato cubes of 5%, experimental and predicted drying time obtained were shown as Table 5. Page model was found to predict the drying time accurately.
On the other hand, the goodness of fit of the tested models to the experimental data was further tested by comparing residuals of moisture ratio and root mean square errors. Larger value of coefficients of determination (R2) and smaller value of the mean of the RMSE were chosen as the criteria for goodness of fit. It was found that Page model described the far-infrared freeze-drying characteristics of sweet potato properly. Accuracy of the prediction shows a good potential for the application of Page model in the prediction of freeze-drying of sweet potato combining with far-infrared radiation.
4. Conclusions Application of far-infrared radiation in freeze-drying could reduce drying time in freeze-drying, and empirical equation could be developed to illustrate the drying rate of the falling rate period. Four mathematical models were fitted to the far-infrared freeze-drying data of sweet potato and Page model gave better predictions than other models. This model was found to be able to describe the drying characteristics of freeze-drying using far-infrared radiation satisfactorily.
References Abe, T., & Afzal, T. M. (1997). Thin-layer infrared radiation drying of rough rice. Journal of Agricultural Engineering Research, 67, 289–297. Afzal, T. M., Abe, T., & Hikida, Y. (1999). Energy and quality aspects during combined FIR-convected drying of barley. Journal of Food Engineering, 42, 177–182. Bruce, D. M. (1985). Exposed-layer barley drying: Three models fitted to new data up to 150 C. Journal of Agricultural Engineering Research, 32, 337–347. Dandamrongrak, R., Young, G., & Mason, R. (2002). Evaluation of various pre-treatment for the dehydration of banana and selection of suitable drying models. Journal of Food Engineering, 55, 139–146. Diamante, L. M., & Munro, P. A. (1993). Mathematical modelling of the thin layer solar drying of sweet potato slices. Solar Energy, 51, 271–276. Dontigny, P., Angers, P., & Supino, M. (1992). Graphite slurry dehydration by infrared radiation under vacuum conditions. In A.
Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255 S. Mujumdar & M. A. Roques (Eds.), Drying’92. New York: Hemisphere. Ginzburg, A. S. (1969). Application of infrared radiation in food processing. Chemical and process engineering series. London: Leonard Hill. Hasatani, M., Arai, N., Itaya, Y., & Onoda, N. (1983). Drying of optically semitransparent materials by combined radiative–convective heating. Drying Technology, 1(2), 193–214. Itoh, K., & Chung, S. H. (1995). Drying of agricultural products using long wave infrared radiation (part 2)––Drying of welsh onion. Journal of the Society of Agricultural Structures, 26, 89– 96. Lahsasni, S., Kouhila, M., Mahrouz, M., & Jaouhari, J. T. (2004). Drying kinetics of prickly pear fruit (Opuntia ficus indica). Journal of Food Engineering, 61, 173–179. Lewis, W. K. (1921). The rate of drying of solid materials. Journal of Industrial Engineering Chemistry, 13(5), 427–432. Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1996). The thinlayer drying characteristics of garlic slices. Journal of Food Engineering, 29, 75–79. Masamura, A., Sado, H., Honda, T., Shimizu, M., Nabethani, H., Hakajima, M., & Watanabe, A. (1988). Drying of potato by far
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infrared radiation. Nippon Shokuhin Kogyo Gakkaishi, 35(5), 309–314. Maskan, A., Kaya, S., & Maskan, M. (2002). Hot air and sun drying of grape leather (pestil). Journal of Food Engineering, 54, 81–88. Mongpraneet, S., Abe, T., & Tsurusaki, T. (2002). Accelerated drying of welsh onion by far infrared radiation under vacuum conditions. Journal of Food Engineering, 55, 147–156. Page, G. E. (1949). Factors Influencing the Maximum Rates of Air Drying Shelled Corn in Thin Layer. Masters Thesis. Lafayette, IN: Purdue University. Panchariya, P. C., Popovic, D., & Sharma, A. L. (2002). Thin-layer modeling of black tea drying process. Journal of Food Engineering, 52, 349–357. Ratti, C., & Mujumdar, A. S. (1995). Infrared drying. In S. M. Arun (Ed.), Handbook of industrial drying (2nd ed.) (pp. 567–588). New York: Marcel Dekker. Yagi, S., & Kunii, D. (1951). Infrared drying characteristics of granular or powdery materials. Kagaku Kikai, 15(3), 108–123. Yamazaki, Y., Hashimoto, T., Honda, T., & Shimizu, M. (1992). Optical characteristics of gelatinous materials in infrared radiation drying. In A. S. Mujumdar & M. A. Roques (Eds.), Drying’92. New York: Hemisphere.
Effects of far-infrared radiation on the freeze-drying of sweet potato Yeu-Pyng Lin
a,b
, Jen-Horng Tsen c, V. An-Erl King
b,*
a
b
Department of Food Science and Technology, Tung-Fang Institute of Technology, 110 Tung-Fang Road, Hu-Nei Hsiang, Kaohsiung 829, Taiwan, ROC Department of Food Science, National Chung-Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan, ROC c Department of Nutrition, China Medical University, 91 Hsueh-Shih Road, Taichung 404, Taiwan, ROC Received 2 January 2004; accepted 31 May 2004
Abstract An experimental dryer was developed to determine the drying characteristics of sweet potato during freeze-drying with far-infrared radiation. The experimental drying time of sweet potato cubes dehydrated by three drying methods, i.e., air-drying, freeze-drying, and freeze-drying with far-infrared radiation, were compared, and freeze-drying with far-infrared radiation was found to be able to reduce the drying time of sweet potato. Both constant and falling rate drying periods were observed, and empirical equations were developed to study the behavior of drying rate in falling rate period. On the other hand, four mathematical models were used to describe the drying characteristics of sweet potato during freeze-drying with far-infrared radiation. The coefficients of determination (R2) in the exponential, Page, and approximate diffusion model were found to be above 0.98, and that of diffusion model was above 0.92. The rank of fitness of those models was Page, approximate diffusion, exponential and diffusion model. The choice of Page model was evident because of the lowest residual as well as RMSE. The Page model described the far-infrared freeze-drying characteristics of sweet potato properly. 2004 Elsevier Ltd. All rights reserved. Keywords: Far-infrared radiation; Freeze-drying; Sweet potato; Model
1. Introduction Sweet potato (Ipomoea batatas Lam.) is an important agricultural product in Taiwan, and applied in both fresh and dried forms. Since its root part is rich in b-carotene, food fiber, and potassium ion, etc., sweet potato is used widely in ready-to-eat foods such as noodles, Chinese style French fries, canned foods, etc. The technique of dehydration is probably the oldest method of food preservation practiced by mankind. The use of artificial drying to preserve agricultural products has been expanding, creating a need for more rapid and efficient drying techniques and methods that reduce energy consumption and cost in drying processes (Afzal, Abe, *
Corresponding author. Tel.: +886 4 22873192; fax: +886 4 22876211. E-mail address: [email protected] (V. An-Erl King). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.05.037
& Hikida, 1999). Innovative techniques that increase drying rates and enhance product quality have acquired considerable attention. Freeze-drying is an expensive process, and the cost might be reduced if processing time could be effectively shortened. This would require an increase in the rate of either mass transfer or heat transfer, whichever acting as the limiting factors. The heat transfer of traditional freeze-drying depends on temperature difference between frozen sample and ambient air as well as thermal conductivity of heating plate. Far-infrared radiation creates internal heating with molecular vibration of material, i.e., molecules absorb the radiation of certain wavelengths and energy, and cause vibration excitedly. Moreover, the mechanism of far-infrared drying is different from hot air drying (Mongpraneet, Abe, & Tsurusaki, 2002), and the electromagnetic wave energy is absorbed directly by the dried food with less energy loss.
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Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
Nomenclature t MR M M0 Me k K N n
drying time, h moisture ratio, dimensionless moisture content at any time, decimal dry basis initial moisture content, decimal dry basis equilibrium moisture content, decimal dry basis drying parameter in Eq. (1), h1 drying parameter in Eq. (2), h1 drying exponent in Eq. (2), dimensionless integer
At present, various driers have been developed by using far-infrared radiators. The utilization of far-infrared is a novel process that could increase the drying efficiency, save working space, and result in a clean working environment, etc. (Ratti & Mujumdar, 1995; Yamazaki, Hashimoto, Honda, & Shimizu, 1992). Ginzburg (1969) and Yagi and Kunii (1951) attempted to apply far-infrared to the drying of agricultural materials and improved results were reported. Combination of far-infrared radiation with convection or vacuum drying had also been tested (Abe & Afzal, 1997; Dontigny, Angers, & Supino, 1992; Hasatani, Arai, Itaya, & Onoda, 1983; Mongpraneet et al., 2002). Far-infrared drying of potato had attained high drying rates by using infrared heaters of high emissive power (Masamura et al., 1988). Although significant product value increases would occur if vacuum- or freeze-drying methods were combined with far-infrared treatment, only studies combining far-infrared and vacuum operation has been studied (Itoh & Chung, 1995; Mongpraneet et al., 2002). Similarly, combination of far-infrared radiation and freeze-drying could increase drying efficiency and enhance product quality. Since freeze-drying operation have to keep samples under low temperature to avoid thawing, temperature control by using far-infrared radiation could not be neglected. The objective of this study is to examine the drying behavior by the combination of freeze-drying and far-infrared radiation on sweet potato, estimating parameters of four drying models, and the accuracy of the prediction of those drying models were investigated. The outcome of this study would provide an innovative approach for further research development.
2. Materials and methods
L D A B W W0 a b R2 RMSE p
thickness of cube, mm diffusion coefficient, m2/h drying parameter in Eq. (6) drying parameter in Eq. (6) weight of sample, g initial weight of sample, g drying parameter in Eqs. (7) and (8), g/h drying parameter in Eqs. (7) and (8) coefficient of determination, dimensionless root mean square error, dimensionless absolute pressure, mm Hg
540, Eyela Co., Japan) and a far-infrared ceramic radiator, was used in this study. The far-infrared ceramic radiator (110 V) possesses a maximum power of 200 W, and emits thermal radiation in a wavelength range of 4–50 lm. The setting temperature of far-infrared ceramic radiator was 35 ± 0.5 C, and temperature was controlled by a micro-processor temperature controller (Model MC2838, Maxthermo Co., Japan). The far-infrared ceramic heater temperature was measured using type K thermocouples. Wire-equipped tray which contained the materials to be dried was fitted in the interior of a stainless drying chamber. The tray was placed under the far-infrared ceramic radiator and the distance between heater and sample was maintained constant at 2 cm through the experiments. The freeze-drying was operated under vacuum at an absolute pressure of 2 mm Hg. 2.2. Experimental procedure Sweet potato (Ipomoea batatas Lam.) was obtained from a local market at Taichung (Taiwan) in August 2003 and stored in a refrigerator at 4 ± 0.5 C for 48 h. Prior to freeze-drying, sweet potato was cut into cubes of 10, 17.5 and 25 mm, respectively. After blanching in 90 C hot water for 3 min, samples were frozen in a refrigerator at 60 ± 0.5 C. The drying system was run at least 1 h to obtain steady conditions before sample loading. Water loss from samples was tracked by a top-loading electronic scale fitted within the drying chamber. The accuracy of the weighing system was 0.01 g. 2.3. Models Four models were used to describe the behavior of freeze-drying with far-infrared radiation during drying process.
2.1. Experimental equipment A bench scale experimental FIR freeze-dryer (Fig. 1), constructed by combining a freeze-dryer (Model FDU-
2.3.1. The exponential model Many empirical equations describing thin layer drying of foods have been proposed in the literatures
Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
251
Fig. 1. Schematic view of experimental freeze-dryer with far-infrared radiation.
(Abe & Afzal, 1997; Bruce, 1985; Lahsasni, Kouhila, Mahrouz, & Jaouhari, 2004; Panchariya, Popovic, & Sharma, 2002), and Eq. (1) was proposed by Lewis (1921) and is known as the exponential model: MR ¼ expðktÞ:
ð1Þ
2.3.2. The Page model An empirical modification of the exponential model was made by Page (1949) , and an additional exponent (N) was involved in the exponential model as follows: MR ¼ expðKtN Þ:
ð2Þ
The Page model has been widely used in thin layer drying studies (Diamante & Munro, 1993; Madamba, Driscoll, & Buckle, 1996). Several researchers have successfully applied both the simple exponential and Page model to describe their results (Dandamrongrak, Young, & Mason, 2002; Lahsasni et al., 2004; Panchariya et al., 2002). 2.3.3. The diffusion model The most widely investigated theoretical model in the thin layer drying of different foods is given by the solution of FickÕs second law, using FickÕs diffusion model oM o2 M ¼D : ot oX 2
ð3Þ
Assuming uniform initial moisture distribution and negligible external resistance, the solution is
1 M Me 8 X 1 Dt 2 exp ð2n þ 1Þ p2 2 : ¼ 2 M 0 M e p n¼0 ð2n þ 1Þ L ð4Þ Simplifying this by taking the first term of the series solution and by assuming that Me = 0, gives M 8 2 Dt MR ¼ ¼ exp p 2 : ð5Þ M 0 p2 L This model was used by Maskan, Kaya, and Maskan (2002) to estimate the effective moisture diffusivity in the drying of grape leather (pestil). 2.3.4. Approximation of the diffusion model Various approximations and variations of the diffusion model have been used. The approximation of the diffusion model is the solution of the first term of the infinite series of FickÕs second law: MR ¼ A expðBtÞ:
ð6Þ
A and B are constants to be determined by the experimental data. Eq. (6) has been used in black tea drying studies (Panchariya et al., 2002). 2.4. Statistical analysis Drying rates of constant rate period and falling rate period were determined using Sigmaplot software (Scientific Graph System, version 7.00, SPSS Inc., 2001, USA). Estimation of parameters in those four models was conducted by using nonlinear regression
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drying rate of sweet potato under freeze-drying with far-infrared radiation could not be found in former literatures, both constant and falling rate drying period were observed in this study, and the constant drying rate were found to be 0.4344, 0.6633 and 1.259 g/h for 10, 17.5, and 25 mm of sweet potato cube, respectively. Samples should be kept under low temperature during freeze-drying to avoid thawing. Far-infrared radia-
analysis and fitness of models were evaluated (SPSS, version 8.0.1C, SPSS Inc., 1998, USA).
3. Results and discussion The experimental drying time of sweet potato cubes with various sizes dehydrated by using different methods was shown in Table 1. Far-infrared freeze-drying used less drying time, less than half the time required by freeze-drying. The size of sweet potato cube was found to be an important influence factor to drying time. Since the penetration of far-infrared radiation decreased with the thickness of sample, the effect of drying time reduction was not significant for 25 mm sweet potato cube. In this study, air drying method was found to spend more drying time. The utilization of far-infrared combined with freeze-drying provides an improved result, and the drying behavior of sweet potato with far-infrared freeze-drying deserves further investigation. 3.1. Analysis of drying rate Drying rate was determined according to the curve representing the variation, i.e., the slope of the weight of sample versus drying time. Since information about
Fig. 2. The change of moisture ratio of sweet potato cubes during freeze-drying with far-infrared treatment.
Table 1 The experimental drying time (h) of sweet potato cubes dried by various drying methodsa Methods
Length of cube (mm)
Freeze-drying with far infrared Freeze-drying (p = 2 mmHg) Air drying (50 C)
10
17.5
25
5.167 12.353 9.966
13.382 23.063 24.105
25.891 30.936 49.147
Table 2 Parameters of falling rate drying obtained in the freeze-drying of sweet potato cubes with far-infrared Falling rate drying equation (W = W0 + a · exp(bt))
Length of cube (mm)
10 17.5 25
W0
a (g/h)
b
R2
0.402 1.425 4.781
0.537 2.999 7.671
0.725 0.252 0.151
0.9946 0.9991 0.9998
Table 3 Coefficients of various models obtained in the freeze-drying of sweet potato cubes with far-infrared Length of cube (mm)
10 17.5 25
Exponential model (MR = exp(kt))
Page model (MR = exp(KtN))
Diffusion model (MR = (8/ p2) exp[(p2/L2) · Dt])
Approximation of the diffusion model (MR = A exp(Bt))
k
R2
K
N
R2
D (m2/h) · 106
R2
A
B
R2
0.544 0.225 0.135
0.9861 0.9872 0.9910
0.430 0.151 0.092
1.286 1.237 1.176
0.9995 0.9984 0.9980
4.606 5.815 7.065
0.9338 0.9281 0.9344
1.109 1.112 1.098
0.597 0.249 0.148
0.9935 0.9958 0.9978
Y.-P. Lin et al. / Journal of Food Engineering 68 (2005) 249–255
tion provided efficient heat transfer, and the temperature of far-infrared ceramic radiator was controlled at 35 C to avoid thawing of the frozen sample in this study. Water removing in freeze-drying is based on sublimation
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of ice. On the other hand, nonexistence of a constant rate period either at high temperature or thin samples might be because of the quick drying on the surface of products at high temperature and a partial barrier is generated to resist the free movement of moisture (Maskan et al., 2002). Therefore, constant drying rate period was clearly observed in this study. Results of falling rate drying were shown in Table 2. Nonlinear regression was used to analyze the falling rate drying curve, and the falling rate drying equation was shown as Eq. (7), in which a and b represent drying parameters. Eq. (8) is the derivative of Eq. (7), and the drying rate of falling rate period could be calculated using a, b values. Falling rate drying equation W ¼ W 0 þ a expðbtÞ:
ð7Þ
Drying rate of falling rate period
dW ¼ a b expðbtÞ: dt
ð8Þ
Table 2 showed that the coefficient of determination (R2) of falling rate drying equation was all above 0.99. It indicated that drying rate of falling rate period could be predicted adequately by using the values of a and b. 3.2. Modelling of drying curves Since the initial moisture content of samples were not identical, the data of percentage dry basis moisture content versus time were transformed to dimensionless parameter as moisture ratio versus time. Fig. 2 shows the drying curve of sweet potato cubes with various sizes during freeze-drying with far-infrared radiation. Drying data obtained were fitted to four drying models, i.e. exponential, Page, diffusion, and approximate diffusion. Nonlinear regression analysis in the SPSS software was used to estimate the parameters of those four models. Coefficients of those four models obtained are listed in Table 3. The coefficients of determination (R2) for exponential, Page, and approximate diffusion model were all above 0.98, and that for diffusion model was lower, but still above 0.92. Largest coefficient of
Table 4 DuncanÕs multiple range test for comparison of mean RMSE values between the experimental and predicted moisture ratiosa
Fig. 3. Plots of moisture ratio residuals versus time of sweet potato cubes with different sizes during freeze-drying with far-infrared treatment.
Model
Mean RMSE
Groupingb
Exponential Page Diffusion Approximate diffusion
0.029137 0.009047 0.069927 0.017100
B D A C
a
5% Significant level. Means of RMSE with the same letter are not different significantly. b
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Table 5 Experimental and predicted drying time (h) of various models obtained in the freeze-drying of sweet potato cubes with far-infrareda Length of cube (mm)
Experimental drying time (h)
Predicted drying time (h) Exponential model (MR = exp(kt))
Page model (MR = exp(KtN))
Diffusion model (MR = (8/p2)exp[(p2/L2) · Dt])
Approximation of the diffusion model (MR = A exp(Bt))
10 17.5 25
5.167 13.382 25.891
7.288 17.620 29.367
5.626 14.038 24.536
8.259 20.007 33.635
6.814 16.348 27.419
a
Final moisture content: 5% (wet basis).
determination (R2) could be found in Page and approximate diffusion model. The larger values of coefficients k, K and B indicated that less drying time was used. Constant N values could be obtained in Page model. Evaluation of the goodness of fit of the tested models to the experimental data was not only determined by the coefficient of determination (R2) but also need other statistical data. Therefore, additional statistical analysis was processed to examine the accuracy of those four drying models. 3.3. Prediction accuracy of the drying models The residual plots and RMSE value were examined to assess the adequacy of each model. Plots of the residuals of moisture ratio against the independent variable of time are shown in Fig. 3. Residual is the difference between experimental results and predicted values obtained from a particular model. The residuals of the Page model were all found to be within 0.05, whereas the residuals of the exponential model and the approximate diffusion model were scattered within the range of 0.1. The residuals of the diffusion model raised up to 0.24 at early stages, and this indicated that it could not describe drying behavior accurately. Means of RMSE of those four models are presented in Table 4. DuncanÕs multiple range test was used for the comparison of the mean RMSE values between the experimental and predicted moisture ratios. The analysis indicated that those four models were significantly different among one another, and the rank of the fitness of models is Page, approximate diffusion, exponential, and diffusion. The choice of Page model was evident because of the smaller residual as well as RMSE. Abe and Afzal (1997) applied those four models to describe the thin-layer infrared radiation drying of rough rice, and Page model showed higher prediction accuracy of the drying model. Their results indicated significant difference between diffusion model and other models, and Page model also possessed smaller residual and RMSE. Based on a drying limit of the moisture content of sweet potato cubes of 5%, experimental and predicted drying time obtained were shown as Table 5. Page model was found to predict the drying time accurately.
On the other hand, the goodness of fit of the tested models to the experimental data was further tested by comparing residuals of moisture ratio and root mean square errors. Larger value of coefficients of determination (R2) and smaller value of the mean of the RMSE were chosen as the criteria for goodness of fit. It was found that Page model described the far-infrared freeze-drying characteristics of sweet potato properly. Accuracy of the prediction shows a good potential for the application of Page model in the prediction of freeze-drying of sweet potato combining with far-infrared radiation.
4. Conclusions Application of far-infrared radiation in freeze-drying could reduce drying time in freeze-drying, and empirical equation could be developed to illustrate the drying rate of the falling rate period. Four mathematical models were fitted to the far-infrared freeze-drying data of sweet potato and Page model gave better predictions than other models. This model was found to be able to describe the drying characteristics of freeze-drying using far-infrared radiation satisfactorily.
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