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Vacuum drying characteristics of eggplants
Journal of Food Engineering 83 (2007) 422–429 www.elsevier.com/locate/jfoodeng
Vacuum drying characteristics of eggplants Long Wu a, Takahiro Orikasa a, Yukiharu Ogawa b, Akio Tagawa a,* a
Graduate School of Science and Technology, Chiba University, 648, Matsudo, Matsudo, Chiba 271-8510, Japan b Faculty of Horticulture, Chiba University, 648, Matsudo, Matsudo, Chiba 271-8510, Japan Received 7 February 2007; received in revised form 15 March 2007; accepted 17 March 2007 Available online 28 March 2007
Abstract The vacuum drying characteristics of eggplant were investigated. Drying experiments were carried out at vacuum chamber pressures of 2.5, 5 and 10 kPa, and drying temperature ranging from 30 to 50 °C. The effects of drying pressure and temperature on the drying rate and drying shrinkage of the eggplant samples were evaluated. The suitable model for describing the vacuum drying process was chosen by fitting four commonly used drying models and a suggested polynomial model to the experimental data; the effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick’s diffusion equation. The results showed that increasing drying temperature accelerated the vacuum drying process, while drying chamber pressure did not show significant effect on the drying process within the temperature range investigated. Drying shrinkage of the samples was observed to be independent of drying temperature, but increased notably with an increase in drying chamber pressure. A linear relationship between drying shrinkage ratio and dry basis moisture content was observed. The goodness of fit tests indicated that the proposed polynomial model gave the best fit to experimental results among the five tested drying models. The temperature dependence of the effective moisture diffusivity for the vacuum drying of the eggplant samples was satisfactorily described by an Arrhenius-type relationship. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Vacuum drying; Eggplant; Drying characteristics; Drying model
1. Introduction Drying is one of the most important methods of longterm food preservation. The removal of moisture from the food materials prevents the growth and reproduction of spoilage microorganisms, slows down the action of enzymes and minimizes many of the moisture mediated deteriorative reactions. Although drying processing effectively extends the shelf life of agricultural products, loss of sensory and nutritive qualities is considered inevitable during traditional drying process due to the undesirable textural and biochemical changes (Watson & Harper, 1988). Compared with conventional atmospheric drying, vacuum drying has some distinctive characteristics such as
*
Corresponding author. Tel./fax: +81 47 308 8847. E-mail address: [email protected] (A. Tagawa).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.03.030
higher drying rate, lower drying temperature and oxygen deficient processing environment etc., these characteristics may help to improve the quality and nutritive value of the dried products. Presently, vacuum drying has been applied to dry various food materials, the vacuum drying kinetics of many fruits and vegetables has been investigated and the effect of vacuum drying conditions on the drying process and the qualities of dried products has been evaluated (Arevalo-Pinedo & Murr, 2006; Arevalo-Pinedo & Murr, 2007; Bazyma et al., 2006; Cui, Xu, & Sun, 2004; Jaya & Das, 2003; Methakhup, Chiewchan, & Devahastin, 2005). Eggplant (Solanum melongena var. esculenta) is an important market vegetable of Asian and Mediterranean countries and has a very limited shelf life for freshness. In order to evaluate the practicability of vacuum drying for improving the quality of dried eggplant, it is necessary to carry out research on the vacuum drying characteristics of eggplant fruit. The objectives of this study were to
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
423
Nomenclature A Deff Ea L M M0 Me MR P P0 R
area (m2) effective moisture diffusivity (m2 s1) activation energy (kJ kg1) sample thickness (m) moisture content (d.b., decimal) initial moisture content (d.b., decimal) equilibrium moisture content (d.b., decimal) moisture ratio pressure (kPa) mean relative deviation (%) gas constant (0.462 kJ kg1 K1)
investigate the vacuum drying characteristics of the eggplant samples, to evaluate the effect of vacuum drying conditions on the drying process, and to choose a suitable drying model for describing the whole drying process. 2. Material and methods 2.1. Sample preparation Fresh eggplants (cultivated in Kochi Prefecture Japan, cultivar: unknown) were purchased from a local market and stored at 8 °C before experiments started, the storage time was not more than 12 h in this study. The central part of each eggplant fruit was cut into a rectangular-shaped block of 45 25 20 mm for drying treatment. The initial moisture content of the sample blocks was determined as 94.00% in wet basis (N = 20, standard deviation: 0.52%) according to the vacuum oven method (i.e., drying at 70 °C and 2.5 kPa for 12 h) (AOAC, 1995). 2.2. Experimental setup A schematic diagram of the experimental vacuum drying system is shown in Fig. 1. The system primarily consists of an oil rotary vacuum pump (TSW-300, SATO VAC, Japan), a vacuum control unit (NVC-2000L, Tokyo Rikakikai, Japan) to obtain various processing pressures in the vacuum drying chamber (a glass desiccator) and a forced convection drying oven (DO600FA, AS ONE, Japan) to maintain desired drying temperatures. A data acquisition system composed of a load cell (LTS-50GA, KYOWA, Japan) which was fixed on a supporting frame, a wire netting sample holder suspended from the load cell, an instrumentation amplifier (WGA-710A, KYOWA, Japan) and a data logger (KEYENCE, NR-1000, Japan) was used to on-line monitor and record the changes in sample weight during drying. Hot air drying runs at 30– 50 °C and atmospheric pressure were also conducted in the same glass desiccator with the top lid removed for comparison.
R2 Rd RMSE t T V Wd a,b h v2
coefficient of determination drying rate (kg m2 h1) root mean square error time (h) temperature (K) volume (m3) weight of dry matter (kg) coefficients in drying model time (s) reduced chi-square
2.3. Experimental procedure The vacuum drying chamber was preheated for 12 h before the experiments started to obtain stable drying temperature. Drying experiments were conducted in the drying chamber at temperatures ranging from 30 to 50 °C, and pressures of 2.5, 5, 10 kPa as well as atmospheric pressure, respectively. One sample was placed on the wire netting basket and dried in each run, its weight was continuously recorded at intervals of 5 min using the data acquisition system throughout the drying process. It was considered that the sample reached the equilibrium moisture content (EMC) of drying when the reading of weight remained the same for 1 h. Fresh samples were dried under the above-mentioned conditions for durations ranging from 1 to 15 h individually to evaluate the drying shrinkage. Approximate volume and surface area of the dried samples were calculated from the measured dimensions data. According to preliminary tests, in which a comparison between the calculated results and the measured volume of the dried samples using liquid displacement method (Maskan, 2001; Orikasa, Tagawa, Nakamura, & Iimoto, 2005; Zogzas, Maroulis, & Marinos-Kouris, 1994) was conducted, the calculated results were proved to be acceptable, similar results were reported by Ratti (1994). 2.4. Data analysis The average moisture content of each sample during drying was calculated from the sample weight recorded by the data acquisition system (moisture distribution in the sample was considered to be uniform in this study). Moisture ratio (MR) of the sample was determined by the following equation: MR ¼
ðM M e Þ ðM 0 M e Þ
ð1Þ
where M is the average moisture content of a sample at any time of drying, M0 and Me stand for the initial and equilibrium moisture content, respectively.
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Fig. 1. Schematic diagram of vacuum drying system: 1. vacuum pump, 2. cold trap, 3. vacuum control unit, 4. forced convection drying oven, 5. glass desiccator, 6. load cell, 7. supporting frame, 8. wire netting sample holder, 9. instrumentation amplifier, and 10. data logger.
Drying curves (MR vs. time) were plotted and fitted by four empirical drying models (i.e., proposed polynomial model, exponential model, Page’s model and logarithmic model), and a theoretical model based on the Fick’s diffusion law; model coefficients were calculated using OriginPro 7.5 software (OriginLab Corp.). The goodness of fit was evaluated by the coefficient of determination (R2), the root mean square error (RMSE), the reduced chisquare (v2) and mean relative deviation modulus (P0 ) defined by the following equation n Y exp;i Y pre;i 100 X 0 P ¼ ð2Þ N i¼1 Y exp;i where Yexp,i is the experimental result of the investigated variable, Ypre,i is the predicted value from various mathematical models, N is the number of observations (Chen & Morey, 1989; Jena & Das, 2007; Madamba, Driscoll, & Buckle, 1996; Sacilik & Elicin, 2006). The best model describing the vacuum drying process of the eggplant samples was chosen as the one with the highest R2 and the least RMSE, v2 and P0 . Comparisons between means were performed in SPSS 12.0 software (SPSS Inc.) using Duncan’s multiple range tests at a significance level of 0.05. 3. Results and discussion 3.1. Effect of vacuum drying conditions on drying process After vacuum drying, the moisture content of the eggplant samples was reduced from a initial value of 15.67 to less than 0.2 kg water/kg dry matter. The effects of drying temperature and pressure on the vacuum drying process are shown in Figs. 2 and 3a,b, in which drying curves (moisture content in dry basis vs. time) under different drying
conditions were plotted. From Fig. 2, the drying time needed to reach the EMC was shortened notably with an increase in drying temperature due to a larger driving force for heat and mass transfer at higher drying temperature. Fig. 3 showed that drying chamber pressure ranging from 2.5 to 10 kPa did not affect the drying process as strongly as drying temperature did. For the present vacuum drying conditions, the effect of drying chamber pressure on the drying process was not significant. According to the reports of Arevalo-Pinedo and Murr (2006) and Arevalo-Pinedo and Murr (2007) for carrot and pumpkin, Cui et al. (2004) for carrot, Giri and Prasad (2007) for mushroom, and Methakhup et al. (2005) for Indian gooseberry, drying pressure had a certain effect on the drying process, the drying time was reduced by decreasing drying pressure. The differentiation between the results of this study and the literature could be attributed to the different processing conditions as well as different degrees of boiling point elevation caused by various plasma concentrations of the tested materials. 3.2. Drying shrinkage Drying shrinkage affects not only the product quality but also the drying process and rehydration capability of the dried food materials (Karathanos, Anglea, & Karel, 1993; Maskan, 2001; Mcminn & Magee, 1997a, 1997b). Ratti (1994) indicated that changes in the dimensions of dried sample were independent of drying conditions but dependent on the geometric shape and type of foodstuff. Souma, Tagawa, and Iimoto (2004) reported that the hot air drying shrinkage of eggplant is very remarkable and the reduction in sample volume was larger than the volume of removed water due to its high porosity, similar tendency were also observed in this study, as shown in Fig. 4. In order to investigate the drying shrinkage of the samples, drying experiments with different drying durations
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
1.0
P = 2.5 kPa 30 °C 40 °C 50 °C
15 10
50 °C Hotair drying
5 0
0
5
10
15
20
25
Drying time (h)
were carried out under various drying conditions, the volume and surface area of the dried samples were calculated. Fig. 5 presents the relationship between the volume shrinkage ratio (V/V0) and the moisture content of the samples dried at 2.5 kPa and various drying temperatures, the results indicated that drying temperature had insignificant effect on the drying shrinkage of the eggplant samples for the investigated temperature range. Fig. 6 shows the effect of drying chamber pressure on the drying shrinkage of the samples at 50 °C, it can be seen that the shrinkage became more severe at higher vacuum chamber pressures. This phenomenon could be explained as follows: when water is removed from the material during drying, a pressure unbalance is generated between the interior of the dried material and the external environment, and induces the contracting stresses that lead to drying shrinkage. The drying shrinkage of eggplant is particularly severe because of the collapse of the unconsolidated porous structure of egg-
0
0.2
0.4
0.6
0.8
1
(V0-V)/V0 Fig. 4. Comparison between volumetric shrinkage of eggplant and volume of removed water during drying at 50 °C and atmospheric pressure.
plant tissue during drying. In contrast with atmospheric drying, the pressure unbalance during vacuum drying is substantially reduced due to the reduction in air pressure, consequently the drying shrinkage could be inhibited. Until now, many theoretical and empirical models for describing drying shrinkage have been proposed (Mayor & Sereno, 2004). Among them, linear equation: V ¼ aM þ b V0
ð3Þ
where V is the volume of a sample at any time of drying (m3), M is the average moisture content of the sample at P = 2.5 kPa
1
V/V0
Moisture content (d.b.decimal)
0.0
T = 30 °C 2.5 kPa 5 kPa 10 kpa
15 10
0.6
30 °C 40 °C 50 °C
0.4 0.2 0
5
0
4
8
12
16
Moisture content (d.b. decimal) 0
5
10
15
20
25
Drying time (h)
T = 50 °C
20
1
2.5 kPa 5 kPa 10 kPa
15 10
T = 50°C
0.8
5 0
Fig. 5. Volume shrinkage ratio (V/V0) as a function of moisture content of samples at 2.5 kPa and different drying temperatures.
V/V0
Moisture content (d.b.decimal)
0.4
0.8
20
0
b
0.6
0.2
Fig. 2. Changes in average moisture content of samples during vacuum drying at 2.5 kPa and 30–50 °C.
a
50 °C 2.5 kPa Vacuum drying
0.8
Vremoved water /V0
Moisture content (d.b.decimal)
20
425
0.6
2.5 kPa 5 kPa 10 kPa Atmospheric pressure
0.4 0.2 0
0
5
10
15
20
Drying time (h) Fig. 3. Changes in average moisture content of samples during vacuum drying at different drying chamber pressures: (a) 30 °C and (b) 50 °C.
0
0.2
0.4
0.6
0.8
1
M/M0 Fig. 6. Volume shrinkage ratio (V/V0) as a function of moisture content of samples at 50 °C and different drying chamber pressures.
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
ð5Þ
Eq. (5) was fitted to the experimental data of surface area and moisture content, the model coefficients and the indexes of goodness of fit (R2 and P0 ) were calculated. The results showed that the linear equation was adequate to describe the changes in surface area with respect to the moisture content of the samples during drying. The experimental data at 30 °C and 2.5 kPa and the results of linear regression are shown in Fig. 7. Table 1 Results of linear regression for modelling drying shrinkage with respect to moisture content Drying condition
Linear equation coefficient
R2
P0 (%)
Vacuum drying (2.5 kPa, 50 °C)
a = 0.6124, b = 0.3961 a = 0.6773, b = 0.3657 a = 0.7238, b = 0.307 a = 0.8438, b = 0.2471
0.9864
3.3819
0.9929
3.0343
0.9919
3.5381
0.9897
6.0831
Vacuum drying (5 kPa, 50 °C) Vacuum drying (10 kPa, 50 °C) Hot air drying (atmospheric pressure, 50 °C)
Surface area (m2)
0.004 0.003
y = 0.0001x + 0.0027
0.002
R = 0.9802 P' = 8%
2
0.001 0 0
4
8
12
16
Moisture content (d.b. decimal) Fig. 7. Variation in surface area with respect to moisture content of samples during drying at 2.5 kPa and 30 °C.
3.3. Rate of vacuum drying According to Toei (1975), drying rate (Rd) is defined as Rd ¼
W d dM A dt
ð6Þ
where Rd is the drying rate (kg m2 h1), Wd is the weight of dry matter of the sample (kg), A is the drying area of the sample (m2), M is the volume-averaged moisture content, t is the drying time (h). Substituting Eq. (5) into Eq. (6) gives Rd ¼
Wd dM 0 þ b dt
ð7Þ
a0 M
The drying rate of the samples under various drying conditions was calculated using Eq. (7) and plotted with respect to the moisture content in dry basis. Fig. 8 shows the changes in drying rate as a function of moisture content at 2.5 kPa and various drying temperatures, similar trends were observed at other drying chamber pressures. From the figure, the drying temperature affected the drying rate significantly, drying at higher temperature was apparently faster than that at lower temperatures. The results also indicated that the drying rates of the samples decreased with decreasing moisture content throughout the drying processes, that is to say, vacuum drying of the eggplant samples under the investigated drying conditions took place in the falling rate period only.
P= 2.5 kPa
0.8
(kg• m • h )
A ¼ a 0 M þ b0
0.005
-1
where A is the surface area of a sample at any time (m2), A0 is initial surface area of the sample. Due to the complexity of drying process of food materials, Eq. (4) lost its accuracy in some cases. According to the results reported by Nakamura, Tagawa, Orikasa, and Iimoto (2005) Orikasa, Tagawa, Soma, Iimoto, and Ogawa (2005), the relationship between surface area and moisture content in dry basis of the sample could be approximately expressed by a linear equation:
30°C 2.5 kPa Experimental
0.006
0.6
30 ºC
40 ºC
50 ºC
5
10
15
-2
the same time, V0 is the sample’s initial volume (2.25 105 m3 (initial moisture content: 15.67) in this study), has been successfully used for describing the drying shrinkage of a wide range of foodstuffs under various drying conditions (Baini & Langrish, 2007; Lozano, Rotstein, & Urbicain, 1980; Lozano, Rotstein, & Urbicain, 1983; Ratti, 1994; Suzuki, Kubota, Tsutomu, & Hosaka, 1976; Zogzas et al., 1994). Eq. (3) was fitted to the experimental data under different drying conditions, goodness of fit of the equation was evaluated by R2 and P0 . The statistical results indicated that under present conditions, linear model was adequate to predict the drying shrinkage of the eggplant samples, the R2 of the linear regression reached about 0.99, and P0 was less than 7%, as shown in Table 1. The results also proved that the drying shrinkage caused by vacuum drying was obviously less than that caused by atmospheric drying at the same drying temperature. Theoretically, the surface area of the sample during drying can be predicted by the following equation (Orikasa et al., 2005; Pabis, 1999; Pabis & Jaros, 2002; Suzuki et al., 1976): 23l 2l A V ¼k ¼ kðaM þ bÞ3 ð4Þ A0 V0
Drying rate
426
0.4 0.2 0
0
20
Moisture content (d.b. decimal) Fig. 8. variation in drying rate with respect to moisture content of samples at 2.5 kPa and different drying temperatures.
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
3.0
P = 2.5 kPa
2.5
30°C 40°C 50°C
2.0
dM/dt
As can be seen in Fig. 9a,b, the warming-up and constant rate period (from initial moisture content to about 5 kg water/kg dry matter) as existed in the hot air drying process were not observed in the vacuum drying at 30– 50 °C. For the investigated drying temperature range, the vacuum drying was apparently faster than the hot air drying at atmospheric pressure and the same temperature, but the difference between the drying rate of the vacuum and hot air drying diminished quickly with increasing drying temperature.
427
1.5 1.0 0.5 0.0 0
5
10
3.4. Modelling vacuum drying process of eggplant sample In this study, perfect linear relationships between dM/dt and drying time t were observed for all the investigated vacuum drying conditions, as shown in Fig. 10. Accordingly, the relationship between dM/dt and t can be expressed as dM ¼ a0 t þ b0 dt
ð8Þ
By integrating Eq. (8) with respect to time (t) Using the initial condition M = M0 at t = 0, Eq. (9) can be obtained: M¼
a0 2 t þ b0 t þ M 0 2
M Me ¼ at2 þ bt þ 1 M0 Me
ð10Þ
where a and b are coefficients to be determined empirically.
a
0.8 0.6
2.5 kPa Atmospheric pressure
-2
-1
(kg• m • h )
Drying rate
T = 30°C
0.4 0.2 0
0
Drying time (h) Fig. 10. dM/dt as a function of drying time at 2.5 kPa and different drying temperatures.
Table 2 Model coefficients and goodness of fit of the proposed drying model fitted to experimental data of 2.5 kPa and 30 °C Equation
Model coefficient
R2
RMSE
v2
P0 (%)
MR = at2 + bt + 1
a = 0.00298, b = 0.10801
0.999
0.008
0.00006
5.31
5
10
15
Eq. (10) described the changes in MR of the eggplant samples during vacuum drying process. Same equation was proposed by Wang and Singh (1978) for modelling the drying process of rough rice. Drying curves (MR vs. time) under various drying conditions were plotted and fitted with Eq. (10) and other four commonly-used drying models. The results indicated that among the five drying models, the suggested polynomial model Eq. (10) had the best goodness of fit indexes (i.e., highest R2 and lowest RMSE, v2 and P0 , as shown in Table 2). A comparison between the drying curves (MR vs. t) at 2.5 kPa and various drying temperatures and the data predicted by Eq. (10) is shown in Fig. 11. The polynomial model equation (10) was proved to be adequate to model the whole vacuum drying process of the eggplant samples.
20
1.2
Moisture content (d.b. decimal)
P = 2.5 kPa 30 °C Predicted 40 °C Predicted 50 °C Predicted 30 °C Experimental 40 °C Experimental 50 °C Experimental
0.6
T = 50°C
2.5 kPa
Moisture ratio
0.8
Drying rate -2 -1 (kg• m • h )
1
b
Atomospheric pressure
0.4 0.2 0
20
ð9Þ
Eq. (9) may be further transformed into a more general form as follows: MR ¼
15
0.8 0.6 0.4 0.2
0
5
10
15
20
Moisture content (d.b. decimal) Fig. 9. Comparison of drying rate between vacuum drying (2.5 kPa) and hot air drying of eggplant sample at same drying temperature: (a) 30 °C and (b) 50 °C.
0
0
4
8
12
16
20
24
Drying time (h) Fig. 11. Comparison of drying curves (MR vs. t) at 2.5 kPa and various drying temperatures and data predicted by drying model equation (10).
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3.5. Calculation of basic drying parameters Drying models based on the diffusion theory sometimes failed to accurately predict the drying process of some foodstuffs due to the complexity of food drying kinetics as well as the incompliance with the basic assumptions for using the model. however, the diffusion equation is still extensively used for the evaluation of the fundamental parameters of drying process. Since the drying of the eggplant samples took place in the falling rate period only, the following infinite series solution of Fick’s second law of diffusion, which was developed for particles with slab geometry assuming unidirectional moisture movement without volume change, constant diffusivity and temperature, uniform initial moisture distribution, was used for the calculation of the effective moisture diffusivity of the samples during drying: ! 1 8 X 1 ð2n þ 1Þ2 p2 Deff h MR ¼ 2 exp ð11Þ p n¼0 ð2n þ 1Þ2 4L2 where MR is the moisture ratio, Deff is the effective moisture diffusivity (m2/s), L is the slab thickness (m), the half slab thickness is used when evaporation occurs on both sides of the slab, and h is the drying time (s) (Crank, 1975; Tutuncu & Labuza, 1996). In this study, notable deviations from the experimental results were observed when using the drying model based on the diffusion theory to describe the latter part (MR < 0.35) of the drying process. Consequently, the effective moisture diffusivity of the eggplant samples for the MR range from 1 to 0.35 was calculated by fitting Eq. (11) to the MR data between 1 and 0.35 under various drying conditions. Fig. 12 showed that the infinite series solution of Fick’s second law of diffusion Equation (11) agreed fairly satisfactorily with the experimental results. For the tested MR range, the values of the Deff of the samples dried at 2.5 kPa and 30, 40 and 50 °C were calculated to be 1.653 109, 2.353 109 and 3.417 109 m2/s, respectively, which was significantly higher than those of the hot air dried samples (varying from 1.005 109 to 2.086 109) at the same temperature, as shown in Fig. 13.
Deff
1.00E-08
1.00E-09
2.5 kPa Atmospheric pressure 1.00E-10 0.003
0.0031
0.0032
0.0033
0.0034
-1
1/T (K ) Fig. 13. Temperature dependence of effective moisture diffusivity.
Under the investigated experimental conditions, the drying chamber pressure showed no significant effect on the Deff of the samples, while increasing drying temperature led to an apparent increase in the effective moisture diffusivity. The temperature dependence of Deff was examined by the following Arrhenius-type equation (Madamba et al., 1996; Pin˜aga, Carbonell, Pen˜a, & Miquel, 1984; Tagawa et al., 2003): Ea Deff ¼ D0 exp ð12Þ RT where Ea is referred to as activation energy for moisture diffusion (kJ), T is the absolute temperature (K). A typical Arrhenius-type relationship between the Deff and drying temperature could be observed by plotting Deff with respect to the reciprocal of absolute temperature in a semi-logarithmic graph (Fig. 13), the activation energy for moisture diffusion, which was obtained from the slopes of the lines fitted to the data in Fig. 13, was found to be 1640 and 1652 kJ/kg for the vacuum drying and hot air drying under atmospheric pressure, respectively. The temperature dependence of the effective moisture diffusivity for the vacuum drying of the eggplant samples could be described by the following equation: 3550:1 Deff ¼ 2:012 104 exp ð13Þ T
10
4. Conclusion
30 °C 2.5 kPa Experimental
MR
Pedicted by Eq. (11) 1
0.1 0
5
10
15
20
25
30
Drying time (×103s) Fig. 12. Comparison of experimental results (30 °C and 2.5 kPa) within MR range from 1 to 0.35 and predicted data using diffusion Eq. (11).
Vacuum drying of the eggplant samples under the investigated drying conditions took place in the falling rate period. Drying chamber pressure had statistically insignificant effect on the vacuum drying process, increasing drying temperature shortened the drying process notably. The drying shrinkage of the samples was independent of the drying temperature, but intensified significantly with an increasing in the drying chamber pressure. The relationship between the vacuum drying shrinkage ratio and moisture content during vacuum drying could be expressed by a linear equation. The suggested polynomial model showed the best fit
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
to the experimental results among the examined drying models, and can be used to describe the vacuum drying characteristics of the eggplant samples under the investigated vacuum drying conditions. The effective moisture diffusivity of the eggplant samples within a moisture ratio range from 1 to 0.35 varied from 1.653 109 to 3.417 109 m2/s according to the drying condition, the temperature dependence of the effective moisture diffusivity was described satisfactorily by the Arrhenius-type equation, the activation energy for moisture diffusion was found to be 1640 kJ/kg. References AOAC (1995). Official methods of analysis (16th ed.). Washington, DC: Association of Official Analytical Chemists. Arevalo-Pinedo, A., & Murr, F. E. M. (2006). Kinetics of vacuum drying of pumpkin (Cucurbita maxima): Modeling with shrinkage. Journal of Food Engineering, 76(4), 562–567. Arevalo-Pinedo, A., & Murr, F. E. M. (2007). Influence of pre-treatments on the drying kinetics during vacuum drying of carrot and pumpkin. Journal of Food Engineering, 80(1), 152–156. Baini, R., & Langrish, T. A. G. (2007). Choosing an appropriate drying model for intermittent and continuous drying of bananas. Journal of Food Engineering, 79(1), 330–343. Bazyma, L. A., Guskov, V. P., Basteev, A. V., Lyashenko, A. M., Lyakhno, V., & Kutuvoy, V. A. (2006). The investigation of low temperature vacuum drying processes of agricultural materials. Journal of Food Engineering, 74(3), 410–415. Chen, C., & Morey, R. V. (1989). Comparison of four ERH/EMC equations. Transaction of the ASAE, 32(3), 983–990. Crank, J. (1975). Mathematics of diffusion (2nd ed.). Oxford: Clarendon Press. Cui, Z. W., Xu, S. Y., & Sun, D. W. (2004). Microwave-vacuum drying kinetics of carrot slices. Journal of Food Engineering, 65(2), 157–164. Giri, S. K., & Prasad, S. (2007). Drying kinetics and rehydration characteristics of microwave-vacuum and convective hot-air dried mushrooms. Journal of Food Engineering, 78(2), 512–521. Jaya, S., & Das, H. (2003). A vacuum drying model for mango pulp. Drying Technology, 21(7), 1215–1234. Jena, S., & Das, H. (2007). Modelling for vacuum drying characteristics of coconut presscake. Journal of Food Engineering, 79(1), 92–99. Karathanos, V., Anglea, S., & Karel, M. (1993). Collapse of structure during drying of celery. Drying Technology, 11(5), 1005–1023. Lozano, J. E., Rotstein, E., & Urbicain, M. J. (1980). Total porosity and open-pore porosity in the drying of fruits. Journal of Food Science, 45, 1403–1407. Lozano, J. E., Rotstein, E., & Urbicain, M. J. (1983). Shrinkage, porosity and bulk density of foodstuffs at changing moisture contents. Journal of Food Science, 48, 1497–1502. Madamba, P. S., Driscoll, R. D., & Buckle, K. A. (1996). The thin-layer drying characteristics of garlic slices. Journal of Food Engineering, 29(1), 75–97. Maskan, M. (2001). Drying, shrinkage and rehydration characteristics of kiwifruits during hot air and microwave drying. Journal of Food Engineering, 48(2), 177–182.
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Mayor, L., & Sereno, A. M. (2004). Modelling shrinkage during convective drying of food materials: A review. Journal of Food Engineering, 61(3), 373–386. Mcminn, W. A. M., & Magee, T. R. A. (1997a). Physical characteristics of dehydrated potatoes – Part I. Journal of Food Engineering, 33(1-2), 37–48. Mcminn, W. A. M., & Magee, T. R. A. (1997b). Physical characteristics of dehydrated potatoes – Part II. Journal of Food Engineering, 33(1-2), 49–55. Methakhup, S., Chiewchan, N., & Devahastin, S. (2005). Effects of drying methods and conditions on drying kinetics and quality of Indian gooseberry flake. LWT – Food Science and Technology, 38(6), 579–587. Nakamura, T., Tagawa, A., Orikasa, T., & Iimoto, M. (2005). Vacuum drying of cooking tomato. Journal of the Japanese Society of Agricultural Machinery, 67(6), 105–112. Orikasa, T., Tagawa, A., Nakamura, T., & Iimoto, M. (2005). Drying characteristics of cooking tomato. Journal of the Japanese Society of Agricultural Machinery, 67(2), 46–52. Orikasa, T., Tagawa, A., Soma, S., Iimoto, M., & Ogawa, Y. (2005). Hot air drying characteristics of fruits and vegetables and surface hardening of samples during drying. Journal of the Japanese Society of Agricultural Machinery, 67(6), 62–70. Pabis, S. (1999). The initial phase of convection drying of vegetables and mushrooms and the effect of shrinkage. Journal of Agricultural research, 72, 187–195. Pabis, S., & Jaros, M. (2002). The first period of convection drying of vegetables and the effect of shape-dependent shrinkage. Biosystem Engineering, 81(2), 201–211. Pin˜aga, F., Carbonell, J. V., Pen˜a, J. L., & Miquel, J. J. (1984). Experimental simulation of solar drying of garlic using an adsorbent energy storage bed. Journal of Food Engineering, 3(3), 187–203. Ratti, C. (1994). Shrinkage during drying of foodstuffs. Journal of Food Engineering, 23(1), 91–105. Sacilik, K., & Elicin, A. K. (2006). The thin layer drying characteristics of organic apple slices. Journal of Food Engineering, 73(3), 281–289. Souma, S., Tagawa, A., & Iimoto, M. (2004). Structural properties for fruits and vegetables during drying. Journal of the Japanese Society for Food Science and Technology, 51(11), 577–584. Suzuki, K., Kubota, K., Tsutomu, H., & Hosaka, H. (1976). Shrinkage in dehydration of root vegetables. Journal of Food Science, 41, 1189–1193. Tagawa, A., Muramatsu, Y., Nagasuna, T., Yano, A., Iimoto, M., & Murata, S. (2003). Water absorption characteristics of wheat and barley during soaking. Transaction of the ASAE, 46(2), 361–366. Toei, R. (1975). Theory and calculation of chemical machine (2nd ed.). Sangyo books: Tokyo. Tutuncu, M. A., & Labuza, T. P. (1996). Effect of geometry on the effective moisture transfer diffusion coefficient. Journal of Food Engineering, 30(3-4), 433–447. Wang, C. Y. & Singh, R. P. (1978). A single layer drying equation for rough rice. ASAE Paper No: 78-3001, ASAE, St. Joseph, MI. Watson, E. L., & Harper, J. C. (1988). Elements of food engineering (2nd ed.). New York: AVI. Zogzas, N. P., Maroulis, Z. B., & Marinos-Kouris, D. (1994). Density, shrinkage and porosity of some vegetables during air drying. Drying Technology, 12(7), 1653–1666.
Vacuum drying characteristics of eggplants Long Wu a, Takahiro Orikasa a, Yukiharu Ogawa b, Akio Tagawa a,* a
Graduate School of Science and Technology, Chiba University, 648, Matsudo, Matsudo, Chiba 271-8510, Japan b Faculty of Horticulture, Chiba University, 648, Matsudo, Matsudo, Chiba 271-8510, Japan Received 7 February 2007; received in revised form 15 March 2007; accepted 17 March 2007 Available online 28 March 2007
Abstract The vacuum drying characteristics of eggplant were investigated. Drying experiments were carried out at vacuum chamber pressures of 2.5, 5 and 10 kPa, and drying temperature ranging from 30 to 50 °C. The effects of drying pressure and temperature on the drying rate and drying shrinkage of the eggplant samples were evaluated. The suitable model for describing the vacuum drying process was chosen by fitting four commonly used drying models and a suggested polynomial model to the experimental data; the effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick’s diffusion equation. The results showed that increasing drying temperature accelerated the vacuum drying process, while drying chamber pressure did not show significant effect on the drying process within the temperature range investigated. Drying shrinkage of the samples was observed to be independent of drying temperature, but increased notably with an increase in drying chamber pressure. A linear relationship between drying shrinkage ratio and dry basis moisture content was observed. The goodness of fit tests indicated that the proposed polynomial model gave the best fit to experimental results among the five tested drying models. The temperature dependence of the effective moisture diffusivity for the vacuum drying of the eggplant samples was satisfactorily described by an Arrhenius-type relationship. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Vacuum drying; Eggplant; Drying characteristics; Drying model
1. Introduction Drying is one of the most important methods of longterm food preservation. The removal of moisture from the food materials prevents the growth and reproduction of spoilage microorganisms, slows down the action of enzymes and minimizes many of the moisture mediated deteriorative reactions. Although drying processing effectively extends the shelf life of agricultural products, loss of sensory and nutritive qualities is considered inevitable during traditional drying process due to the undesirable textural and biochemical changes (Watson & Harper, 1988). Compared with conventional atmospheric drying, vacuum drying has some distinctive characteristics such as
*
Corresponding author. Tel./fax: +81 47 308 8847. E-mail address: [email protected] (A. Tagawa).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.03.030
higher drying rate, lower drying temperature and oxygen deficient processing environment etc., these characteristics may help to improve the quality and nutritive value of the dried products. Presently, vacuum drying has been applied to dry various food materials, the vacuum drying kinetics of many fruits and vegetables has been investigated and the effect of vacuum drying conditions on the drying process and the qualities of dried products has been evaluated (Arevalo-Pinedo & Murr, 2006; Arevalo-Pinedo & Murr, 2007; Bazyma et al., 2006; Cui, Xu, & Sun, 2004; Jaya & Das, 2003; Methakhup, Chiewchan, & Devahastin, 2005). Eggplant (Solanum melongena var. esculenta) is an important market vegetable of Asian and Mediterranean countries and has a very limited shelf life for freshness. In order to evaluate the practicability of vacuum drying for improving the quality of dried eggplant, it is necessary to carry out research on the vacuum drying characteristics of eggplant fruit. The objectives of this study were to
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
423
Nomenclature A Deff Ea L M M0 Me MR P P0 R
area (m2) effective moisture diffusivity (m2 s1) activation energy (kJ kg1) sample thickness (m) moisture content (d.b., decimal) initial moisture content (d.b., decimal) equilibrium moisture content (d.b., decimal) moisture ratio pressure (kPa) mean relative deviation (%) gas constant (0.462 kJ kg1 K1)
investigate the vacuum drying characteristics of the eggplant samples, to evaluate the effect of vacuum drying conditions on the drying process, and to choose a suitable drying model for describing the whole drying process. 2. Material and methods 2.1. Sample preparation Fresh eggplants (cultivated in Kochi Prefecture Japan, cultivar: unknown) were purchased from a local market and stored at 8 °C before experiments started, the storage time was not more than 12 h in this study. The central part of each eggplant fruit was cut into a rectangular-shaped block of 45 25 20 mm for drying treatment. The initial moisture content of the sample blocks was determined as 94.00% in wet basis (N = 20, standard deviation: 0.52%) according to the vacuum oven method (i.e., drying at 70 °C and 2.5 kPa for 12 h) (AOAC, 1995). 2.2. Experimental setup A schematic diagram of the experimental vacuum drying system is shown in Fig. 1. The system primarily consists of an oil rotary vacuum pump (TSW-300, SATO VAC, Japan), a vacuum control unit (NVC-2000L, Tokyo Rikakikai, Japan) to obtain various processing pressures in the vacuum drying chamber (a glass desiccator) and a forced convection drying oven (DO600FA, AS ONE, Japan) to maintain desired drying temperatures. A data acquisition system composed of a load cell (LTS-50GA, KYOWA, Japan) which was fixed on a supporting frame, a wire netting sample holder suspended from the load cell, an instrumentation amplifier (WGA-710A, KYOWA, Japan) and a data logger (KEYENCE, NR-1000, Japan) was used to on-line monitor and record the changes in sample weight during drying. Hot air drying runs at 30– 50 °C and atmospheric pressure were also conducted in the same glass desiccator with the top lid removed for comparison.
R2 Rd RMSE t T V Wd a,b h v2
coefficient of determination drying rate (kg m2 h1) root mean square error time (h) temperature (K) volume (m3) weight of dry matter (kg) coefficients in drying model time (s) reduced chi-square
2.3. Experimental procedure The vacuum drying chamber was preheated for 12 h before the experiments started to obtain stable drying temperature. Drying experiments were conducted in the drying chamber at temperatures ranging from 30 to 50 °C, and pressures of 2.5, 5, 10 kPa as well as atmospheric pressure, respectively. One sample was placed on the wire netting basket and dried in each run, its weight was continuously recorded at intervals of 5 min using the data acquisition system throughout the drying process. It was considered that the sample reached the equilibrium moisture content (EMC) of drying when the reading of weight remained the same for 1 h. Fresh samples were dried under the above-mentioned conditions for durations ranging from 1 to 15 h individually to evaluate the drying shrinkage. Approximate volume and surface area of the dried samples were calculated from the measured dimensions data. According to preliminary tests, in which a comparison between the calculated results and the measured volume of the dried samples using liquid displacement method (Maskan, 2001; Orikasa, Tagawa, Nakamura, & Iimoto, 2005; Zogzas, Maroulis, & Marinos-Kouris, 1994) was conducted, the calculated results were proved to be acceptable, similar results were reported by Ratti (1994). 2.4. Data analysis The average moisture content of each sample during drying was calculated from the sample weight recorded by the data acquisition system (moisture distribution in the sample was considered to be uniform in this study). Moisture ratio (MR) of the sample was determined by the following equation: MR ¼
ðM M e Þ ðM 0 M e Þ
ð1Þ
where M is the average moisture content of a sample at any time of drying, M0 and Me stand for the initial and equilibrium moisture content, respectively.
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Fig. 1. Schematic diagram of vacuum drying system: 1. vacuum pump, 2. cold trap, 3. vacuum control unit, 4. forced convection drying oven, 5. glass desiccator, 6. load cell, 7. supporting frame, 8. wire netting sample holder, 9. instrumentation amplifier, and 10. data logger.
Drying curves (MR vs. time) were plotted and fitted by four empirical drying models (i.e., proposed polynomial model, exponential model, Page’s model and logarithmic model), and a theoretical model based on the Fick’s diffusion law; model coefficients were calculated using OriginPro 7.5 software (OriginLab Corp.). The goodness of fit was evaluated by the coefficient of determination (R2), the root mean square error (RMSE), the reduced chisquare (v2) and mean relative deviation modulus (P0 ) defined by the following equation n Y exp;i Y pre;i 100 X 0 P ¼ ð2Þ N i¼1 Y exp;i where Yexp,i is the experimental result of the investigated variable, Ypre,i is the predicted value from various mathematical models, N is the number of observations (Chen & Morey, 1989; Jena & Das, 2007; Madamba, Driscoll, & Buckle, 1996; Sacilik & Elicin, 2006). The best model describing the vacuum drying process of the eggplant samples was chosen as the one with the highest R2 and the least RMSE, v2 and P0 . Comparisons between means were performed in SPSS 12.0 software (SPSS Inc.) using Duncan’s multiple range tests at a significance level of 0.05. 3. Results and discussion 3.1. Effect of vacuum drying conditions on drying process After vacuum drying, the moisture content of the eggplant samples was reduced from a initial value of 15.67 to less than 0.2 kg water/kg dry matter. The effects of drying temperature and pressure on the vacuum drying process are shown in Figs. 2 and 3a,b, in which drying curves (moisture content in dry basis vs. time) under different drying
conditions were plotted. From Fig. 2, the drying time needed to reach the EMC was shortened notably with an increase in drying temperature due to a larger driving force for heat and mass transfer at higher drying temperature. Fig. 3 showed that drying chamber pressure ranging from 2.5 to 10 kPa did not affect the drying process as strongly as drying temperature did. For the present vacuum drying conditions, the effect of drying chamber pressure on the drying process was not significant. According to the reports of Arevalo-Pinedo and Murr (2006) and Arevalo-Pinedo and Murr (2007) for carrot and pumpkin, Cui et al. (2004) for carrot, Giri and Prasad (2007) for mushroom, and Methakhup et al. (2005) for Indian gooseberry, drying pressure had a certain effect on the drying process, the drying time was reduced by decreasing drying pressure. The differentiation between the results of this study and the literature could be attributed to the different processing conditions as well as different degrees of boiling point elevation caused by various plasma concentrations of the tested materials. 3.2. Drying shrinkage Drying shrinkage affects not only the product quality but also the drying process and rehydration capability of the dried food materials (Karathanos, Anglea, & Karel, 1993; Maskan, 2001; Mcminn & Magee, 1997a, 1997b). Ratti (1994) indicated that changes in the dimensions of dried sample were independent of drying conditions but dependent on the geometric shape and type of foodstuff. Souma, Tagawa, and Iimoto (2004) reported that the hot air drying shrinkage of eggplant is very remarkable and the reduction in sample volume was larger than the volume of removed water due to its high porosity, similar tendency were also observed in this study, as shown in Fig. 4. In order to investigate the drying shrinkage of the samples, drying experiments with different drying durations
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
1.0
P = 2.5 kPa 30 °C 40 °C 50 °C
15 10
50 °C Hotair drying
5 0
0
5
10
15
20
25
Drying time (h)
were carried out under various drying conditions, the volume and surface area of the dried samples were calculated. Fig. 5 presents the relationship between the volume shrinkage ratio (V/V0) and the moisture content of the samples dried at 2.5 kPa and various drying temperatures, the results indicated that drying temperature had insignificant effect on the drying shrinkage of the eggplant samples for the investigated temperature range. Fig. 6 shows the effect of drying chamber pressure on the drying shrinkage of the samples at 50 °C, it can be seen that the shrinkage became more severe at higher vacuum chamber pressures. This phenomenon could be explained as follows: when water is removed from the material during drying, a pressure unbalance is generated between the interior of the dried material and the external environment, and induces the contracting stresses that lead to drying shrinkage. The drying shrinkage of eggplant is particularly severe because of the collapse of the unconsolidated porous structure of egg-
0
0.2
0.4
0.6
0.8
1
(V0-V)/V0 Fig. 4. Comparison between volumetric shrinkage of eggplant and volume of removed water during drying at 50 °C and atmospheric pressure.
plant tissue during drying. In contrast with atmospheric drying, the pressure unbalance during vacuum drying is substantially reduced due to the reduction in air pressure, consequently the drying shrinkage could be inhibited. Until now, many theoretical and empirical models for describing drying shrinkage have been proposed (Mayor & Sereno, 2004). Among them, linear equation: V ¼ aM þ b V0
ð3Þ
where V is the volume of a sample at any time of drying (m3), M is the average moisture content of the sample at P = 2.5 kPa
1
V/V0
Moisture content (d.b.decimal)
0.0
T = 30 °C 2.5 kPa 5 kPa 10 kpa
15 10
0.6
30 °C 40 °C 50 °C
0.4 0.2 0
5
0
4
8
12
16
Moisture content (d.b. decimal) 0
5
10
15
20
25
Drying time (h)
T = 50 °C
20
1
2.5 kPa 5 kPa 10 kPa
15 10
T = 50°C
0.8
5 0
Fig. 5. Volume shrinkage ratio (V/V0) as a function of moisture content of samples at 2.5 kPa and different drying temperatures.
V/V0
Moisture content (d.b.decimal)
0.4
0.8
20
0
b
0.6
0.2
Fig. 2. Changes in average moisture content of samples during vacuum drying at 2.5 kPa and 30–50 °C.
a
50 °C 2.5 kPa Vacuum drying
0.8
Vremoved water /V0
Moisture content (d.b.decimal)
20
425
0.6
2.5 kPa 5 kPa 10 kPa Atmospheric pressure
0.4 0.2 0
0
5
10
15
20
Drying time (h) Fig. 3. Changes in average moisture content of samples during vacuum drying at different drying chamber pressures: (a) 30 °C and (b) 50 °C.
0
0.2
0.4
0.6
0.8
1
M/M0 Fig. 6. Volume shrinkage ratio (V/V0) as a function of moisture content of samples at 50 °C and different drying chamber pressures.
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
ð5Þ
Eq. (5) was fitted to the experimental data of surface area and moisture content, the model coefficients and the indexes of goodness of fit (R2 and P0 ) were calculated. The results showed that the linear equation was adequate to describe the changes in surface area with respect to the moisture content of the samples during drying. The experimental data at 30 °C and 2.5 kPa and the results of linear regression are shown in Fig. 7. Table 1 Results of linear regression for modelling drying shrinkage with respect to moisture content Drying condition
Linear equation coefficient
R2
P0 (%)
Vacuum drying (2.5 kPa, 50 °C)
a = 0.6124, b = 0.3961 a = 0.6773, b = 0.3657 a = 0.7238, b = 0.307 a = 0.8438, b = 0.2471
0.9864
3.3819
0.9929
3.0343
0.9919
3.5381
0.9897
6.0831
Vacuum drying (5 kPa, 50 °C) Vacuum drying (10 kPa, 50 °C) Hot air drying (atmospheric pressure, 50 °C)
Surface area (m2)
0.004 0.003
y = 0.0001x + 0.0027
0.002
R = 0.9802 P' = 8%
2
0.001 0 0
4
8
12
16
Moisture content (d.b. decimal) Fig. 7. Variation in surface area with respect to moisture content of samples during drying at 2.5 kPa and 30 °C.
3.3. Rate of vacuum drying According to Toei (1975), drying rate (Rd) is defined as Rd ¼
W d dM A dt
ð6Þ
where Rd is the drying rate (kg m2 h1), Wd is the weight of dry matter of the sample (kg), A is the drying area of the sample (m2), M is the volume-averaged moisture content, t is the drying time (h). Substituting Eq. (5) into Eq. (6) gives Rd ¼
Wd dM 0 þ b dt
ð7Þ
a0 M
The drying rate of the samples under various drying conditions was calculated using Eq. (7) and plotted with respect to the moisture content in dry basis. Fig. 8 shows the changes in drying rate as a function of moisture content at 2.5 kPa and various drying temperatures, similar trends were observed at other drying chamber pressures. From the figure, the drying temperature affected the drying rate significantly, drying at higher temperature was apparently faster than that at lower temperatures. The results also indicated that the drying rates of the samples decreased with decreasing moisture content throughout the drying processes, that is to say, vacuum drying of the eggplant samples under the investigated drying conditions took place in the falling rate period only.
P= 2.5 kPa
0.8
(kg• m • h )
A ¼ a 0 M þ b0
0.005
-1
where A is the surface area of a sample at any time (m2), A0 is initial surface area of the sample. Due to the complexity of drying process of food materials, Eq. (4) lost its accuracy in some cases. According to the results reported by Nakamura, Tagawa, Orikasa, and Iimoto (2005) Orikasa, Tagawa, Soma, Iimoto, and Ogawa (2005), the relationship between surface area and moisture content in dry basis of the sample could be approximately expressed by a linear equation:
30°C 2.5 kPa Experimental
0.006
0.6
30 ºC
40 ºC
50 ºC
5
10
15
-2
the same time, V0 is the sample’s initial volume (2.25 105 m3 (initial moisture content: 15.67) in this study), has been successfully used for describing the drying shrinkage of a wide range of foodstuffs under various drying conditions (Baini & Langrish, 2007; Lozano, Rotstein, & Urbicain, 1980; Lozano, Rotstein, & Urbicain, 1983; Ratti, 1994; Suzuki, Kubota, Tsutomu, & Hosaka, 1976; Zogzas et al., 1994). Eq. (3) was fitted to the experimental data under different drying conditions, goodness of fit of the equation was evaluated by R2 and P0 . The statistical results indicated that under present conditions, linear model was adequate to predict the drying shrinkage of the eggplant samples, the R2 of the linear regression reached about 0.99, and P0 was less than 7%, as shown in Table 1. The results also proved that the drying shrinkage caused by vacuum drying was obviously less than that caused by atmospheric drying at the same drying temperature. Theoretically, the surface area of the sample during drying can be predicted by the following equation (Orikasa et al., 2005; Pabis, 1999; Pabis & Jaros, 2002; Suzuki et al., 1976): 23l 2l A V ¼k ¼ kðaM þ bÞ3 ð4Þ A0 V0
Drying rate
426
0.4 0.2 0
0
20
Moisture content (d.b. decimal) Fig. 8. variation in drying rate with respect to moisture content of samples at 2.5 kPa and different drying temperatures.
L. Wu et al. / Journal of Food Engineering 83 (2007) 422–429
3.0
P = 2.5 kPa
2.5
30°C 40°C 50°C
2.0
dM/dt
As can be seen in Fig. 9a,b, the warming-up and constant rate period (from initial moisture content to about 5 kg water/kg dry matter) as existed in the hot air drying process were not observed in the vacuum drying at 30– 50 °C. For the investigated drying temperature range, the vacuum drying was apparently faster than the hot air drying at atmospheric pressure and the same temperature, but the difference between the drying rate of the vacuum and hot air drying diminished quickly with increasing drying temperature.
427
1.5 1.0 0.5 0.0 0
5
10
3.4. Modelling vacuum drying process of eggplant sample In this study, perfect linear relationships between dM/dt and drying time t were observed for all the investigated vacuum drying conditions, as shown in Fig. 10. Accordingly, the relationship between dM/dt and t can be expressed as dM ¼ a0 t þ b0 dt
ð8Þ
By integrating Eq. (8) with respect to time (t) Using the initial condition M = M0 at t = 0, Eq. (9) can be obtained: M¼
a0 2 t þ b0 t þ M 0 2
M Me ¼ at2 þ bt þ 1 M0 Me
ð10Þ
where a and b are coefficients to be determined empirically.
a
0.8 0.6
2.5 kPa Atmospheric pressure
-2
-1
(kg• m • h )
Drying rate
T = 30°C
0.4 0.2 0
0
Drying time (h) Fig. 10. dM/dt as a function of drying time at 2.5 kPa and different drying temperatures.
Table 2 Model coefficients and goodness of fit of the proposed drying model fitted to experimental data of 2.5 kPa and 30 °C Equation
Model coefficient
R2
RMSE
v2
P0 (%)
MR = at2 + bt + 1
a = 0.00298, b = 0.10801
0.999
0.008
0.00006
5.31
5
10
15
Eq. (10) described the changes in MR of the eggplant samples during vacuum drying process. Same equation was proposed by Wang and Singh (1978) for modelling the drying process of rough rice. Drying curves (MR vs. time) under various drying conditions were plotted and fitted with Eq. (10) and other four commonly-used drying models. The results indicated that among the five drying models, the suggested polynomial model Eq. (10) had the best goodness of fit indexes (i.e., highest R2 and lowest RMSE, v2 and P0 , as shown in Table 2). A comparison between the drying curves (MR vs. t) at 2.5 kPa and various drying temperatures and the data predicted by Eq. (10) is shown in Fig. 11. The polynomial model equation (10) was proved to be adequate to model the whole vacuum drying process of the eggplant samples.
20
1.2
Moisture content (d.b. decimal)
P = 2.5 kPa 30 °C Predicted 40 °C Predicted 50 °C Predicted 30 °C Experimental 40 °C Experimental 50 °C Experimental
0.6
T = 50°C
2.5 kPa
Moisture ratio
0.8
Drying rate -2 -1 (kg• m • h )
1
b
Atomospheric pressure
0.4 0.2 0
20
ð9Þ
Eq. (9) may be further transformed into a more general form as follows: MR ¼
15
0.8 0.6 0.4 0.2
0
5
10
15
20
Moisture content (d.b. decimal) Fig. 9. Comparison of drying rate between vacuum drying (2.5 kPa) and hot air drying of eggplant sample at same drying temperature: (a) 30 °C and (b) 50 °C.
0
0
4
8
12
16
20
24
Drying time (h) Fig. 11. Comparison of drying curves (MR vs. t) at 2.5 kPa and various drying temperatures and data predicted by drying model equation (10).
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3.5. Calculation of basic drying parameters Drying models based on the diffusion theory sometimes failed to accurately predict the drying process of some foodstuffs due to the complexity of food drying kinetics as well as the incompliance with the basic assumptions for using the model. however, the diffusion equation is still extensively used for the evaluation of the fundamental parameters of drying process. Since the drying of the eggplant samples took place in the falling rate period only, the following infinite series solution of Fick’s second law of diffusion, which was developed for particles with slab geometry assuming unidirectional moisture movement without volume change, constant diffusivity and temperature, uniform initial moisture distribution, was used for the calculation of the effective moisture diffusivity of the samples during drying: ! 1 8 X 1 ð2n þ 1Þ2 p2 Deff h MR ¼ 2 exp ð11Þ p n¼0 ð2n þ 1Þ2 4L2 where MR is the moisture ratio, Deff is the effective moisture diffusivity (m2/s), L is the slab thickness (m), the half slab thickness is used when evaporation occurs on both sides of the slab, and h is the drying time (s) (Crank, 1975; Tutuncu & Labuza, 1996). In this study, notable deviations from the experimental results were observed when using the drying model based on the diffusion theory to describe the latter part (MR < 0.35) of the drying process. Consequently, the effective moisture diffusivity of the eggplant samples for the MR range from 1 to 0.35 was calculated by fitting Eq. (11) to the MR data between 1 and 0.35 under various drying conditions. Fig. 12 showed that the infinite series solution of Fick’s second law of diffusion Equation (11) agreed fairly satisfactorily with the experimental results. For the tested MR range, the values of the Deff of the samples dried at 2.5 kPa and 30, 40 and 50 °C were calculated to be 1.653 109, 2.353 109 and 3.417 109 m2/s, respectively, which was significantly higher than those of the hot air dried samples (varying from 1.005 109 to 2.086 109) at the same temperature, as shown in Fig. 13.
Deff
1.00E-08
1.00E-09
2.5 kPa Atmospheric pressure 1.00E-10 0.003
0.0031
0.0032
0.0033
0.0034
-1
1/T (K ) Fig. 13. Temperature dependence of effective moisture diffusivity.
Under the investigated experimental conditions, the drying chamber pressure showed no significant effect on the Deff of the samples, while increasing drying temperature led to an apparent increase in the effective moisture diffusivity. The temperature dependence of Deff was examined by the following Arrhenius-type equation (Madamba et al., 1996; Pin˜aga, Carbonell, Pen˜a, & Miquel, 1984; Tagawa et al., 2003): Ea Deff ¼ D0 exp ð12Þ RT where Ea is referred to as activation energy for moisture diffusion (kJ), T is the absolute temperature (K). A typical Arrhenius-type relationship between the Deff and drying temperature could be observed by plotting Deff with respect to the reciprocal of absolute temperature in a semi-logarithmic graph (Fig. 13), the activation energy for moisture diffusion, which was obtained from the slopes of the lines fitted to the data in Fig. 13, was found to be 1640 and 1652 kJ/kg for the vacuum drying and hot air drying under atmospheric pressure, respectively. The temperature dependence of the effective moisture diffusivity for the vacuum drying of the eggplant samples could be described by the following equation: 3550:1 Deff ¼ 2:012 104 exp ð13Þ T
10
4. Conclusion
30 °C 2.5 kPa Experimental
MR
Pedicted by Eq. (11) 1
0.1 0
5
10
15
20
25
30
Drying time (×103s) Fig. 12. Comparison of experimental results (30 °C and 2.5 kPa) within MR range from 1 to 0.35 and predicted data using diffusion Eq. (11).
Vacuum drying of the eggplant samples under the investigated drying conditions took place in the falling rate period. Drying chamber pressure had statistically insignificant effect on the vacuum drying process, increasing drying temperature shortened the drying process notably. The drying shrinkage of the samples was independent of the drying temperature, but intensified significantly with an increasing in the drying chamber pressure. The relationship between the vacuum drying shrinkage ratio and moisture content during vacuum drying could be expressed by a linear equation. The suggested polynomial model showed the best fit
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