Study of the drying behaviour in peeled and unpeeled whole figs

Journal of Food Engineering 97 (2010) 419–424

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Study of the drying behaviour in peeled and unpeeled whole figs G. Xanthopoulos a,*, S. Yanniotis b, Gr. Lambrinos a a b

Agricultural University of Athens, Department of Natural Resources & Agricultural Engineering, 75 Iera Odos Str., 118 55 Athens, Greece Agricultural University of Athens, Department of Food Science and Technology, 75 Iera Odos Str., 118 55 Athens, Greece

a r t i c l e

i n f o

Article history: Received 30 September 2009 Received in revised form 17 October 2009 Accepted 25 October 2009 Available online 31 October 2009 Keywords: Peel effect Effective diffusion coefficient Drying constant Drying of figs

a b s t r a c t Aim of this study was to estimate the effect of peeling on drying kinetics and effective diffusivity Deff of figs (Ficus carica L. var. tsapela) during air-drying. For this purpose three temperatures (45, 55 and 65 °C) were tested. The Logarithmic model was chosen to describe the drying curves among seven drying models. The estimated drying constants were associated with the drying temperature by an Arrhenius type equation. The ratio of peeled to unpeeled relaxation times was found to be 0.54 ± 0.16. The Deff of figs (peeled and unpeeled) was estimated by the method of slopes. The Deff of the peeled figs was higher than this of the unpeeled figs presenting smaller differences as drying temperature was increased. This behaviour was attributed to the case hardening effect which is faster developed as the drying rate increases during high temperature drying. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Dried figs (Ficus carica, Moraceae) are considered as prestigious snack food among other dried fruits. Figs are characterised from high levels of sugars of 16% (fresh product) or 48% (dried product) according to USDA (2002). Figs cohesive peel in conjunction with the case hardening effect, the mechanism of which is described by Brennan (2006), makes their drying process rigorous and sometimes unpredictable. In the literature, a number of studies have been published in which various pre-treatment have been tested aiming to reduce browning (Demirel and Turhan, 2003; Gonzalez-Fesler et al., 2008; Vega-Galvez et al., 2008; Perez and Schmalko, 2009) of the final dried product or to weaken peel resistance (Doymaz, 2006, 2007a,b) to water transfer from the inside of the product to the surface, increasing likewise the drying rate. Research on drying of figs is limited (Piga et al., 2004; Babalis and Belessiotis, 2004; Doymaz, 2005; Babalis et al., 2006; Xanthopoulos et al., 2007a, 2009) but no study has been conducted on the effect of peel on the drying kinetics and the effective diffusivity of figs during air-drying. The aim of this study was to investigate the role of the figs peel in drying. Initially seven drying models were tested and the best fitted model was used to describe the drying curves of the peeled and unpeeled figs. Then, the drying constants from the tested drying cases were associated to the drying temperatures adopting an Arrhenius type equation. The relaxation times of peeled and unpeeled figs were also estimated and compared. Finally the effective water diffusivity was estimated for all the drying experiments * Corresponding author. Tel.: +30 210 529 4031; fax: +30 210 529 4032. E-mail address: [email protected] (G. Xanthopoulos). 0260-8774/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2009.10.037

employing the method of slopes. The, effective diffusivities were also associated with the tested drying temperatures using an Arrhenius type equation.

2. Theory The moisture ratio MR of the peeled and unpeeled figs was calculated from the drying curves of figs, M = f (t), where M is the moisture content of figs in dry basis and t the drying time in h, and fitted to seven single-layer drying models tabulated in Table 1. These models have been used in our previous study (Xanthopoulos et al., 2007a) and have been proved to work well for whole unpeeled figs of the same variety. The drying process was taken place in the falling rate period as has been also explained in our previous study (Xanthopoulos et al., 2009). The drying models in Table 1 are semiempirical incorporating the assumption that the resistance of water diffusion occurs mainly in the outer layer of the produce (Brooker et al., 1992; Pabis et al., 1998). The previous models have been proved to describe well the falling rate period of many foodstuffs during drying (Jayas et al., 1991; Karathanos, 1999; Karathanos and Belessiotis, 1999; Phoungchandang and Woods, 2000). Regression analysis of the experimental drying data was carried out mainly by Statgraphics Plus 5.1 (Statistical Graphics Corp., 2001) as well the Levenberg–Marquardt algorithm (Xanthopoulos et al., 2007b). The drying models were assessed for their fitting efficiency based on the adjusted coefficient of determination R2adj , the standard error of estimate SSE and chi–square v2. When the best model was chosen, then the effect of the drying air temperature, based on the analysis of variance ANOVA (P 6 0.05), on the drying

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Nomenclature Symbols a, c 0 a Bim D de Do, ko Ea Fo k M MR Mt n P r

t R2adj SEE T

universal gas constant (8.31143 J mol1 K1) mean geometric radius (m) root mean square error (%) chi–square drying time (in h or s) coefficient of determination adjusted for the d.f. standard error of estimate drying air temperature (°C or K)

Indices e eff o s

equilibrium moisture content effective initial surface

R re RMSE

parameters of the Logarithmic model correction factor, Eq. (4) Biot number for mass transfer water diffusion coefficient (m2 s1) mean geometric diameter (m) Arrhenius factors (m2 s1) energy of activation (J mol1) Fourier number drying constant (h1) figs water content (kgw/kgdm) moisture ratio average water content of figs (kgw/kgdm) number of terms taken in series, Eq. (3) statistical significance level radius of a sphere (m)

v2

constant values was determined employing an Arrhenius type equation. The effective diffusivity Deff of figs was estimated using the well known method of slopes (Karathanos et al., 1990; Perry and Green, 1999) which is based on Fick’s law for water diffusion. The onedimensional Fick’s law in spherical coordinates (radial diffusion) is given by Eq. (1) accompanied by the appropriate initial and boundary conditions

  @Mðr; tÞ 1 @ @M ¼ 2 r2  D  @t r @r @r Mðt ¼ 0; 0  r < r o Þ ¼ M o

ð1Þ

M s ðt  0; r ¼ r s Þ ¼ M e

ð2Þ

The initial geometric mean radius re of the figs was calculated based on formulation presented by Mohsenin (1978) for an ellipsoidal. Afterwards the theoretical MR curves were estimated numerically for a range of Fo numbers based on Eq. (4). The experimental MR curves were evaluated again from the experimental data. The derived curves for the experimental and the theoretical MR were plotted against drying time and Fo respectively on a semi-logarithmic plot as shown in Fig. 1 for a drying case of 55 °C and 3 m s1. Finally the Deff was calculated based on Eq. (5) for all moisture contents and drying experiments

dMR=dt exp  r2 dMR=dFotheor e

ðt > 0; r ¼ 0Þ; @M ¼0 @r

Deff ¼

The analytical solution of Eq. (1) has been described in detail by Crank (1975) in Eq. (3). In Eq. (3) the radius r and water diffusivity D are assumed to be constant throughout the drying process. Eq. (3) can be used for Deff estimation only if the drying curves MR = f (t) are linear or quasi-linear when are plotted in semi-logarithmic scale. In other cases the Deff can be estimated either by the method of the slopes (Karathanos et al., 1990; Perry and Green, 1999) or using a numerical method to solve Eq. (1)

The calculated Deff was assumed to remain constant for short successive time intervals and no shrinkage was considered. From the previous analysis, the Deff values, based on the analysis of variance ANOVA (P 6 0.05), were estimated as function of the drying air temperature adopting an Arrhenius type equation. As in our previous study (Xanthopoulos et al., 2009) the predominant effect of the internal water diffusion was also validated in this study using the Biot number Bim of mass transfer. In air-drying the boundary layer resistance is negligible compared to the internal mass resistance by a factor of 105 and drying is controlled by the properties of the drying material. This is confirmed from the Bim [Bim = km  re/Deff], which is defined as the ratio of the internal to external mass transfer resistance. For the different geometric radius and drying cases, the estimated superficial mass transfer coefficient km (Xanthopoulos et al., 2009) was ranged from 0.022 up to 0.047 m s1. For Deff values between 3.97  1010 and 7.80  1010 m2 s1, estimated by the method of slopes, the respective Bim numbers were ranged between 1.4  106 and 2.3  106.

MR ¼

1 Mt  Me 6 X 1 ¼ 2  expðn2  p2  FoÞ Mo  Me p n¼1 n2

ð3Þ

where Fo ¼ Deff  t=r2e is the Fourier number. In this study, a modified form of Eq. (3), presented by Efremov and Kudra (2005), Eq. (4), was employed due to accuracy reasons as has been described in detail by Xanthopoulos et al. (2009)

  0 MR ¼ exp p2  F ao

ð4Þ

where a0 = 0.83 is given for sphere.

ð5Þ

Table 1 Seven single-layer drying models. Model name

Model expression

Reference

Newton Page Henderson & Pabis Logarithmic Two term Wang & Singh Mod. Henderson & Pabis

MR = exp(k  t) MR = exp(k  tn) MR = a exp(k  t) MR = a exp(k  t) + c MR = a exp(ko  t) + b exp(k1  t) MR = 1 + a t + b t2 MR = a exp(k  t) + b exp(g  t) + c exp(h  t)

Brooker et al. (1992) Brooker et al. (1992) Zhang and Litchfield (1991) Yaldiz and Ertekin (2002) Henderson (1974) Wang and Singh (1978) Karathanos (1999)

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G. Xanthopoulos et al. / Journal of Food Engineering 97 (2010) 419–424 Drying time, h 100.0

0

10

Drying time, h

20

30

0

100.0

MR experimental MR theoretical

Moisture ratio, MR

Moisture ratio, MR

9 8 7 6

40

5 4 3

2

10-1.0

10

20

30

9 8 7 6

40

MR experimental MR theoretical

5 4 3

2

10-1.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fo= Deff t / re 2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fo= Deff t / re 2

Fig. 1. Evaluation of Deff (m2 s1) by the method of slopes [55 °C, 3 m s1 peeled (right), unpeeled (left) figs].

3. Materials and methods 3.1. Experimental facility The drying of figs was carried out in two experimental drying cabinets, designed and manufactured in ‘‘Agricultural Machinery Laboratory” of Agricultural University of Athens (Greece). In our previous study (Xanthopoulos et al., 2007b) the experimental apparatus was described in detail. 3.2. Sample preparation and drying conditions The experiments were conducted using fresh figs of Tsapela variety during the 2008 harvest period, cultivated in Kalamata– Greece. Figs were carefully hand-picked to achieve uniform physiological state and geometric dimensions and transported back to the laboratory within a day. The mean initial water content was 2.74 ± 0.44 kgw/kgdm for unpeeled figs and 2.69 ± 0.52 kgw/kgdm for peeled figs (P 6 0.05) and the mean geometric initial diameter was 40.50 ± 2.65 mm for unpeeled figs and 39.32 ± 1.30 mm for peeled figs (P 6 0.05). In each drying case, four whole figs with and four without peel figs were placed together in the drying cabinet in a single layer. Peeling of the figs was carried out carefully by hand. The following air temperature and velocity combinations were tested 45 °C (3.0, 4.0 m s1), 55 and 65 °C (1.0, 3.0, 5.0 m s1). High air velocities were used to study heat and mass transfer during drying of figs. The drying process was concluded when the final water content was below 20% w.b. [19.83 ± 2.30% w.b. unpeeled figs and 20.56 ± 2.64% w.b. peeled figs, (P 6 0.05)] in order to achieve edible conditions, in terms of texture, of the final dried product. The average drying time, based on final MR = 0.10 was 48 h at 45 °C, 33 h at 55 °C and 28 h at 65 °C for unpeeled figs and 34 h at 45 °C, 29 h at 55 °C and 26 h at 65 °C for unpeeled figs. The mean absolute humidity of the drying air was 11.25 ± 0.66 gw/kgda (P 6 0.05). The weight of each drying fig was manually recorded in regular intervals. The dry matter of the fresh commodities was determined at 105 °C until steady weight was achieved (AOAC, 1997). The initial geometric diameter of the figs was estimated from three initial diameters, two longitudinal-in normal directions and one axial measured by a digital vernier gauge. 3.3. The moisture equilibrium equation The equilibrium moisture content Me, of figs was calculated employing the GAB (Guggenheim–Anderson–DeBoer) sorption iso-

therm relation, which is widely used for drying of foods (Rahman, 1995). The sorption model and the accompanied parameters are described in our previous work (Xanthopoulos et al., 2007a). 4. Results and discussion 4.1. Estimation of the drying constants for peeled and unpeeled figs The calculated MR curves were regressed against the seven single-layer drying models displayed in Table 1. The derived drying models were sorted in descending order of R2 and ascending order of SEE and v2. As in our previous study (Xanthopoulos et al., 2007a), the Logarithmic model was the best fitted model for the unpeeled figs. For the peeled figs the best fitted model was the Modified Henderson & Pabis model although the discrepancy with the Logarithmic model was less than 3% of RMSE and therefore the Logarithmic model was chosen to describe the MR curves of the unpeeled figs also in order to simplify the comparison process. The drying constant (k, h1) and the coefficients (a and c) of the Logarithmic model for all the drying experiments as well the calculated statistical coefficients R2adj , SEE and v2 are tabulated in Table 2. In Table 2, are also included the relaxation times which according to Karathanos (1999) are times (in s or h) in which the corresponding effect described by the solution of the general drying differential equation is decreased by 63.2%. In this case, it can be seen that the mean value of the peeled to unpeeled relaxation time ratio is 0.54 ± 0.16 which means that in the absence of peel the theoretical drying time is expected to be half of the respective one with peel although this behaviour can only be achieved under ideal drying conditions. Besides, one has always to consider that the errors originated from the regressions may alter the relaxation time to some extent. Drying at 65 °C gave small differences between the drying curves [MR = f (t)] of peeled and unpeeled figs as can be seen in Fig. 2, probably due to case hardening effect. In this case, the peeled figs were dehydrated faster at the beginning of the process and therefore sugars were moved to the surface faster than in the unpeeled figs which resulted in faster appearance of the phenomenon in the peeled than in the unpeeled figs. The effect of the air-drying temperature on the drying constant was assessed employing an Arrhenius type equation. From the regression of the drying constants with the respective air-drying temperatures, Eq. (6) for peeled figs and Eq. (7) for unpeeled figs, were derived with R2adj and SEE for unpeeled figs 0.9999 and 0.0033 and for peeled figs 0.9550 and 0.1225 respectively. The experimental k values for peeled and unpeeled figs as well the respective predicted k values from Eqs. (6) and (7) are showed in Fig. 3

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Table 2 Regression analysis coefficients of Logarithmic drying model. Case

a

k (h1)

c

Relaxation time (h)

R2

SEE

v2

Unpeeled figs 45 °C, 3 m s1 45 °C, 4 m s1 55 °C, 1 m s1 55 °C, 3 m s1 55 °C, 5 m s1 65 °C, 1 m s1 65 °C, 3 m s1 65 °C, 5 m s1

1.041139 1.139682 0.922861 0.934888 1.125931 0.912990 1.005695 1.089643

0.039112 0.037675 0.066221 0.076578 0.063764 0.138895 0.103097 0.117878

0.053161 0.153579 0.065827 0.061811 0.124019 0.088298 0.015939 0.085395

25.57 26.54 15.10 13.06 15.68 7.20 9.70 8.49

0.9991 0.9985 0.9987 0.9995 0.9989 0.9992 0.9987 0.9988

0.008521 0.011277 0.009948 0.006066 0.010213 0.008250 0.010437 0.010767

0.001960 0.002925 0.002474 0.000809 0.001564 0.001157 0.002396 0.001507

Peeled figs 45 °C, 3 m s1 45 °C, 4 m s1 55 °C, 1 m s1 55 °C, 3 m s1 55 °C, 5 m s1 65 °C, 1 m s1 65 °C, 3 m s1 65 °C, 5 m s1

0.849090 0.873407 0.815398 0.834776 0.867116 0.859105 0.864326 0.849765

0.078386 0.089058 0.126308 0.161405 0.152355 0.156481 0.160783 0.241475

0.081217 0.065064 0.133211 0.109495 0.081939 0.099130 0.112704 0.113919

12.76 11.23 7.92 6.20 6.56 6.39 6.22 4.14

0.9930 0.9937 0.9948 0.9943 0.9931 0.9961 0.9983 0.9955

0.022474 0.021756 0.018045 0.019710 0.024347 0.017531 0.014110 0.017527

0.010101 0.008519 0.007815 0.007770 0.007706 0.004916 0.002601 0.004915

45oC

55oC

65oC

45oC 1.0

0.8

0.8

0.6

0.6

55oC

65oC

MR

MR

1.0

0.4

0.4

0.2

0.2 0.0

0.0 0

10

20

30

40

50

Drying time, h

0

10

20

30

40

50

Drying time, h

Fig. 2. Drying curves of unpeeled (left) and peeled (right) figs for air-drying velocity 3 m s1.

Unpeeled_exp Unpeeled_pred

From the correlation of the parameters [ko (h1) and Ea (J mol1)] from Eqs. (6) and (7) Eqs. (8a), (8b), and (8c) were derived.

Peeled_exp Peeled_pred

0.25

ko jpeeled =ko junpeeled ¼ 0:006

ð8aÞ ð8bÞ

0.15

ln ko jpeeled ¼ 0:68 ) ko j0:68 unpeeled ¼ ko jpeeled ln ko junpeeled Ea jpeeled =Ea junpeeled ¼ 0:69

ð8cÞ

k, h

-1

0.20

0.10

Based on Eqs. (8b) and (8c) a general relation between the kpeeled and kunpeeled can be derived, as shown in Eq. (9)

0.05

  0:69  Ea junpeeled kpeeled ¼ ko j0:68 : unpeeled  exp  RT

0.00

40

45

50

55

60

65

ð9Þ

70

o

Drying temperature, C Fig. 3. The experimental (mean ± SD) and the predicted drying constant values from Eqs. (6) and (7).





35; 676:15 RT   51; 413:84 ¼ 10; 581; 312:17  exp  RT

kpeeled ¼ 63; 786:70  exp 

ð6Þ

kunpeeled

ð7Þ

where R is the universal gas constant (8.31143 J mol1 K1) and T the air-drying temperature in K.

4.2. Estimation of the effective water diffusivity for peeled and unpeeled figs The Deff was estimated based on the method of slopes as it was previously described. The mean Deff values for the three drying temperatures (45, 55 and 65 °C) and the two treatments (peeled, unpeeled figs) are presented in the Table 3. The estimated Deff values lie within the range of 1011 to 1009 m2 s1 for food stuff (Saravacos and Maroulis, 2001). Based on the analysis of variance (P 6 0.05) and Saravacos (2005), who has referred that Deff depends mainly on the porosity and the temperature while moisture content has minor effect and any dependency of the Deff from the moisture content is probably due to indirect effect of the porosity which is strongly affected by the moisture content, the Deff was as-

G. Xanthopoulos et al. / Journal of Food Engineering 97 (2010) 419–424 Table 3 The experimental Deff (m2 s1) values (mean ± SD) estimated by the method of slopes. T (°C)

Unpeeled figs

Peeled figs

10

10

5.54  1010 ± 1.28  1010 6.52  1010 ± 1.80  1010 7.80  1010 ± 2.01  1010

± 1.24  10 3.97  10 5.12  1010 ± 2.03  1010 10 7.52  10 ± 3.10  1010

45 55 65

sumed to vary only with drying temperature. The Duncan’s multiple comparison procedure showed statistically significant differences of the Deff in-between the three air-drying temperatures for both treatments (peeled and unpeeled figs). The effect of the air-drying temperature on Deff was assessed employing an Arrhenius type equation. From the regression of the mean Deff and the corresponding air-drying temperatures, Eq. (10) for peeled figs and Eq. (11) for unpeeled figs were derived with R2adj and SEE for unpeeled figs 0.9652 and 0.0600 and for peeled figs 0.9961 and 0.0106 respectively

  15; 302:84 Deff jpeeled ¼ 1:80  107  exp  RT   28; 537:87 5 Deff junpeeled ¼ 1:88  10  exp  RT

ð10Þ ð11Þ

Plotting the mean experimental and predicted Deff values, Fig. 4 was derived. The peeled figs had higher Deff values, a fact that was expected, the respective drying times were shorter (faster drying) since the peel, a water transfer barrier, had been removed. As it was previously noted, the drying curves of the peeled and unpeeled figs were quite close at 65 °C exhibiting similar drying behaviour. This fact is showed in Fig. 4 where as the drying temperature is increased the difference of the Deff between peeled and unpeeled figs is gradually reduced. Probably products having high sugar content, like figs, exhibit this behaviour in high drying temperatures (>60 °C) due to case hardening effect, although more research is needed in this area. Achanta and Okos (1996) stated that case hardening can be reduced by drying at lower temperatures where drying rate is slow enough to allow water loss from the surface of the product to be replenished by water from the inside of the product. The previous statement enforces the assumption that in the case of the peeled figs, Deff was higher than in the unpeeled figs but drying at 65 °C resulted in faster water removal and consequently faster appearance of case hardening which in turn limited further increase in Deff. The energy of activation Ea in the unpeeled figs is 1.86 times higher than in the peeled figs as shown in Eq. (12b). From Eqs.

Unpeeled_exp Unpeeled_pred

Peeled_exp Peeled_pred

9.0E-10 8.0E-10

Deff, m s

2. -1

7.0E-10

6.0E-10

5.0E-10

4.0E-10

3.0E-10

40

45

50

55

60

65

70

o

Drying temperature, C Fig. 4. The experimental mean and the predicted Deff values from Eqs. (10) and (11).

423

(10) and (11) the correlation of the parameters [Do (m2 s1) and Ea (J mol1)] can be derived as shown in Eqs. (12a) and (12b)

Do junpeeled ¼ 0:7 ) Do j0:7 peeled ¼ Do junpeeled ln Do jpeeled

ð12aÞ

Ea junpeeled =Ea jpeeled ¼ 1:86

ð12bÞ

Using Eqs. (12a) and (12b), a general relation between the Deff for peeled and unpeeled figs can be derived as shown in Eq. (13).

  0:536  Ea junpeeled : Deff jpeeled ¼ Do junpeeled Þ1=0:7  exp  RT

ð13Þ

5. Conclusions The drying behaviour of whole figs with and without peel was investigated for three drying temperatures (45, 55 and 65 °C). The drying kinetics in both treatments was estimated testing seven drying models. The chosen Logarithmic model was used to describe the drying behaviour of peeled and unpeeled figs based on the fitting efficiency of the model. The drying constants and the respective relaxation times were also estimated. The estimated ratio of peeled to unpeeled relaxation times was 0.54 ± 0.16. The estimated drying constants were associated with the respective drying temperatures implementing an Arrhenius type equation. The Deff of peeled and unpeeled figs was also estimated implementing the method of slopes to handle the non linearity of the semi-logarithmic MR curves. The mean Deff values for unpeeled figs was 3.97  1010, 5.12  1010 and 7.52  1010 m2 s1 and for peeled figs was 5.54  1010, 6.52  1010 and 7.80  1010 m2 s1 at 45, 55 and 65 °C. The peeled and unpeeled figs at 65 °C exhibited similar drying behaviour which can be seen in the drying curves and from the Deff values which are quite close. This behaviour was attributed to the fact that drying at 65 °C resulted in faster water removal from the peeled figs and consequently faster appearance of case hardening which in turn reduced the drying rate and the respective Deff value. References Achanta, S., Okos, M.R., 1996. Predicting the quality of dehydrated foods and biopolymers – research needs and opportunities. Drying Technology 14 (6), 1329–1368. AOAC, 1997. Official Methods of Analysis, 16th ed. Association of Official Analytical Chemists, Washington, DC. Babalis, S.J., Belessiotis, V.G., 2004. Influence of the drying conditions on the drying constants and moisture diffusivity during the thin-layer drying of figs. Journal of Food Engineering 65, 449–458. Babalis, S.J., Papanicolaou, E., Kyriakis, N., Belessiotis, V.G., 2006. Evaluation of thinlayer drying models for describing drying kinetics of figs (Ficus carica). Journal of Food Engineering 75 (2), 205–214. Brennan, J.G., 2006. Evaporation and dehydration. In: Brennan, J.G. (Ed.), Food Processing Handbook. Wiley-VCH Verlag CmbH & Co., Weinheim, pp. 71–121. Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W., 1992. Drying and Storage of Grains and Oilseeds, first ed. Van Nostrand Reinhold, New York. pp. 212–213. Crank, J., 1975. Mathematics of Diffusion, second ed. Oxford University Press, London. Demirel, D., Turhan, M., 2003. Air-drying behaviour of Dwarf Cavendish and Gros Michel banana slices. Journal of Food Engineering 59, 1–11. Doymaz, I., 2005. Sun drying of figs: an experimental study. Journal of Food Engineering 71, 403–407. Doymaz, I., 2006. Drying kinetics of black grapes treated with different solutions. Journal of Food Engineering 76, 212–217. Doymaz, I., 2007a. Air-drying characteristics of tomatoes. Journal of Food Engineering 78, 1291–1297. Doymaz, I., 2007b. Influence of pretreatment solution on the drying of sour cherry. Journal of Food Engineering 78, 591–596. Efremov, G., Kudra, T., 2005. Model-based estimate for time-dependent apparent diffusivity. Drying Technology 23, 2513–2522. Gonzalez-Fesler, M., Salvatori, D., Gomez, P., Alzamora, S.M., 2008. Convective air drying of apples as affected by blanching and calcium impregnation. Journal of Food Engineering 87, 323–332. Henderson, S.M., 1974. Progress in developing the thin-layer drying equation. Transactions of the ASAE 17, 1167–1172.

424

G. Xanthopoulos et al. / Journal of Food Engineering 97 (2010) 419–424

Jayas, D.S., Cenkowski, S., Pabis, S., Muir, W.E., 1991. Review of thin-layer drying and wetting equations. Drying Technology 9 (3), 551–588. Karathanos, V.T., 1999. Determination of water content of dried fruits by drying kinetics. Journal of Food Engineering 39, 337–344. Karathanos, V.T., Belessiotis, V.G., 1999. Application of a thin-layer equation to drying data of fresh and semi-dried fruits. Journal of Agricultural Engineering Research 74, 355–361. Karathanos, V.T., Villalobos, G., Saravacos, G.D., 1990. Comparison of two methods of estimation of the effective water diffusivity from drying data. Journal of Food Science 55 (1), 218–223. 231. Mohsenin, N.N., 1978. Physical Properties of Plant and Animal Materials, second ed. Gordon and Breach Science Publishers, New York. Pabis, S., Jayas, D.S., Cenkowski, S., 1998. Grain Drying: Theory and Practice, first ed. John Wiley & Sons, New York. pp. 110–111. Perez, N.E., Schmalko, M.E., 2009. Convective drying of pumpkin: influence of pretreatment and drying temperature. Journal of Food Process Engineering 32, 88– 103. Perry, R.H., Green, D.W., 1999. Perry’s Chemical Engineers’ Handbook, eighth ed. McGraw-Hill, New York. p. 346. Phoungchandang, S., Woods, J.L., 2000. Moisture diffusion and desorption isotherms for banana. Journal of Food Science 65 (4), 651–657. Piga, F., Pinna, I., Özer, K.D., Agabbio, V., Aksoy, U., 2004. Hot air dehydration of figs (Ficus carica L.): drying kinetics and quality loss. International Journal of Food Science and Technology 39, 793–799. Rahman, S., 1995. Food Properties Handbook, first ed. CRC Press, Florida. pp. 29–46.

Saravacos, G.D., 2005. Mass transfer properties of foods. In: Rao, M.A., Rizvi, S.S.H., Datta, A.K. (Eds.), Engineering Properties of Foods. Taylors & Francis, New York, pp. 327–372. Saravacos, G.D., Maroulis, Z.B., 2001. Transport Properties of Foods, first ed. Marcel Decker, Inc., New York. 163–236. Statistical Graphics Corp., 2001. Statgraphics Plus 5.1. Online Manual, Statistical Graphics Corp. USDA, 2002. Nutrient Database for Standard Reference, Release 15. Vega-Galvez, A., Lemus-Mondaca, R., Bilbao-Sainz, C., Fito, P., Andres, A., 2008. Effect of air drying temperature on the quality of rehydrated dried red bell pepper (var. Lamuyo). Journal of Food Engineering 85, 42–50. Wang, C.Y., Singh, R.P., 1978. A single layer drying equation for rough rice. ASAE Paper No. 3001. Xanthopoulos, G., Oikonomou, N., Lambrinos, G., 2007a. Applicability of a singlelayer model to predict the drying rate of whole figs. Journal of Food Engineering 81, 553–559. Xanthopoulos, G., Lambrinos, Gr., Manolopoulou, H., 2007b. Evaluation of thin-layer models for mushroom (Agaricus bisporus) drying. Drying Technology 25, 1471– 1481. Xanthopoulos, G., Yanniotis, S., Lambrinos, Gr., 2009. Water diffusivity and drying kinetics of air drying of figs. Drying Technology 27, 502–512. Yaldiz, O., Ertekin, C., 2002. Thin-layer solar drying of some vegetables. Drying Technology 19, 583–596. Zhang, Q., Litchfield, J.B., 1991. An optimisation of intermittent corn drying in a laboratory scale thin-layer dryer. Drying Technology 9, 383–395.