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Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying
Journal of Food Engineering 65 (2004) 609–617 www.elsevier.com/locate/jfoodeng
Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying G.P. Sharma a
a,*
, Suresh Prasad
b
Processing and Food Engineering Department, College of Technology and Engineering, Udaipur 313 001, India b Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur 721 302, India Received 13 January 2002; received in revised form 6 January 2004; accepted 18 February 2004
Abstract Drying of garlic cloves was done using microwave-convective technique, using microwave power of 10–40 W, air temperature of 40–70 C and at air velocity of 1–2 m/s. The effective moisture diffusivity varied from 1.29 to 31.68 · 1010 m2 /s. A third order polynomial relationship was found to correlate the effective moisture diffusivity (Deff ) with moisture content. The Deff increased for the same values of drying air temperatures and velocities as the applied microwave power was increased. However, Deff decreased at all temperatures and applied microwave power with increase in air velocity. The activation energy in the microwave-convective drying ranged between 4.08 and 10.50 kJ/mol, which was much lower than the convectionally heating activation energy values for moisture diffusivities for most vegetables. 2004 Elsevier Ltd. All rights reserved.
1. Introduction Microwave drying has several advantages over conventional hot air drying, such as higher drying rate, minimal heating at locations with less water thus reducing overheating of locations where heating is not required. However, for microwave drying to be more useful at the industrial level, it needs information on moisture diffusion models that could describe the process accurately. The diffusion coefficient of a food is material property and its value depends upon the conditions within the material. Effective moisture diffusivity describes all possible mechanisms of moisture movement within the foods, such as liquid diffusion, vapour diffusion, surface diffusion, capillary flow and hydrodynamic flow (Kim & Bhowmik, 1995). The heating mechanism and conditions within a material during microwave drying are different from those during conventional drying. A knowledge of effective moisture diffusivity is necessary for designing and modeling mass-transfer processes such as dehydration, adsorption and desorption of moisture during storage. The literature surveyed revealed that moisture diffusivity for garlic cloves under MW-convective drying conditions has not been docu*
Corresponding author. E-mail address: [email protected] (G.P. Sharma).
0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.02.027
mented. The objective of this study has, therefore, been to determine the effective moisture diffusivity of garlic cloves during a microwave-convective drying process and its dependence on factors such as microwave power, air temperature and air velocity that essentially influence drying rates.
2. Material and methods Fresh garlic (Allium sativum) bulbs of Mainpuri variety were used in the investigation, which were procured in bulk from the local market of Kharagpur in the state of West Bengal (India). The garlic had moisture contents ranging between 1.89 and 1.85 g water/ g dry matter and were stored in a cold chamber maintained approximately at a temperature of 1 C and 70% relative humidity. The vacuum oven method was used to determine the initial moisture content of the garlic cloves. Garlic samples of approximately 15 g were placed in pre-dried aluminum dishes in a vacuum oven for about 24 h, with sulfuric acid as a desiccant. The operating temperature of the oven was 70 C with a gauge pressure of 85 kPa (Madamba, Driscoll, & Buckle, 1995). The samples were taken out of the oven, cooled in a dessicator and weighed using a ANAMED top pan electronic balance with a sensitivity of 0.01 g.
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The fresh and dry weights were used to calculate the moisture content which was expressed as g water/ g dry matter. Microwave-hot-air-drying experiments for garlic cloves were conducted in a laboratory microwave-convective dryer. The constructional details of the dryer are presented elsewhere (Sharma & Prasad, 2001). As stated above, fresh garlic cloves of Mainpuri variety were procured from the nearby market and stored at 1 C in perforated plastic bags until use (at most two months). A sample size of approximately 100 g of peeled garlic cloves was used in each drying experiment. The sample lot consisted of cloves of uniform size, each clove weighing between 0.87 and 1.12 g. Microwave power in the range 10–40 W in steps of 10 W was applied continuously, in conjunction with hot air at temperatures of 40, 50, 60 and 70 C and at velocities of 1.0 and 2.0 m/s. The velocity was measured by anemometer (1–50 m/s ± 2%; Kanomax, Japan). The microwave power in the drying chamber was measured by a calorimetric method (Metaxas & Meredith, 1983; Tulasidas, Raghavan, & Norris, 1993). On-line weighing of sample was carried out every 5 min during the drying process, under all drying conditions, until it reduced to a level corresponding to a moisture content of approximately 6% (d.b.). The moisture content was calculated from the weight of the sample and expressed as g water/ g dry matter.
1 X Mt Me 4 ¼ MR ¼ exp 2 M0 Me n¼1 kn
The method of slopes was used in the estimation of effective moisture diffusivity of garlic at corresponding moisture contents under different drying conditions. The garlic cloves were assumed as infinite cylinders i.e. moisture diffusion occurring radially outwards only (Crank, 1975) and following assumptions were made for the infinite cylindrical shaped body of the garlic clove. 1. Moisture is initially uniformly distributed throughout the mass of a sample. 2. Mass transfer is symmetric with respect to the centre of the cylinder. 3. Surface moisture content of the sample instantaneously reaches equilibrium with the condition of surrounding air. 4. Resistance to mass transfer at the surface is negligible compared to internal resistance of the sample. 5. Mass transfer is by diffusion only. 6. Diffusion coefficient is constant and shrinkage is negligible. The following solution to the Fickian equation was, therefore, used
k2 Dt n2 r
ð1Þ
where MR is the moisture ratio, dimensionless; M0 , the moisture content at time t ¼ 0, g water/g dry matter; Mt , the moisture content at time t, g water/g dry matter; Me , the equilibrium moisture content, g water/g dry matter; D, the moisture diffusivity, m2 /s; r, the radius of the cylinder, m; t, the drying time, s; kn is the nth root of the Bessel function of zero order, n ¼ 1; 2; 3; . . . The final moisture content of the dehydrated garlic (0.06 g water/g dry matter) was assumed to be equilibrium moisture content Me in each run. Several researchers (Prabhanjan, Ramaswamy, & Raghavan, 1995; Ren & Chen, 1998) have used final moisture content of the dried product as equilibrium moisture content for studying drying kinetics of the product in microwave-convective drying process. Eq. (1) is evaluated numerically for Fourier number, F0 ¼ D t=r2 , for diffusion and thus can be re-written as MR ¼
4 expðk21 F0 Þ k21
For n ¼ 1 and k1 ¼ 2:405 (Eq. (1)), the above equation takes the following form, F0 ¼ 0:173 lnðMRÞ 0:0637 where F0 ¼ Dt=r2 and Deff ¼
2.1. Theoretical approach
ðF0 Þth ðt=r2 Þexp
ð2Þ
The effective moisture diffusivity (Deff ) was estimated by substituting the positive values of ðF0 Þth and the drying time t along with the average radius of the garlic clove (3.6 mm) in Eq. (2), for each corresponding moisture content under different drying conditions. The diameter of was measured at places along the length of the fresh cloves, using a Vernier caliper. About 100 such measurements were taken and the average value for the diameter was obtained as 7.2 mm.
3. Results and discussion The drying of garlic cloves exhibited a falling rate period under combined microwave-convective drying conditions. An analysis of the falling rate period was carried out to understand the drying kinetics by determination of effective moisture diffusivity (Deff ), the influence of moisture content on the effective moisture diffusivity and the activation energy involved under various conditions of microwave-convective drying. Generally, an effective moisture diffusivity is used due to limited information on the mechanism of moisture movement during drying and the complexity of the process (Madamba, Driscoll, & Buckle, 1996).
G.P. Sharma, S. Prasad / Journal of Food Engineering 65 (2004) 609–617
3.1. Effective moisture diffusivity (Deff )
3.2. Effect of moisture content on effective moisture diffusivity
The logarithm of moisture ratio values (lnMR) were plotted against average drying time (t) for different drying conditions and the plots for MW drying of garlic cloves is shown in Figs. 1 and 2. It is noted from the figures that the relationships were non-linear in nature under all the drying conditions studied. This non-linearity in the relationship may be due to the reasons like shrinkage in the product, non-uniform distribution of initial moisture, variation in moisture diffusivity with moisture content and change in product temperature during drying (Adu & Otten, 1996; Khraisheh, Cooper, & Magee, 1997). The non-linearity of the curves is indicative of the variation in moisture diffusivity with moisture content. A second order polynomial relationship between lnMR and drying time t fitted well and is given below: lnMR ¼ A0 þ A1 t þ A2 t2
611
ð3Þ
Regression coefficients A0 , A1 and A2 and the corresponding values of coefficients of determination (r2 ) for convective and MW drying are presented in Table 1.
The variation in moisture diffusivity with moisture content is a complex and system specific function. The effective moisture diffusivity (Deff ) of a food material characterizes its intrinsic moisture mass transport property and includes molecular diffusion, liquid diffusion, vapour diffusion, hydrodynamic flow and other possible mass transport mechanisms (Karathanos, Villalobos, & Saravacos, 1990). The values of Deff corresponding to positive F0 values were plotted against moisture content under all drying conditions and the variations are presented in Figs. 3 and 4. The Deff values increased with decrease in moisture content under all drying conditions. Bouraoui, Richard, and Durance (1994) reported an increase in the effective moisture diffusivity with decrease in moisture content during microwave-convective drying of potato. This may indicate that as moisture content decreased, the permeability to vapour increased, provided the pore structure remained open. The temperature of the product rises rapidly in the initial stages of drying, due to more absorption of microwave heat, as the product has a high
Fig. 1. Plot of lnðMRÞ vs drying time for garlic cloves at various microwave power levels at air velocity of 1.0 m/s.
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Fig. 2. Plot of lnðMRÞ vs drying time for garlic cloves at various microwave power levels at air velocity of 2.0 m/s.
loss factor at higher moisture content. This increases the water vapour pressure inside the pores and results in pressure induced opening of pores. In the first stage of drying, liquid diffusion of moisture could be the main mechanism of moisture transport. As drying progressed further, vapour diffusion could have been the dominant mode of moisture diffusion in the latter part of drying. A third order polynomial relationship was found to correlate the effective moisture diffusivity (Deff ) with corresponding moisture content (M) of garlic and is given by Eq. (4) Deff ¼ A þ BM þ CM 2 þ DM 3
ð4Þ
where Deff is the effective moisture diffusivity, m2 /s; M, the moisture content, g water/g dry matter and A; B; C; D ¼ constants of regression for MW-convective drying of garlic in different drying conditions are presented in Table 2. The high values of r2 are indicative of good fit of the empirical relationship to represent the variation in Deff with M of garlic cloves during drying under different conditions. 3.3. Effect of process variables on average effective moisture diffusivity (Deff )Avg The average effective moisture diffusivity, ðDeff ÞAvg , was calculated by taking the arithmetic mean of the
effective moisture diffusivities that were estimated at various levels of moisture contents during the course of drying. The values of average effective moisture diffusivity ðDeff ÞAvg for all drying condition prevalent in microwave-convective drying are presented in Table 3. The ðDeff ÞAvg increased from 1.593 · 1010 to 9.7 · 1010 m2 /s as the air temperature increased from 40 to 70 C at an air velocity of 1.0 m/s when microwave power of 10 W was applied. The values of ðDeff ÞAvg increased progressively for the same values of drying air temperatures and velocities as the applied microwave power (P ) was increased. This reduced the drying time dramatically. The increase in P resulted in rapid heating of the product, thus increasing the vapour pressure inside the product that made the diffusion of moisture towards the surface faster. However, at an air velocity of 2.0 m/s, the value of ðDeff ÞAvg decreased at all air temperatures and applied microwave power compared to the similar MW drying conditions at an air velocity of 1.0 m/s, a trend contrary to one observed in convective drying. This was due to cooling of the garlic cloves at higher velocity (because product temperature remained higher than the surrounding air resulting in negative temperature gradient), again due to increase in outside heat transfer coefficient (h) as h / v0:4 for crossflow air (Rao & Rizvi, 1986). An ANOVA carried out to study the effect the process variables on ðDeff ÞAvg revealed that
G.P. Sharma, S. Prasad / Journal of Food Engineering 65 (2004) 609–617
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Table 1 Regression coefficients and coefficient of determination (r2 ) for different microwave-convective drying conditions Drying conditions
Regression coefficients
r2
MW power (W)
Air velocity (m/s)
Temperature (C)
A0
A1
A2
10
1.0
40 50 60 70
)0.3025 )0.3041 )0.2326 )0.0912
+0.0031 +0.0083 +0.0037 )0.0195
)0.3025 )0.3040 )0.0003 )0.0002
0.942 0.913 0.979 0.994
2.0
40 50 60 70
)0.3779 )0.3097 )0.3385 )0.2468
+0.0044 +0.0062 +0.0023 )0.0129
)0.3779 )0.3097 )0.0003 )0.0002
0.904 0.934 0.942 0.979
1.0
40 50 60 70
)0.3008 )0.0654 )0.2401 )0.1383
+0.0011 )0.0163 )0.0047 )0.0092
)0.0003 )0.0002 )0.0005 )0.0006
0.989 0.987 0.966 0.988
2.0
40 50 60 70
)0.3984 )0.1716 )0.1721 )0.0530
)0.0090 )0.0143 +0.0001 )0.0182
)1 · 104 )0.0002 )0.0008 )0.0009
0.956 0.981 0.990 0.995
1.0
40 50 60 70
)0.3312 +0.0281 )0.1031 )0.0051
)0.0094 )0.0323 )0.0392 )0.0621
)0.0002 )0.0003 )0.0005 )0.0007
0.951 0.983 0.990 0.993
2.0
40 50 60 70
)0.3437 )0.1827 )0.1033 )0.0055
0.0078 )0.0213 )0.0392 )0.0621
)0.0002 )0.0003 )0.0005 )0.0007
0.962 0.972 0.994 0.993
1.0
40 50 60 70
)0.1786 )0.0765 )0.1652 )0.2082
)0.0371 +0.0411 )0.0254 +0.0123
)7 · 105 )0.0003 )0.0011 )0.0045
0.991 0.995 0.973 0.964
2.0
40 50 60 70
)0.4104 )0.2342 )0.0405 )0.2161
)0.0131 )0.0260 )0.0503 )0.0442
)0.0001 )0.0002 )0.0002 )0.0008
0.955 0.956 0.997 0.955
20
30
40
microwave power (P ), air temperature (T ), air velocity (v) and their interactions had a significant effect on ðDeff Þavg (at 5% level). A linear regression analysis on the average diffusion coefficient, ðDeff ÞAvg with the processing variables resulted in the following relationships: ðDeff ÞAvg ¼ ½0:46P 1:71v þ 0:42T 17:89 1010 ðr2 ¼ 0:90; SE ¼ 2:39Þ
ð5Þ
where P is the applied microwave power, W; V , the air velocity, m/s and T is the drying air temperature, C. 3.4. Activation energy The dependence of average effective moisture diffusivity ðDeff ÞAvg on drying air temperature was obtained by an Arrhenius-type relationship (Eq. (6))
ðDeff ÞAvg ¼ D0 exp
Ea RTabs
ð6Þ
where ðDeff ÞAvg is the average effective moisture diffusivity, m2 /s; D0 , the constant equivalent to diffusivity at infinite temperature, m2 /s; Ea , the activation energy, kJ/ kg mol; R, the universal gas constant, 3.814 kJ/kg mol K and Tabs is the absolute drying air temperature, K. The Influence of drying air temperature on moisture transport, at a microwave power level between 10 and 40 W is shown in Figs. 5 and 6 at air velocities 1.0 and 2.0 respectively. The activation energies involved in MWconvective drying of garlic cloves, under different drying conditions, was estimated from the slopes of Eq. (6) which ranged between 4.05 and 10.50 kJ/mol. These are presented in Table 4. Thermodynamically, activation energy is the relative ease with which the water
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Fig. 3. Variation in effective moisture diffusivity with moisture content at various air temperature at air velocity 1.0 m/s.
Fig. 4. Variation in effective moisture diffusivity with moisture content at various air temperature at air velocity 2.0 m/s.
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Table 2 Regression coefficients of effective moisture diffusivity during MW-convective drying conditions MW power (W)
10
20
30
40
Air velocity (m/s)
Air temperature (C)
r2
Regression coefficients A
B
C
D
1.0
40 50 60 70
5.013 8.281 13.92 14.55
)15.69 )27.33 )42.89 )27.78
22.23 38.67 66.45 39.53
)11.12 )19.17 )36.59 )23.21
0.96 0.95 0.92 0.96
2.0
40 50 60 70
5.021 7.87 13.22 13.53
)17.53 )26.181 )58.73 )29.37
26.88 38.23 117.87 47.57
)14.11 )19.41 )79.10 )27.83
0.90 0.95 0.86 0.90
1.0
40 50 60 70
15.80 17.38 22.51 26.47
)18.60 )37.57 )60.97 )71.63
73.08 48.16 88.53 103.30
)37.87 )24.34 )45.54 )52.55
0.94 0.95 0.87 0.93
2.0
40 50 60 70
11.14 16.05 26.69 31.33
)27.11 )38.54 )72.64 )69.15
56.04 63.34 99.69 79.55
)36.90 )36.88 )49.09 )35.17
0.92 0.94 0.97 0.97
1.0
40 50 60 70
15.172 21.76 28.73 37.10
)48.32 )43.27 )60.21 )73.91
90.93 62.15 103.36 124.99
)54.14 )34.91 )64.02 )78.21
0.86 0.95 0.95 0.95
2.0
40 50 60 70
14.35 20.75 26.47 24.17
)38.31 )56.34 )71.74 )14.89
68.35 103.77 115.15 28.59
)41.34 )62.75 )60.91 )27.65
0.98 0.89 0.88 0.84
1.0
40 50 60 70
16.29 25.59 34.87 39.37
)12.26 )42.15 )80.67 )34.50
28.03 61.93 119.13 17.76
)25.40 )37.78 )64.92 )11.67
0.93 0.95 0.89 0.99
2.0
40 50 60 70
13.01 18.07 23.62 31.21
)36.37 )30.60 )30.83 )45.58
88.35 59.81 46.39 103.94
)61.29 )40.57 )30.95 )81.82
0.91 0.83 0.96 0.88
Table 3 Effect of process variables on average effective moisture diffusivity ðDeff ÞAvg 1010 (m2 /s)
Drying air condition Air velocity (m/s)
Air temperature (C)
10 W
20 W
30 W
40 W
1.0
40 50 60 70
1.593 3.306 6.860 9.707
4.331 8.214 8.226 16.875
7.432 15.269 18.837 23.708
14.095 20.001 23.708 31.685
2.0
40 50 60 70
1.291 2.518 5.506 9.54
3.998 8.549 12.464 16.213
5.788 11.311 15.892 22.552
7.212 13.011 18.098 25.657
molecules pass the energy hurdle when migrating within the product. The lower activation energy translates to higher moisture diffusivity in the drying process.
The activation energy in the processes was much lower than the convectionally heating activation energy values for moisture diffusivity for vegetables ranging
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Fig. 5. Influence of drying air temperature on average effective moisture diffusivity in microwave-convective drying of garlic cloves at air velocity of 1.0 m/s.
drying process. The reduction in the energy of activation of a process results from an increase in the average energy of the molecules, which take part in the process. This view is predicted by the thermodynamics of polarized systems, which indicate that microwaves, through polarization, provide additional energy to the dipolar molecules they polarize. Bound molecules participating in microwave heat generation are those that have been mobile enough to rotate. In the mobilized state, molecules will require less energy to transfer from a porous material. Thus, the results indicate that the higher drying rates observed during microwaveconvective drying are due to lower activation energy for moisture desorption. The activation energy for a given microwave power was lower at 1.0 m/s velocity compared to air velocity of 2.0 m/s. Adu and Otten (1996) reported similar trend in the change of activation energy during microwave drying of soybeans. 4. Conclusions
Fig. 6. Influence of drying air temperature on average effective moisture diffusivity in microwave-convective drying of garlic cloves at air velocity of 2.0 m/s.
Table 4 Activation energy (Ea ) for MW-convective drying processes MW-convective drying process
Activation energy, Ea (kJ/mol)
Air velocity (m/s)
MW power (W)
1.0
10 20 30 40
9.67 7.11 6.05 4.08
2.0
10 20 30 40
10.50 7.39 7.05 6.56
between 130 and 280 kJ/mol (Feng & Tang, 1999). The activation energy in microwave-convective drying was lower at an air velocity of 1.0 m/s compared to an air velocity of 2.0 m/s for a given value of applied MW power. This indicates the higher drying rates at 1.0 m/s as compared to 2.0 m/s during the microwave-convective
Effective moisture diffusivity depends on the moisture content, and increases with decrease in moisture content. It increases with increase in both drying air temperature and microwave power at a given air velocity, but with increase in air velocity, diffusivity values were lower for the similar drying conditions resulting into slower drying of the product. The activation energy in the microwave-convective drying process was much lower than the convectionally heating activation energy values for moisture diffusivity for vegetables ranging between 130 and 280 kJ/mol as reported in the literature by many researchers.
References Adu, B., & Otten, L. (1996). Microwave heating and mass transfer characteristics of white beans. Journal of Agricultural Engineering Research, 64, 71–78. Bouraoui, M., Richard, P., & Durance, T. (1994). Microwave and convective drying of potato slices. Journal of Food Process Engineering, 17, 353–363. Crank, J. (1975). The mathematics of diffusion. Oxford, UK: Oxford University Press. Feng, H., & Tang, J. (1999). Combined microwave and spouted bed drying of diced apples: Effect of drying conditions on drying kinetics and product temperature. Drying Technology, 17(10), 1981–1998. Karathanos, V. T., Villalobos, G., & Saravacos, G. D. (1990). Comparison of two methods of estimation of the effective moisture diffusivity from drying data. Journal of Food Science, 55(1), 218–231. Khraisheh, M. A. M., Cooper, T. J. R., & Magee, T. R. A. (1997). Shrinkage characteristics of potatoes dehydrated under combined microwave and convective air conditions. Drying Technology, 15(3&4), 1003–1022. Kim, S. S., & Bhowmik, S. R. (1995). Effective moisture diffusivity of plain yogurt undergoing microwave vacuum drying. Journal of Food Engineering, 24, 137–148.
G.P. Sharma, S. Prasad / Journal of Food Engineering 65 (2004) 609–617 Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1995). Models for the specific heat and thermal conductivity of garlic. Drying Technology, 13(1&2), 295–317. Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1996). Enthalpy– entropy compensation models for sorption and browning of garlic. Journal of Food Engineering, 28, 109–119. Metaxas, A. C., & Meredith, R. J. (1983). Industrial microwave heating. Herts, England: Peter Peregrinus Ltd. Prabhanjan, D. G., Ramaswamy, H. S., & Raghavan, G. S. V. (1995). Microwave-assisted convective air drying of thin-layer carrots. Journal of Food Engineering, 25, 283–293.
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Rao, M. A., & Rizvi, S. S. H. (1986). Engineering properties of foods. New York: Marcel Dekker Inc. Ren, G., & Chen, F. (1998). Drying of American ginseng (Panax quinquefolium) roots by microwave–hot air combination. Journal of Food Engineering, 35, 433–443. Sharma, G. P., & Prasad, S. (2001). Drying of garlic (Allium sativum) cloves by microwave-hot air combination. Journal of Food Engineering, 50, 99–105. Tulasidas, T. N., Raghavan, G. S. V., & Norris, E. R. (1993). Microwave and convective drying of grapes. Transactions of ASAE, 36(6), 1861–1865.
Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying G.P. Sharma a
a,*
, Suresh Prasad
b
Processing and Food Engineering Department, College of Technology and Engineering, Udaipur 313 001, India b Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur 721 302, India Received 13 January 2002; received in revised form 6 January 2004; accepted 18 February 2004
Abstract Drying of garlic cloves was done using microwave-convective technique, using microwave power of 10–40 W, air temperature of 40–70 C and at air velocity of 1–2 m/s. The effective moisture diffusivity varied from 1.29 to 31.68 · 1010 m2 /s. A third order polynomial relationship was found to correlate the effective moisture diffusivity (Deff ) with moisture content. The Deff increased for the same values of drying air temperatures and velocities as the applied microwave power was increased. However, Deff decreased at all temperatures and applied microwave power with increase in air velocity. The activation energy in the microwave-convective drying ranged between 4.08 and 10.50 kJ/mol, which was much lower than the convectionally heating activation energy values for moisture diffusivities for most vegetables. 2004 Elsevier Ltd. All rights reserved.
1. Introduction Microwave drying has several advantages over conventional hot air drying, such as higher drying rate, minimal heating at locations with less water thus reducing overheating of locations where heating is not required. However, for microwave drying to be more useful at the industrial level, it needs information on moisture diffusion models that could describe the process accurately. The diffusion coefficient of a food is material property and its value depends upon the conditions within the material. Effective moisture diffusivity describes all possible mechanisms of moisture movement within the foods, such as liquid diffusion, vapour diffusion, surface diffusion, capillary flow and hydrodynamic flow (Kim & Bhowmik, 1995). The heating mechanism and conditions within a material during microwave drying are different from those during conventional drying. A knowledge of effective moisture diffusivity is necessary for designing and modeling mass-transfer processes such as dehydration, adsorption and desorption of moisture during storage. The literature surveyed revealed that moisture diffusivity for garlic cloves under MW-convective drying conditions has not been docu*
Corresponding author. E-mail address: [email protected] (G.P. Sharma).
0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.02.027
mented. The objective of this study has, therefore, been to determine the effective moisture diffusivity of garlic cloves during a microwave-convective drying process and its dependence on factors such as microwave power, air temperature and air velocity that essentially influence drying rates.
2. Material and methods Fresh garlic (Allium sativum) bulbs of Mainpuri variety were used in the investigation, which were procured in bulk from the local market of Kharagpur in the state of West Bengal (India). The garlic had moisture contents ranging between 1.89 and 1.85 g water/ g dry matter and were stored in a cold chamber maintained approximately at a temperature of 1 C and 70% relative humidity. The vacuum oven method was used to determine the initial moisture content of the garlic cloves. Garlic samples of approximately 15 g were placed in pre-dried aluminum dishes in a vacuum oven for about 24 h, with sulfuric acid as a desiccant. The operating temperature of the oven was 70 C with a gauge pressure of 85 kPa (Madamba, Driscoll, & Buckle, 1995). The samples were taken out of the oven, cooled in a dessicator and weighed using a ANAMED top pan electronic balance with a sensitivity of 0.01 g.
610
G.P. Sharma, S. Prasad / Journal of Food Engineering 65 (2004) 609–617
The fresh and dry weights were used to calculate the moisture content which was expressed as g water/ g dry matter. Microwave-hot-air-drying experiments for garlic cloves were conducted in a laboratory microwave-convective dryer. The constructional details of the dryer are presented elsewhere (Sharma & Prasad, 2001). As stated above, fresh garlic cloves of Mainpuri variety were procured from the nearby market and stored at 1 C in perforated plastic bags until use (at most two months). A sample size of approximately 100 g of peeled garlic cloves was used in each drying experiment. The sample lot consisted of cloves of uniform size, each clove weighing between 0.87 and 1.12 g. Microwave power in the range 10–40 W in steps of 10 W was applied continuously, in conjunction with hot air at temperatures of 40, 50, 60 and 70 C and at velocities of 1.0 and 2.0 m/s. The velocity was measured by anemometer (1–50 m/s ± 2%; Kanomax, Japan). The microwave power in the drying chamber was measured by a calorimetric method (Metaxas & Meredith, 1983; Tulasidas, Raghavan, & Norris, 1993). On-line weighing of sample was carried out every 5 min during the drying process, under all drying conditions, until it reduced to a level corresponding to a moisture content of approximately 6% (d.b.). The moisture content was calculated from the weight of the sample and expressed as g water/ g dry matter.
1 X Mt Me 4 ¼ MR ¼ exp 2 M0 Me n¼1 kn
The method of slopes was used in the estimation of effective moisture diffusivity of garlic at corresponding moisture contents under different drying conditions. The garlic cloves were assumed as infinite cylinders i.e. moisture diffusion occurring radially outwards only (Crank, 1975) and following assumptions were made for the infinite cylindrical shaped body of the garlic clove. 1. Moisture is initially uniformly distributed throughout the mass of a sample. 2. Mass transfer is symmetric with respect to the centre of the cylinder. 3. Surface moisture content of the sample instantaneously reaches equilibrium with the condition of surrounding air. 4. Resistance to mass transfer at the surface is negligible compared to internal resistance of the sample. 5. Mass transfer is by diffusion only. 6. Diffusion coefficient is constant and shrinkage is negligible. The following solution to the Fickian equation was, therefore, used
k2 Dt n2 r
ð1Þ
where MR is the moisture ratio, dimensionless; M0 , the moisture content at time t ¼ 0, g water/g dry matter; Mt , the moisture content at time t, g water/g dry matter; Me , the equilibrium moisture content, g water/g dry matter; D, the moisture diffusivity, m2 /s; r, the radius of the cylinder, m; t, the drying time, s; kn is the nth root of the Bessel function of zero order, n ¼ 1; 2; 3; . . . The final moisture content of the dehydrated garlic (0.06 g water/g dry matter) was assumed to be equilibrium moisture content Me in each run. Several researchers (Prabhanjan, Ramaswamy, & Raghavan, 1995; Ren & Chen, 1998) have used final moisture content of the dried product as equilibrium moisture content for studying drying kinetics of the product in microwave-convective drying process. Eq. (1) is evaluated numerically for Fourier number, F0 ¼ D t=r2 , for diffusion and thus can be re-written as MR ¼
4 expðk21 F0 Þ k21
For n ¼ 1 and k1 ¼ 2:405 (Eq. (1)), the above equation takes the following form, F0 ¼ 0:173 lnðMRÞ 0:0637 where F0 ¼ Dt=r2 and Deff ¼
2.1. Theoretical approach
ðF0 Þth ðt=r2 Þexp
ð2Þ
The effective moisture diffusivity (Deff ) was estimated by substituting the positive values of ðF0 Þth and the drying time t along with the average radius of the garlic clove (3.6 mm) in Eq. (2), for each corresponding moisture content under different drying conditions. The diameter of was measured at places along the length of the fresh cloves, using a Vernier caliper. About 100 such measurements were taken and the average value for the diameter was obtained as 7.2 mm.
3. Results and discussion The drying of garlic cloves exhibited a falling rate period under combined microwave-convective drying conditions. An analysis of the falling rate period was carried out to understand the drying kinetics by determination of effective moisture diffusivity (Deff ), the influence of moisture content on the effective moisture diffusivity and the activation energy involved under various conditions of microwave-convective drying. Generally, an effective moisture diffusivity is used due to limited information on the mechanism of moisture movement during drying and the complexity of the process (Madamba, Driscoll, & Buckle, 1996).
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3.1. Effective moisture diffusivity (Deff )
3.2. Effect of moisture content on effective moisture diffusivity
The logarithm of moisture ratio values (lnMR) were plotted against average drying time (t) for different drying conditions and the plots for MW drying of garlic cloves is shown in Figs. 1 and 2. It is noted from the figures that the relationships were non-linear in nature under all the drying conditions studied. This non-linearity in the relationship may be due to the reasons like shrinkage in the product, non-uniform distribution of initial moisture, variation in moisture diffusivity with moisture content and change in product temperature during drying (Adu & Otten, 1996; Khraisheh, Cooper, & Magee, 1997). The non-linearity of the curves is indicative of the variation in moisture diffusivity with moisture content. A second order polynomial relationship between lnMR and drying time t fitted well and is given below: lnMR ¼ A0 þ A1 t þ A2 t2
611
ð3Þ
Regression coefficients A0 , A1 and A2 and the corresponding values of coefficients of determination (r2 ) for convective and MW drying are presented in Table 1.
The variation in moisture diffusivity with moisture content is a complex and system specific function. The effective moisture diffusivity (Deff ) of a food material characterizes its intrinsic moisture mass transport property and includes molecular diffusion, liquid diffusion, vapour diffusion, hydrodynamic flow and other possible mass transport mechanisms (Karathanos, Villalobos, & Saravacos, 1990). The values of Deff corresponding to positive F0 values were plotted against moisture content under all drying conditions and the variations are presented in Figs. 3 and 4. The Deff values increased with decrease in moisture content under all drying conditions. Bouraoui, Richard, and Durance (1994) reported an increase in the effective moisture diffusivity with decrease in moisture content during microwave-convective drying of potato. This may indicate that as moisture content decreased, the permeability to vapour increased, provided the pore structure remained open. The temperature of the product rises rapidly in the initial stages of drying, due to more absorption of microwave heat, as the product has a high
Fig. 1. Plot of lnðMRÞ vs drying time for garlic cloves at various microwave power levels at air velocity of 1.0 m/s.
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Fig. 2. Plot of lnðMRÞ vs drying time for garlic cloves at various microwave power levels at air velocity of 2.0 m/s.
loss factor at higher moisture content. This increases the water vapour pressure inside the pores and results in pressure induced opening of pores. In the first stage of drying, liquid diffusion of moisture could be the main mechanism of moisture transport. As drying progressed further, vapour diffusion could have been the dominant mode of moisture diffusion in the latter part of drying. A third order polynomial relationship was found to correlate the effective moisture diffusivity (Deff ) with corresponding moisture content (M) of garlic and is given by Eq. (4) Deff ¼ A þ BM þ CM 2 þ DM 3
ð4Þ
where Deff is the effective moisture diffusivity, m2 /s; M, the moisture content, g water/g dry matter and A; B; C; D ¼ constants of regression for MW-convective drying of garlic in different drying conditions are presented in Table 2. The high values of r2 are indicative of good fit of the empirical relationship to represent the variation in Deff with M of garlic cloves during drying under different conditions. 3.3. Effect of process variables on average effective moisture diffusivity (Deff )Avg The average effective moisture diffusivity, ðDeff ÞAvg , was calculated by taking the arithmetic mean of the
effective moisture diffusivities that were estimated at various levels of moisture contents during the course of drying. The values of average effective moisture diffusivity ðDeff ÞAvg for all drying condition prevalent in microwave-convective drying are presented in Table 3. The ðDeff ÞAvg increased from 1.593 · 1010 to 9.7 · 1010 m2 /s as the air temperature increased from 40 to 70 C at an air velocity of 1.0 m/s when microwave power of 10 W was applied. The values of ðDeff ÞAvg increased progressively for the same values of drying air temperatures and velocities as the applied microwave power (P ) was increased. This reduced the drying time dramatically. The increase in P resulted in rapid heating of the product, thus increasing the vapour pressure inside the product that made the diffusion of moisture towards the surface faster. However, at an air velocity of 2.0 m/s, the value of ðDeff ÞAvg decreased at all air temperatures and applied microwave power compared to the similar MW drying conditions at an air velocity of 1.0 m/s, a trend contrary to one observed in convective drying. This was due to cooling of the garlic cloves at higher velocity (because product temperature remained higher than the surrounding air resulting in negative temperature gradient), again due to increase in outside heat transfer coefficient (h) as h / v0:4 for crossflow air (Rao & Rizvi, 1986). An ANOVA carried out to study the effect the process variables on ðDeff ÞAvg revealed that
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Table 1 Regression coefficients and coefficient of determination (r2 ) for different microwave-convective drying conditions Drying conditions
Regression coefficients
r2
MW power (W)
Air velocity (m/s)
Temperature (C)
A0
A1
A2
10
1.0
40 50 60 70
)0.3025 )0.3041 )0.2326 )0.0912
+0.0031 +0.0083 +0.0037 )0.0195
)0.3025 )0.3040 )0.0003 )0.0002
0.942 0.913 0.979 0.994
2.0
40 50 60 70
)0.3779 )0.3097 )0.3385 )0.2468
+0.0044 +0.0062 +0.0023 )0.0129
)0.3779 )0.3097 )0.0003 )0.0002
0.904 0.934 0.942 0.979
1.0
40 50 60 70
)0.3008 )0.0654 )0.2401 )0.1383
+0.0011 )0.0163 )0.0047 )0.0092
)0.0003 )0.0002 )0.0005 )0.0006
0.989 0.987 0.966 0.988
2.0
40 50 60 70
)0.3984 )0.1716 )0.1721 )0.0530
)0.0090 )0.0143 +0.0001 )0.0182
)1 · 104 )0.0002 )0.0008 )0.0009
0.956 0.981 0.990 0.995
1.0
40 50 60 70
)0.3312 +0.0281 )0.1031 )0.0051
)0.0094 )0.0323 )0.0392 )0.0621
)0.0002 )0.0003 )0.0005 )0.0007
0.951 0.983 0.990 0.993
2.0
40 50 60 70
)0.3437 )0.1827 )0.1033 )0.0055
0.0078 )0.0213 )0.0392 )0.0621
)0.0002 )0.0003 )0.0005 )0.0007
0.962 0.972 0.994 0.993
1.0
40 50 60 70
)0.1786 )0.0765 )0.1652 )0.2082
)0.0371 +0.0411 )0.0254 +0.0123
)7 · 105 )0.0003 )0.0011 )0.0045
0.991 0.995 0.973 0.964
2.0
40 50 60 70
)0.4104 )0.2342 )0.0405 )0.2161
)0.0131 )0.0260 )0.0503 )0.0442
)0.0001 )0.0002 )0.0002 )0.0008
0.955 0.956 0.997 0.955
20
30
40
microwave power (P ), air temperature (T ), air velocity (v) and their interactions had a significant effect on ðDeff Þavg (at 5% level). A linear regression analysis on the average diffusion coefficient, ðDeff ÞAvg with the processing variables resulted in the following relationships: ðDeff ÞAvg ¼ ½0:46P 1:71v þ 0:42T 17:89 1010 ðr2 ¼ 0:90; SE ¼ 2:39Þ
ð5Þ
where P is the applied microwave power, W; V , the air velocity, m/s and T is the drying air temperature, C. 3.4. Activation energy The dependence of average effective moisture diffusivity ðDeff ÞAvg on drying air temperature was obtained by an Arrhenius-type relationship (Eq. (6))
ðDeff ÞAvg ¼ D0 exp
Ea RTabs
ð6Þ
where ðDeff ÞAvg is the average effective moisture diffusivity, m2 /s; D0 , the constant equivalent to diffusivity at infinite temperature, m2 /s; Ea , the activation energy, kJ/ kg mol; R, the universal gas constant, 3.814 kJ/kg mol K and Tabs is the absolute drying air temperature, K. The Influence of drying air temperature on moisture transport, at a microwave power level between 10 and 40 W is shown in Figs. 5 and 6 at air velocities 1.0 and 2.0 respectively. The activation energies involved in MWconvective drying of garlic cloves, under different drying conditions, was estimated from the slopes of Eq. (6) which ranged between 4.05 and 10.50 kJ/mol. These are presented in Table 4. Thermodynamically, activation energy is the relative ease with which the water
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Fig. 3. Variation in effective moisture diffusivity with moisture content at various air temperature at air velocity 1.0 m/s.
Fig. 4. Variation in effective moisture diffusivity with moisture content at various air temperature at air velocity 2.0 m/s.
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Table 2 Regression coefficients of effective moisture diffusivity during MW-convective drying conditions MW power (W)
10
20
30
40
Air velocity (m/s)
Air temperature (C)
r2
Regression coefficients A
B
C
D
1.0
40 50 60 70
5.013 8.281 13.92 14.55
)15.69 )27.33 )42.89 )27.78
22.23 38.67 66.45 39.53
)11.12 )19.17 )36.59 )23.21
0.96 0.95 0.92 0.96
2.0
40 50 60 70
5.021 7.87 13.22 13.53
)17.53 )26.181 )58.73 )29.37
26.88 38.23 117.87 47.57
)14.11 )19.41 )79.10 )27.83
0.90 0.95 0.86 0.90
1.0
40 50 60 70
15.80 17.38 22.51 26.47
)18.60 )37.57 )60.97 )71.63
73.08 48.16 88.53 103.30
)37.87 )24.34 )45.54 )52.55
0.94 0.95 0.87 0.93
2.0
40 50 60 70
11.14 16.05 26.69 31.33
)27.11 )38.54 )72.64 )69.15
56.04 63.34 99.69 79.55
)36.90 )36.88 )49.09 )35.17
0.92 0.94 0.97 0.97
1.0
40 50 60 70
15.172 21.76 28.73 37.10
)48.32 )43.27 )60.21 )73.91
90.93 62.15 103.36 124.99
)54.14 )34.91 )64.02 )78.21
0.86 0.95 0.95 0.95
2.0
40 50 60 70
14.35 20.75 26.47 24.17
)38.31 )56.34 )71.74 )14.89
68.35 103.77 115.15 28.59
)41.34 )62.75 )60.91 )27.65
0.98 0.89 0.88 0.84
1.0
40 50 60 70
16.29 25.59 34.87 39.37
)12.26 )42.15 )80.67 )34.50
28.03 61.93 119.13 17.76
)25.40 )37.78 )64.92 )11.67
0.93 0.95 0.89 0.99
2.0
40 50 60 70
13.01 18.07 23.62 31.21
)36.37 )30.60 )30.83 )45.58
88.35 59.81 46.39 103.94
)61.29 )40.57 )30.95 )81.82
0.91 0.83 0.96 0.88
Table 3 Effect of process variables on average effective moisture diffusivity ðDeff ÞAvg 1010 (m2 /s)
Drying air condition Air velocity (m/s)
Air temperature (C)
10 W
20 W
30 W
40 W
1.0
40 50 60 70
1.593 3.306 6.860 9.707
4.331 8.214 8.226 16.875
7.432 15.269 18.837 23.708
14.095 20.001 23.708 31.685
2.0
40 50 60 70
1.291 2.518 5.506 9.54
3.998 8.549 12.464 16.213
5.788 11.311 15.892 22.552
7.212 13.011 18.098 25.657
molecules pass the energy hurdle when migrating within the product. The lower activation energy translates to higher moisture diffusivity in the drying process.
The activation energy in the processes was much lower than the convectionally heating activation energy values for moisture diffusivity for vegetables ranging
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Fig. 5. Influence of drying air temperature on average effective moisture diffusivity in microwave-convective drying of garlic cloves at air velocity of 1.0 m/s.
drying process. The reduction in the energy of activation of a process results from an increase in the average energy of the molecules, which take part in the process. This view is predicted by the thermodynamics of polarized systems, which indicate that microwaves, through polarization, provide additional energy to the dipolar molecules they polarize. Bound molecules participating in microwave heat generation are those that have been mobile enough to rotate. In the mobilized state, molecules will require less energy to transfer from a porous material. Thus, the results indicate that the higher drying rates observed during microwaveconvective drying are due to lower activation energy for moisture desorption. The activation energy for a given microwave power was lower at 1.0 m/s velocity compared to air velocity of 2.0 m/s. Adu and Otten (1996) reported similar trend in the change of activation energy during microwave drying of soybeans. 4. Conclusions
Fig. 6. Influence of drying air temperature on average effective moisture diffusivity in microwave-convective drying of garlic cloves at air velocity of 2.0 m/s.
Table 4 Activation energy (Ea ) for MW-convective drying processes MW-convective drying process
Activation energy, Ea (kJ/mol)
Air velocity (m/s)
MW power (W)
1.0
10 20 30 40
9.67 7.11 6.05 4.08
2.0
10 20 30 40
10.50 7.39 7.05 6.56
between 130 and 280 kJ/mol (Feng & Tang, 1999). The activation energy in microwave-convective drying was lower at an air velocity of 1.0 m/s compared to an air velocity of 2.0 m/s for a given value of applied MW power. This indicates the higher drying rates at 1.0 m/s as compared to 2.0 m/s during the microwave-convective
Effective moisture diffusivity depends on the moisture content, and increases with decrease in moisture content. It increases with increase in both drying air temperature and microwave power at a given air velocity, but with increase in air velocity, diffusivity values were lower for the similar drying conditions resulting into slower drying of the product. The activation energy in the microwave-convective drying process was much lower than the convectionally heating activation energy values for moisture diffusivity for vegetables ranging between 130 and 280 kJ/mol as reported in the literature by many researchers.
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