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Drying behaviour of brined onion slices
Journal of Food Engineering 40 (1999) 219±226
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Drying behaviour of brined onion slices P.N. Sarsavadia b, R.L. Sawhney a,*, D.R. Pangavhane a, S.P. Singh a a
School of Energy and Environmental Studies, Devi Ahilya University, Takshashila Campus, Khandwa Road, Indore-452017, Madhya Pradesh, India b Gujarat Agricultural University, M.R.R.S, Nawagam-387540, Gujarat, India Received 22 October 1998; received in revised form 22 February 1999; accepted 22 February 1999
Abstract A batch-type experimental dryer with an online weighing mechanism was developed for determining the thin-layer drying behaviour of onion. Thin-layer drying rates of brined onion slices were experimentally determined at four levels of drying air temperature (range of 50±80°C), four levels of air ¯ow velocity (range of 0.25±1.00 m/s) and three levels of air relative humidity (range of 10±20%). The experimental data obtained were ®tted into an Arrhenius-type model and power model using non-linear regression analysis. The Arrhenius-type model was found to be more suitable for predicting drying rate constants. Ó 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction
Notation
*
COD exp GAB ha H k L M MR MSD N n a0 , a1 , a2 , a3 c0; c1; c2; c3 b0 , b1 , b2 , b3 d0; d1; d2; d3 RH t T V
Coecient of determination (r2 ) Exponential Guggenheim±Anderson±de Boer equation Hectare Absolute humidity (kg/kg dry basis) Drying rate constant (minÿ1 ) Thickness (m) Moisture content (% dry basis) Moisture ratio Mean square deviation Number of observations Number of constants Empirical constants for Eq. (3) Empirical constants for Eq. (4) Empirical constants for Eq. (5) Empirical constants for Eq. (6) Relative humidity (%) Time (min) Air temperature (o C) Air ¯ow velocity (m/s)
Subscripts ab cali e expi f o
Absolute values of temperature in K Calculated values at observation i Equilibrium Experimental values at observation i Final Initial
Corresponding author.
Onion ranks third highest in production in the world among seven major vegetables, namely onion, garlic, cauli¯ower, greenpeas, cabbage, tomato and greenbeans. About 27.9 million tonne of onion are produced in the world from about 1.98 million ha land. The four major onion producing countries in the world are China with largest production of 3.93 million tonnes, followed by India with 3.35 million tonnes, USA 2.45 million tonnes and Turkey 1.55 million tonnes. In India, about 35±40% of onion is lost during post harvest, due to the lack of proper processing and storage facilities. Drying is the most common form of food preservation and extends the food shelf life. Dehydration of foods is aimed at producing a high density product, which when adequately packaged has a long shelf life, after which the food can be rapidly and simply reconstituted without substantial loss of ¯avour, taste, colour and aroma. Onions are generally dried from an initial moisture content of about 86% (wet basis) to 7% or less for ecient storage and processing. Dehydrated onions in the form of ¯akes or powder are in extensive demand in several parts of the world, for example UK, Japan, Russia, Germany, Netherlands, Spain etc. Dehydrated onions are a product of considerable importance in world trade. According to the International Trade Centre (ITC), Geneva, the demand for dehydrated onions alone in the European Union (EU) was estimated at more than 45,000 tonnes per year (Rao & Ranganath, 1995).
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 5 8 - 8
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Mathematical modelling of the dehydration process is very useful in the design and optimisation of dryers (Brook & Bakker-Arkema, 1978; Bertin & Blazquez, 1986; Vagenas & Marinos-Kouris, 1991). However, theoretical simulations of the drying process (moisture migrations in the product being dried) require a substantial amount of computing time because of the complexity (although realistic) of the diusion equations governing the process (Sharp, 1982; Parry, 1985). For nonisotropic, and nonhomogeneous nature of the agricultural products along with their irregular shape and changes in shape during drying, most of the work reported on thin-layer drying of agricultural crops is mainly empirical in nature. But work on onion drying in particular and other vegetables drying in general has been very limited. Mazza and LeMaguer (1980), as well as Saravacos and Charm (1962) have developed theoretical models for onion drying for heated ambient air conditions. Rapusas and Driscoll (1995), and Kiranoudis, Maroulis and Marinos-Kouris (1992) have developed empirical relations for onions in the form of Arrhenius-type and power models, respectively. Kiranoudis et al. (1992) have obtained the drying characteristics of shredded onions with characteristic dimensions and air velocities high as compared to the values usually used in commercial onion dehydration. Rapusas and Driscoll (1995) have obtained these results for sliced onions. The air temperatures generally considered for drying onions range between 50°C and 80°C. For storage and further processes, ®nal moisture content of the dried onions must be less than 7±8% (wb). As, with drying air of relative humidity more than 20% at 50°C, the equilibrium moisture content of onion will be more than 8% (wb) (Kiranoudis, Maroulis, Tsami & Marinos-Kouris, 1993), the relative humidity of the drying air in the experiment was kept below 20% for all levels of drying air temperature. To obtain drying rate constants covering air conditions in the above range heating ambient air for a particular climate will not be adequate. Hence, it was necessary to use controlled drying air conditions (in which humidity level at a given temperature can be changed to 20%) for obtaining drying rate constants. The basic aim of this work was to determine the drying rate constants of onion under relevant drying air conditions. For this purpose a suitable thin-layer drying apparatus was developed. 2. Mathematical model The ¯ow of moisture from the agricultural material to the surrounding can be considered as analogous to the heat transfer from a body immersed in cold ¯uid (Hukill & Schmidt, 1960). Comparing the drying phenomenon
with NewtonÕs law of cooling, the drying rate will be approximately proportional to the dierence in moisture content between the material being dried and the equilibrium moisture content at the drying air state. Mathematically, this can be written as follows: dM ÿk M ÿ Me : dt On integration, Eq. (1) yields M ÿ Me c exp ÿkt Mo ÿ Me
1
2
M ÿ Me = Mo ÿ Me is known as the moisture ratio. The equilibrium moisture content, Me can be obtained from the well known GAB equation (after Kiranoudis et al., 1993). The dependence of the drying rate constant, k on the drying air variables is modelled as an Arrhenius-type equation and/or power model. Rapusas and Driscoll (1995) have also investigated in¯uence of the drying variables on the constant, c. Both the constants can be expressed in the following form. Arrhenius-type equation: ÿa3 a1 a2 ; 3 k a0 V H exp Tab ÿc3 c c0 V c1 H c2 exp : 4 Tab Power model: k b0 V b1 H b2 T b3 ;
5
c d0 V d1 H d2 T d3 :
6
3. Materials and methods Fresh, medium grade (55±70 mm diameter), fully matured white onions (Allium cepa-L, variety: Agrifound white-1) were used for the study and procured from the National Horticulture Research and Development Foundation (Indore, India). The total soluble solids content of the fresh onion sample was found to be 14.0 o Brix which was measured with the help of hand refractometer. Drying behaviour of onion was determined experimentally with the help of an experimental laboratory apparatus speci®cally developed for the purpose (described subsequently in this section) . The experiments were conducted at four levels of temperature (50°C, 60°C, 70°C and 80°C), four levels of velocity (0.25, 0.50, 0.75 and 1.00 m/s); and three levels of relative humidity (10%, 15% and 20%) of the drying air. In the dehydration process of onion, generally slices of thickness varying between 2.5 and 5.0 mm are used (Girdharilal, Siddappa & Tandon, 1976). 5.0 mm thick slices were used for the study, as the largest thickness
P.N. Sarsavadia et al. / Journal of Food Engineering 40 (1999) 219±226
will provide the bench mark information on as upper limit to the energy required for dehydration of onion. Similar thickness was also considered by Rapusas, Driscoll and Srzednicki (1995) based on the average thickness commonly employed in the commercial manufacturer of dehydrated onion ¯akes (Barta, Lazer & Rasmussen, 1973). 3.1. Experimental laboratory set-up Based on the experience of set-up used earlier (Huizhen & Morey, 1984; Bruce and Sykes, 1983 as well as Syarief, Morey & Gustafson, 1984), a suitable thin layer drying apparatus was developed for providing controlled drying air conditions and online weighing measurement (air ¯ow was stopped whilst weighing). The schematic diagram of the dryer is shown in Fig. 1. The dryer essentially consists of a centrifugal blower, air heating chamber, steam generator, drying chamber, and online weighing system. Air supplied by the centrifugal blower (capacity: 3 m3 /min) was heated to the required temperature in a heating chamber. A gate valve (V1) was provided for regulating the ¯ow rate of air to the drying chamber. Four electrical heaters, each having 1 kW capacity, were installed in the heating chamber. The drying air temperature was controlled by a variable auto transformer which regulated the required voltage to the electrical heaters. The dry bulb and wet bulb temperatures of the air in the drying chamber were measured by two Pt-100 sensors (accuracy 0.1°C) installed at a distance of
221
25 mm above the drying product. The humidity of the air was maintained by injecting a controlled amount of steam from the steam generator into the main air duct pipe. A hand shut o valve was provided for controlling the steam ¯ow rate. The main vertical column of the drying chamber (360 mm ´ 360 mm cross sectional area and overall height of 880 mm) was made from 8 mm thick waterproof plywood sheet. A straightener (100 mm long) was ®tted inside the chamber for streamlining the air ¯ow. A door (with viewing glass) was provided on the front side of the chamber for placing and removing the sample holding tray. A wooden platform (10 mm thick), ®tted with an oil channel was provided below the straightener as shown in Fig. 1. Light oil ®lling the channel was used to provide an air seal. All sides and the platform of the chamber was innerlined with aluminium foil to provide re¯ective insulation. All units of the set-up were connected to each other through 50 mm G.I. pipe. Ball valves (V2) and (V3) were provided for disconnecting the drying chamber from the air circuit when required. Air ¯ow rate was measured with the help of an ori®ce plate and U-tube water manometer connected to the line. A special weighing system was developed for online measurement of the weight of the product while it is being dried. The weighing unit consisted of an electrical balance (200 g capacity and 0.0001 g accuracy), weighing pan, sample holding tray and oil channel. The weighing pan was suspended in the oil of the oil channel. A removable sample holding tray (size 100 mm ´ 100
Fig. 1. Experimental dryer set up.
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mm) having a wire mesh (5 mm ´ 5 mm made from 0.3 mm diameter copper wire) was used for placing the onion slices on the weighing pan. This arrangement allowed online measurement of the weight of the product and also provided an oil seal to the air ¯ow forcing it to pass through the product placed on the wire mesh of the sample holding tray.
Verma, 1986; Ajibola, 1989; Rapusas & Driscoll, 1995). The lower is the values of reduced chi-square, the better will be the goodness of ®t. By de®nition: PN 2 MRexpi ÿ MRcali 2 v i1 : 7 N ÿn
3.2. Sample preparation
4. Results and discussion
Onions were hand peeled and sliced (5 mm thick) at right angle to the vertical axis with the help of a hand operated slicing machine. Ten slices of about 50 mm diameter were selected. The diameter and thickness of the slices were measured with the help of a vernier caliper having a least count of 0.05 mm. The slices were then brined by steeping in 5% NaCl solution for 10 min in a petridish. After draining the solution from the dish, the surface water of the slices was removed by ®lter paper. Out of these ten slices, four slices were used for drying measurement. The average weight of the sample used was about 36 g. The remaining six slices were used for determination of the initial moisture content of the onion samples by the vacuum oven method at 70°C and 50 mm Hg for 6 h (AOAC, 1975).
4.1. Eect of moisture content on drying rate Variation of the drying rate with moisture content for only four experimental runs (out of forty eight) are shown in Fig. 2. As indicated in these curves (and also seen in those of remaining forty four experimental runs) the constant drying rate period was found to be absent in the drying of sliced onions. This shows that diusion is the most dominant physical mechanism governing moisture movement in the onion slices. These results are in agreement with the observation of Mazza and LeMaguer (1980), made on 0.0015 m thick onion slice at air velocity of 0.29 m/s and air temperatures higher than the 40°C, and also con®rmed by Rapusas and Driscoll (1995).
3.3. Drying measurement
4.2. Drying rate constants
For achieving stable environmental conditions in the test chamber, the experimental set-up was operated continuously for two hours at no load condition. During the drying run, the air pressure, on the sample holding tray changes continuously due to the shrinkage of the sample. For removing the eect of the variable air pressure on the balance reading, the air supply to the test chamber was cut o for a very short time (about 30 s) at given intervals with the help of ball valves V2, V3 and stop valve V6. The balance reading was recorded during this time. For the ®rst two reading the air supply was cut o at 5 min intervals while for all remaining reading it was cut o at 15 min intervals.
The variation of moisture ratios with time for each run was used for calculating the drying constants c and k of a single term exponential model (Eq. (2)) using nonlinear regression as was done by earlier workers (Rapusas & Driscoll, 1995; Kiranoudis et al., 1992). The coecient of determination and reduced chi-square be-
3.4. Mathematical modelling procedure Mathematical modelling and analysis of the drying kinetic data was performed on a personal computer using Scienti®c and Technical Graphics (Microcal Origin, 1991). Non-linear regression was used for data analysis. The term used to evaluate goodness of ®t of the tested models to the experimental data are the coecient of determination (COD, r2 ) and the reduced chi-square (v2 ), as the mean square of the deviations (MSD) between the experimental and calculated values for the tested models. The MSD has been used previously by many workers for evaluating goodness of ®t of thinlayer drying models to experimental data (Noomhorm &
Fig. 2. Observed drying rate of onion slices at dierent temperatures for 0.5 m/s V and 10% RH. ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C).
P.N. Sarsavadia et al. / Journal of Food Engineering 40 (1999) 219±226
223
Fig. 3. Eect of temperature on thin-layer drying curve of onion at 0.5 m/s V and 10% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C, (A) predicted model 2).
Fig. 5. Eect of absolute humidity on thin-layer drying curve of onion at 60°C T and 0.75 m/s V ((s) 0.1250 kg/kg, (+) 0.01875 kg/kg, (h) 0.02550 kg/kg, (A) predicted model 2).
tween the experimental and calculated moisture ratio were also obtained. It was found that the COD (r2 ) was more than 0.996 for all of the 48 runs while the value of reduced chi-square ranged between 5.163 ´ 10ÿ4 and 3.03 ´ 10ÿ6 (which is very low) indicating that the model ®tted reasonably well with the experimental data for each drying run. It was also observed that the model ®t was very good for all of the experimental drying air conditions. However, at higher drying air temperatures and lower air velocities the ®tness was only good (a value of r2 between 0.996 and 0.998). This is further shown by Figs. 3±5, in which the drying curves are plotted using Eq. (2) with calculated values of c and k and experimentally obtained values for selected experimental runs of drying air conditions. It is further seen from these Figures that the drying rate of the sliced onions increases with increase in the temperature and air ¯ow velocity, whereas it decreases with increase in ab-
solute humidity of the drying air. However, the in¯uence of temperature on the drying rate is more pronounced as compared to the in¯uence of the air ¯ow velocity and absolute humidity. These observations are in accordance with that of Rapusas and Driscoll (1995) as well as Mazza and LeMaguer (1980).
Fig. 4. Eect of air velocity on thin-layer drying curve of onion at 70°C T and 15% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, (A) predicted model 2).
4.3. Eect of drying air variables on drying rate constants Variation of the drying rate constant, k with drying air condition variables T, V and H as obtained from the experimental runs, is shown in Figs. 6±8, respectively. It is seen from Fig. 6 that the value of the constant, k decreases exponentially with increase in inverse of absolute temperature, showing the Arrhenius-type behaviour. With the increase in temperature of the drying medium, the drying potential increases and the moisture removal rate increases. Similarly, it can also be seen from Figs. 7 and 8 that the drying rate constant, k in-
Fig. 6. Eect of inverse of absolute temperature on drying constant, k at 10% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, V).
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cases of 48 runs). The reduced chi-square was also very low and ranged between 6.134 ´ 10ÿ4 and 4.737 ´ 10ÿ6 indicating that all the experimental drying runs ®t very well in the single term exponential model (Kiranoudis et al., 1992). 4.4. Determination of model constants
Fig. 7. Eect of air velocity on drying constant, k at 15% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C T).
Fig. 8. Eect of absolute humidity on drying constant, k at 70°C ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, V).
creases with increase in drying air velocity and decreases with increase in absolute humidity of the drying air. From this discussion, it can be safely said that the drying rate constant, k is greatly in¯uenced by the external drying conditions over the range of experimental conditions explored. It was found that the value of c does not vary signi®cantly (varying between values of 0.99 to 1.02 for all 48 experimental runs) with the drying air variables of temperature, velocity and absolute humidity. Hence, the value of c can be taken to be the equal to the mean values (1.01) of all the 48 runs. These values of c are in accordance with the value of c (0.98 0.04) obtained by Rapusas and Driscoll (1995). For the obtained mean value of c (1.01) very near to one, and considering the physical reality at the initial time t equal to zero, it will be more appropriate to take the value of c equal to one. The drying rate constant, k was further recalculated, considering only k as sole variable in Eq. (2) (i.e. taking c 1.00) for all of the 48 runs. It was observed that the COD, r2 was also good (more than 0.995 in all of the
The dependence of drying rate constant, k on drying air variables (temperature, velocity and absolute humidity) in the form of the Arrhenius-type equation (Eq. (3)) and power model (Eq. (4)) was analysed using non-linear regression to determine model constants a0 , a1 , a2 , a3 and b0 , b1 , b2 , b3 for the two models, respectively. The resulting values of these constants are given in Table 1 along with coecient of determination (r2 ) and reduced chi-square (v2 ) for both the cases, taking c equal to its mean value (1.01) and equal to 1.00 (cases (a) and (b), respectively). It is seen from Table 1 that the experimental data ®ts remarkably well, both for the Arrhenius-type model and power model, based on high values of COD (r2 ) and low values of v2 for both the cases (a) and (b). As the Arrhenious-type relationship provided slightly higher values of COD (r2 ) and lower values of reduced chi-square (v2 ) than the power model, the Arrhenius-type model is comparatively more suitable for describing the drying behaviour of onion slices. These observations are in agreement with those of Henderson and Pabis (1961), who provided rigorous theoretical justi®cation for the use of the Arrhenius-type relation for describing temperature dependence of the drying rate of food materials. Using the values of a0; a1; a2 and a3 , given in Table 1, the values of k were obtained using the Arrhenius-type model (Eq. (3)) for each experimental condition of the drying air. Taking the mean value of c as equal to 1.01 for all experimental conditions, the variation of the moisture ratio with time was calculated and plotted along with the measured value for the purpose of validation of the Arrhenius-type model. The experimental and predicted thin-layer drying curves using Arrheniustype model at four levels of temperature, four levels of air ¯ow velocity and three levels of humidity are shown in Figs. 9±11, respectively. It can be seen from these Figures that the results of predicated and calculated moisture ratios agreed closely with each other. Various workers have studied the drying rate behaviour of onion for dierent experimental conditions. For comparison, the range of drying rate constant, k obtained for their experimental conditions along with that of the present study are given in Table 2. It is seen from the Table 2 that the value of k signi®cantly depends on experimental conditions, material characteristics, material preparation (especially brining) and the material grown in dierent agro-climatic conditions.
P.N. Sarsavadia et al. / Journal of Food Engineering 40 (1999) 219±226
225
Table 1 Results of non-linear regression analysis for four parameter models of Arrhenius-type and power model for thin-layer drying of onion slices ((a) for the exponential model, MR c exp(ÿkt); (b) for the exponential model, MR exp(ÿkt)) Model
Arrhenius (a) (b)
Power (a) (b)
Parameters a0 (minÿ1 )
a1
a2
a3
47.57 38.85
0.31 0.32
ÿ0.20 ÿ0.20
3034 2961
b0 (minÿ1 )
b1
b2
b3
4.96 ´ 10ÿ6 5.96 ´ 10ÿ6
0.31 0.32
ÿ0.20 ÿ0.19
1.71 1.67
Fig. 9. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent temperatures for 0.5 m/s V and 15% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C, (A) predicted).
r2
v2
0.9882 0.9878
1.0173 ´ 10ÿ7 1.0165 ´ 10ÿ7
0.9845 0.9846
1.3326 ´ 10ÿ7 1.2785 ´ 10ÿ7
Fig. 11. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent absolute humidity for 70°C and 0.5 m/s V ((s) 0.0195 kg/kg, (+) 0.03 kg/kg, (h) 0.041 kg/kg, (A) predicted).
An experimental thin-layer drying system was developed and used to establish thin-layer drying behaviour of brined onion slices under wide range of drying conditions similar to those generally employed in commercial onion dehydration. It can be said that the single term exponential model (with c 1.00) adequately describes the drying behaviour of brined onion slices. The correlation of the drying constant, k with the drying air parameters (drying air temperature, ¯ow rate and absolute humidity) for Arrhenius-type and power model have also been established. Acknowledgements Fig. 10. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent air ¯ow velocity for 70°C and 10% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, (A) predicted).
P.N. Sarsavadia gratefully acknowledges to the vicechancellor, Gujarat Agricultural University, Sardar Krushi Nagar (Gujarat) India, for deputation granted to him.
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Table 2 Compiled values of drying rate constant, k with their experimental condition along with the present study on thin-layer drying of onions Source
Saravacos and Charm (1962) Mazza and LeMaguer (1980) Kiranoudis et al. (1992) Rapusas and Driscoll (1995) Present study a
Experimental conditions
k (minÿ1 )
Remark (variety)
sliced (ÿ) sliced (yellow globe) shredded (ÿ) sliced (white globe) sliced (Agfound white)
Range
T (°C)
H (kg/kg)
V (m/s)
Mo (% db)
L (m)
Min Max Min Max Min Max Min Max Min Max
62
0.0180
2.00
ÿ
0.0040
0.00600
40 65 60 81 42 90 50 80
ÿ
0.29 0.55 2.50 5.10 0.60 1.40 0.25 1.00
670a
0.0015
ÿ ÿ 385 452 612 641
0.0050 0.0150 0.0020 0.0080 0.0050
0.01050 0.01878 0.00800a 0.10000 0.00459 0.15430 0.00605 0.01838
0.0063 0.0374 0.0093 0.0440 0.0075 0.0640
Value obtained from the graph.
References AOAC (1975). Ocial methods of analysis (12 th ed.), Association of Ocial Analytical Chemists. Washington, DC. Ajibola, O. O. (1989). Thin-layer drying of melon seed. Journal of Food Engineering, 9, 306±320. Barta, E. J., Lazer, M. E., & Rasmussen, C. L. (1973). Dehydration plant Operations. In W. B. Arsdel, M. J. Copley, & A. I. Morgan Jr., Food Dehydration. Drying Methods and Phenomena (2nd ed.), vol. 1. AVI, Westport, CT. Bertin, R., & Blazquez, M. (1986). Modelling and optimisation of a dryer. Drying Technology, 4(1), 45±66. Brook, R. C., & Bakker-Arkema, F. W. (1978). Dynamic programming for process optimisation, 1. An algorithm for design of multistage grain dryers. Journal of Food Process Engineering, 2, 199±211. Bruce, D. M., & Sykes, R. A. (1983). Apparatus for determining mass transfer coecient at high temperatures for exposed particulate crop with initial results for wheat and hops. Journal of Agricultural Engineering Research, 28, 385±400. Girdharilal, Siddappa, G. S., & Tandon, G. L. (1976). Preservation of fruits and vegetables, ICAR, New Delhi (India). Henderson, S. M, & Pabis, S. (1961). Grain drying theory I temperature eect on drying coecient. Journal of Agricultural Engineering Research, 6(3), 169±174. Huizhen, L., & Morey, R. V. (1984). Thin layer drying of yellow dent corn. Transactions of the ASAE, 27(2), 581±585. Hukill, W. V., & Schmidt, J. L. (1960). Drying rate of fully exposed grain kernels. Transactions of the ASAE, 3(2), 71±80. Kiranoudis, C. T., Maroulis, Z. B., & Marinos-Kouris, D. (1992). Drying kinetics of onion and green pepper. Drying Technology, 10(4), 995±1011.
Kiranoudis, C. T., Maroulis, Z. B., Tsami, E., & Marinos-Kouris, D. (1993). Equilibrium moisture content and heat of desorption of some vegetables. Journal of Food Engineering, 20, 55±74. Mazza, G., & LeMaguer, M. (1980). Dehydration of onion: some theoretical and practical considerations. Journal of Food Technology, 15, 181±194. Noomhorm, A., & Verma, L. R. (1986). Generalized single-layer rice drying models. Transactions of the ASAE, 29(2), 587±591. Parry, J. L. (1985). Mathematical modelling and computer simulation of heat and mass transfer in agricultural grain drying: a review. Journal of Agricultural Engineering Research, 32, 1±29. Rao, V. K., & Ranganath, (1995). Onion exports. Food Digest, 18(2), 75. Rapusas, R. S., & Driscoll, R. H. (1995). The thin-layer drying characteristics of white onion slices. Drying Technology, 13(8 & 9), 1905±31. Rapusas, R. S., Driscoll, R. H., & Srzednicki, G. S. (1995). Bulk density and resistance to air¯ow of sliced onions. Journal of Food Engineering, 26, 67±80. Saravacos, G. D., & Charm, S. E. (1962). A study of the mechanism of fruit and vegetable dehydration. Food Technology, 16(1), 78±81. Sharp, J. R. (1982). A review of low temperature drying simulation models. Journal of Agricultural Engineering Research, 27, 169. Syarief, A. M., Morey, R. V., & Gustafson, R. J. (1984). Thin-layer drying rates of sun¯ower seed. Transactions of the ASAE, 27(1), 195±200. Vagenas, G. K., & Marinos-Kouris, D. (1991). The design and optimisation of an industrial dryer for sultana raisins. Drying Technology, 9(2), 439±461.
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Drying behaviour of brined onion slices P.N. Sarsavadia b, R.L. Sawhney a,*, D.R. Pangavhane a, S.P. Singh a a
School of Energy and Environmental Studies, Devi Ahilya University, Takshashila Campus, Khandwa Road, Indore-452017, Madhya Pradesh, India b Gujarat Agricultural University, M.R.R.S, Nawagam-387540, Gujarat, India Received 22 October 1998; received in revised form 22 February 1999; accepted 22 February 1999
Abstract A batch-type experimental dryer with an online weighing mechanism was developed for determining the thin-layer drying behaviour of onion. Thin-layer drying rates of brined onion slices were experimentally determined at four levels of drying air temperature (range of 50±80°C), four levels of air ¯ow velocity (range of 0.25±1.00 m/s) and three levels of air relative humidity (range of 10±20%). The experimental data obtained were ®tted into an Arrhenius-type model and power model using non-linear regression analysis. The Arrhenius-type model was found to be more suitable for predicting drying rate constants. Ó 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction
Notation
*
COD exp GAB ha H k L M MR MSD N n a0 , a1 , a2 , a3 c0; c1; c2; c3 b0 , b1 , b2 , b3 d0; d1; d2; d3 RH t T V
Coecient of determination (r2 ) Exponential Guggenheim±Anderson±de Boer equation Hectare Absolute humidity (kg/kg dry basis) Drying rate constant (minÿ1 ) Thickness (m) Moisture content (% dry basis) Moisture ratio Mean square deviation Number of observations Number of constants Empirical constants for Eq. (3) Empirical constants for Eq. (4) Empirical constants for Eq. (5) Empirical constants for Eq. (6) Relative humidity (%) Time (min) Air temperature (o C) Air ¯ow velocity (m/s)
Subscripts ab cali e expi f o
Absolute values of temperature in K Calculated values at observation i Equilibrium Experimental values at observation i Final Initial
Corresponding author.
Onion ranks third highest in production in the world among seven major vegetables, namely onion, garlic, cauli¯ower, greenpeas, cabbage, tomato and greenbeans. About 27.9 million tonne of onion are produced in the world from about 1.98 million ha land. The four major onion producing countries in the world are China with largest production of 3.93 million tonnes, followed by India with 3.35 million tonnes, USA 2.45 million tonnes and Turkey 1.55 million tonnes. In India, about 35±40% of onion is lost during post harvest, due to the lack of proper processing and storage facilities. Drying is the most common form of food preservation and extends the food shelf life. Dehydration of foods is aimed at producing a high density product, which when adequately packaged has a long shelf life, after which the food can be rapidly and simply reconstituted without substantial loss of ¯avour, taste, colour and aroma. Onions are generally dried from an initial moisture content of about 86% (wet basis) to 7% or less for ecient storage and processing. Dehydrated onions in the form of ¯akes or powder are in extensive demand in several parts of the world, for example UK, Japan, Russia, Germany, Netherlands, Spain etc. Dehydrated onions are a product of considerable importance in world trade. According to the International Trade Centre (ITC), Geneva, the demand for dehydrated onions alone in the European Union (EU) was estimated at more than 45,000 tonnes per year (Rao & Ranganath, 1995).
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 5 8 - 8
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Mathematical modelling of the dehydration process is very useful in the design and optimisation of dryers (Brook & Bakker-Arkema, 1978; Bertin & Blazquez, 1986; Vagenas & Marinos-Kouris, 1991). However, theoretical simulations of the drying process (moisture migrations in the product being dried) require a substantial amount of computing time because of the complexity (although realistic) of the diusion equations governing the process (Sharp, 1982; Parry, 1985). For nonisotropic, and nonhomogeneous nature of the agricultural products along with their irregular shape and changes in shape during drying, most of the work reported on thin-layer drying of agricultural crops is mainly empirical in nature. But work on onion drying in particular and other vegetables drying in general has been very limited. Mazza and LeMaguer (1980), as well as Saravacos and Charm (1962) have developed theoretical models for onion drying for heated ambient air conditions. Rapusas and Driscoll (1995), and Kiranoudis, Maroulis and Marinos-Kouris (1992) have developed empirical relations for onions in the form of Arrhenius-type and power models, respectively. Kiranoudis et al. (1992) have obtained the drying characteristics of shredded onions with characteristic dimensions and air velocities high as compared to the values usually used in commercial onion dehydration. Rapusas and Driscoll (1995) have obtained these results for sliced onions. The air temperatures generally considered for drying onions range between 50°C and 80°C. For storage and further processes, ®nal moisture content of the dried onions must be less than 7±8% (wb). As, with drying air of relative humidity more than 20% at 50°C, the equilibrium moisture content of onion will be more than 8% (wb) (Kiranoudis, Maroulis, Tsami & Marinos-Kouris, 1993), the relative humidity of the drying air in the experiment was kept below 20% for all levels of drying air temperature. To obtain drying rate constants covering air conditions in the above range heating ambient air for a particular climate will not be adequate. Hence, it was necessary to use controlled drying air conditions (in which humidity level at a given temperature can be changed to 20%) for obtaining drying rate constants. The basic aim of this work was to determine the drying rate constants of onion under relevant drying air conditions. For this purpose a suitable thin-layer drying apparatus was developed. 2. Mathematical model The ¯ow of moisture from the agricultural material to the surrounding can be considered as analogous to the heat transfer from a body immersed in cold ¯uid (Hukill & Schmidt, 1960). Comparing the drying phenomenon
with NewtonÕs law of cooling, the drying rate will be approximately proportional to the dierence in moisture content between the material being dried and the equilibrium moisture content at the drying air state. Mathematically, this can be written as follows: dM ÿk M ÿ Me : dt On integration, Eq. (1) yields M ÿ Me c exp ÿkt Mo ÿ Me
1
2
M ÿ Me = Mo ÿ Me is known as the moisture ratio. The equilibrium moisture content, Me can be obtained from the well known GAB equation (after Kiranoudis et al., 1993). The dependence of the drying rate constant, k on the drying air variables is modelled as an Arrhenius-type equation and/or power model. Rapusas and Driscoll (1995) have also investigated in¯uence of the drying variables on the constant, c. Both the constants can be expressed in the following form. Arrhenius-type equation: ÿa3 a1 a2 ; 3 k a0 V H exp Tab ÿc3 c c0 V c1 H c2 exp : 4 Tab Power model: k b0 V b1 H b2 T b3 ;
5
c d0 V d1 H d2 T d3 :
6
3. Materials and methods Fresh, medium grade (55±70 mm diameter), fully matured white onions (Allium cepa-L, variety: Agrifound white-1) were used for the study and procured from the National Horticulture Research and Development Foundation (Indore, India). The total soluble solids content of the fresh onion sample was found to be 14.0 o Brix which was measured with the help of hand refractometer. Drying behaviour of onion was determined experimentally with the help of an experimental laboratory apparatus speci®cally developed for the purpose (described subsequently in this section) . The experiments were conducted at four levels of temperature (50°C, 60°C, 70°C and 80°C), four levels of velocity (0.25, 0.50, 0.75 and 1.00 m/s); and three levels of relative humidity (10%, 15% and 20%) of the drying air. In the dehydration process of onion, generally slices of thickness varying between 2.5 and 5.0 mm are used (Girdharilal, Siddappa & Tandon, 1976). 5.0 mm thick slices were used for the study, as the largest thickness
P.N. Sarsavadia et al. / Journal of Food Engineering 40 (1999) 219±226
will provide the bench mark information on as upper limit to the energy required for dehydration of onion. Similar thickness was also considered by Rapusas, Driscoll and Srzednicki (1995) based on the average thickness commonly employed in the commercial manufacturer of dehydrated onion ¯akes (Barta, Lazer & Rasmussen, 1973). 3.1. Experimental laboratory set-up Based on the experience of set-up used earlier (Huizhen & Morey, 1984; Bruce and Sykes, 1983 as well as Syarief, Morey & Gustafson, 1984), a suitable thin layer drying apparatus was developed for providing controlled drying air conditions and online weighing measurement (air ¯ow was stopped whilst weighing). The schematic diagram of the dryer is shown in Fig. 1. The dryer essentially consists of a centrifugal blower, air heating chamber, steam generator, drying chamber, and online weighing system. Air supplied by the centrifugal blower (capacity: 3 m3 /min) was heated to the required temperature in a heating chamber. A gate valve (V1) was provided for regulating the ¯ow rate of air to the drying chamber. Four electrical heaters, each having 1 kW capacity, were installed in the heating chamber. The drying air temperature was controlled by a variable auto transformer which regulated the required voltage to the electrical heaters. The dry bulb and wet bulb temperatures of the air in the drying chamber were measured by two Pt-100 sensors (accuracy 0.1°C) installed at a distance of
221
25 mm above the drying product. The humidity of the air was maintained by injecting a controlled amount of steam from the steam generator into the main air duct pipe. A hand shut o valve was provided for controlling the steam ¯ow rate. The main vertical column of the drying chamber (360 mm ´ 360 mm cross sectional area and overall height of 880 mm) was made from 8 mm thick waterproof plywood sheet. A straightener (100 mm long) was ®tted inside the chamber for streamlining the air ¯ow. A door (with viewing glass) was provided on the front side of the chamber for placing and removing the sample holding tray. A wooden platform (10 mm thick), ®tted with an oil channel was provided below the straightener as shown in Fig. 1. Light oil ®lling the channel was used to provide an air seal. All sides and the platform of the chamber was innerlined with aluminium foil to provide re¯ective insulation. All units of the set-up were connected to each other through 50 mm G.I. pipe. Ball valves (V2) and (V3) were provided for disconnecting the drying chamber from the air circuit when required. Air ¯ow rate was measured with the help of an ori®ce plate and U-tube water manometer connected to the line. A special weighing system was developed for online measurement of the weight of the product while it is being dried. The weighing unit consisted of an electrical balance (200 g capacity and 0.0001 g accuracy), weighing pan, sample holding tray and oil channel. The weighing pan was suspended in the oil of the oil channel. A removable sample holding tray (size 100 mm ´ 100
Fig. 1. Experimental dryer set up.
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mm) having a wire mesh (5 mm ´ 5 mm made from 0.3 mm diameter copper wire) was used for placing the onion slices on the weighing pan. This arrangement allowed online measurement of the weight of the product and also provided an oil seal to the air ¯ow forcing it to pass through the product placed on the wire mesh of the sample holding tray.
Verma, 1986; Ajibola, 1989; Rapusas & Driscoll, 1995). The lower is the values of reduced chi-square, the better will be the goodness of ®t. By de®nition: PN 2 MRexpi ÿ MRcali 2 v i1 : 7 N ÿn
3.2. Sample preparation
4. Results and discussion
Onions were hand peeled and sliced (5 mm thick) at right angle to the vertical axis with the help of a hand operated slicing machine. Ten slices of about 50 mm diameter were selected. The diameter and thickness of the slices were measured with the help of a vernier caliper having a least count of 0.05 mm. The slices were then brined by steeping in 5% NaCl solution for 10 min in a petridish. After draining the solution from the dish, the surface water of the slices was removed by ®lter paper. Out of these ten slices, four slices were used for drying measurement. The average weight of the sample used was about 36 g. The remaining six slices were used for determination of the initial moisture content of the onion samples by the vacuum oven method at 70°C and 50 mm Hg for 6 h (AOAC, 1975).
4.1. Eect of moisture content on drying rate Variation of the drying rate with moisture content for only four experimental runs (out of forty eight) are shown in Fig. 2. As indicated in these curves (and also seen in those of remaining forty four experimental runs) the constant drying rate period was found to be absent in the drying of sliced onions. This shows that diusion is the most dominant physical mechanism governing moisture movement in the onion slices. These results are in agreement with the observation of Mazza and LeMaguer (1980), made on 0.0015 m thick onion slice at air velocity of 0.29 m/s and air temperatures higher than the 40°C, and also con®rmed by Rapusas and Driscoll (1995).
3.3. Drying measurement
4.2. Drying rate constants
For achieving stable environmental conditions in the test chamber, the experimental set-up was operated continuously for two hours at no load condition. During the drying run, the air pressure, on the sample holding tray changes continuously due to the shrinkage of the sample. For removing the eect of the variable air pressure on the balance reading, the air supply to the test chamber was cut o for a very short time (about 30 s) at given intervals with the help of ball valves V2, V3 and stop valve V6. The balance reading was recorded during this time. For the ®rst two reading the air supply was cut o at 5 min intervals while for all remaining reading it was cut o at 15 min intervals.
The variation of moisture ratios with time for each run was used for calculating the drying constants c and k of a single term exponential model (Eq. (2)) using nonlinear regression as was done by earlier workers (Rapusas & Driscoll, 1995; Kiranoudis et al., 1992). The coecient of determination and reduced chi-square be-
3.4. Mathematical modelling procedure Mathematical modelling and analysis of the drying kinetic data was performed on a personal computer using Scienti®c and Technical Graphics (Microcal Origin, 1991). Non-linear regression was used for data analysis. The term used to evaluate goodness of ®t of the tested models to the experimental data are the coecient of determination (COD, r2 ) and the reduced chi-square (v2 ), as the mean square of the deviations (MSD) between the experimental and calculated values for the tested models. The MSD has been used previously by many workers for evaluating goodness of ®t of thinlayer drying models to experimental data (Noomhorm &
Fig. 2. Observed drying rate of onion slices at dierent temperatures for 0.5 m/s V and 10% RH. ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C).
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223
Fig. 3. Eect of temperature on thin-layer drying curve of onion at 0.5 m/s V and 10% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C, (A) predicted model 2).
Fig. 5. Eect of absolute humidity on thin-layer drying curve of onion at 60°C T and 0.75 m/s V ((s) 0.1250 kg/kg, (+) 0.01875 kg/kg, (h) 0.02550 kg/kg, (A) predicted model 2).
tween the experimental and calculated moisture ratio were also obtained. It was found that the COD (r2 ) was more than 0.996 for all of the 48 runs while the value of reduced chi-square ranged between 5.163 ´ 10ÿ4 and 3.03 ´ 10ÿ6 (which is very low) indicating that the model ®tted reasonably well with the experimental data for each drying run. It was also observed that the model ®t was very good for all of the experimental drying air conditions. However, at higher drying air temperatures and lower air velocities the ®tness was only good (a value of r2 between 0.996 and 0.998). This is further shown by Figs. 3±5, in which the drying curves are plotted using Eq. (2) with calculated values of c and k and experimentally obtained values for selected experimental runs of drying air conditions. It is further seen from these Figures that the drying rate of the sliced onions increases with increase in the temperature and air ¯ow velocity, whereas it decreases with increase in ab-
solute humidity of the drying air. However, the in¯uence of temperature on the drying rate is more pronounced as compared to the in¯uence of the air ¯ow velocity and absolute humidity. These observations are in accordance with that of Rapusas and Driscoll (1995) as well as Mazza and LeMaguer (1980).
Fig. 4. Eect of air velocity on thin-layer drying curve of onion at 70°C T and 15% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, (A) predicted model 2).
4.3. Eect of drying air variables on drying rate constants Variation of the drying rate constant, k with drying air condition variables T, V and H as obtained from the experimental runs, is shown in Figs. 6±8, respectively. It is seen from Fig. 6 that the value of the constant, k decreases exponentially with increase in inverse of absolute temperature, showing the Arrhenius-type behaviour. With the increase in temperature of the drying medium, the drying potential increases and the moisture removal rate increases. Similarly, it can also be seen from Figs. 7 and 8 that the drying rate constant, k in-
Fig. 6. Eect of inverse of absolute temperature on drying constant, k at 10% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, V).
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cases of 48 runs). The reduced chi-square was also very low and ranged between 6.134 ´ 10ÿ4 and 4.737 ´ 10ÿ6 indicating that all the experimental drying runs ®t very well in the single term exponential model (Kiranoudis et al., 1992). 4.4. Determination of model constants
Fig. 7. Eect of air velocity on drying constant, k at 15% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C T).
Fig. 8. Eect of absolute humidity on drying constant, k at 70°C ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, V).
creases with increase in drying air velocity and decreases with increase in absolute humidity of the drying air. From this discussion, it can be safely said that the drying rate constant, k is greatly in¯uenced by the external drying conditions over the range of experimental conditions explored. It was found that the value of c does not vary signi®cantly (varying between values of 0.99 to 1.02 for all 48 experimental runs) with the drying air variables of temperature, velocity and absolute humidity. Hence, the value of c can be taken to be the equal to the mean values (1.01) of all the 48 runs. These values of c are in accordance with the value of c (0.98 0.04) obtained by Rapusas and Driscoll (1995). For the obtained mean value of c (1.01) very near to one, and considering the physical reality at the initial time t equal to zero, it will be more appropriate to take the value of c equal to one. The drying rate constant, k was further recalculated, considering only k as sole variable in Eq. (2) (i.e. taking c 1.00) for all of the 48 runs. It was observed that the COD, r2 was also good (more than 0.995 in all of the
The dependence of drying rate constant, k on drying air variables (temperature, velocity and absolute humidity) in the form of the Arrhenius-type equation (Eq. (3)) and power model (Eq. (4)) was analysed using non-linear regression to determine model constants a0 , a1 , a2 , a3 and b0 , b1 , b2 , b3 for the two models, respectively. The resulting values of these constants are given in Table 1 along with coecient of determination (r2 ) and reduced chi-square (v2 ) for both the cases, taking c equal to its mean value (1.01) and equal to 1.00 (cases (a) and (b), respectively). It is seen from Table 1 that the experimental data ®ts remarkably well, both for the Arrhenius-type model and power model, based on high values of COD (r2 ) and low values of v2 for both the cases (a) and (b). As the Arrhenious-type relationship provided slightly higher values of COD (r2 ) and lower values of reduced chi-square (v2 ) than the power model, the Arrhenius-type model is comparatively more suitable for describing the drying behaviour of onion slices. These observations are in agreement with those of Henderson and Pabis (1961), who provided rigorous theoretical justi®cation for the use of the Arrhenius-type relation for describing temperature dependence of the drying rate of food materials. Using the values of a0; a1; a2 and a3 , given in Table 1, the values of k were obtained using the Arrhenius-type model (Eq. (3)) for each experimental condition of the drying air. Taking the mean value of c as equal to 1.01 for all experimental conditions, the variation of the moisture ratio with time was calculated and plotted along with the measured value for the purpose of validation of the Arrhenius-type model. The experimental and predicted thin-layer drying curves using Arrheniustype model at four levels of temperature, four levels of air ¯ow velocity and three levels of humidity are shown in Figs. 9±11, respectively. It can be seen from these Figures that the results of predicated and calculated moisture ratios agreed closely with each other. Various workers have studied the drying rate behaviour of onion for dierent experimental conditions. For comparison, the range of drying rate constant, k obtained for their experimental conditions along with that of the present study are given in Table 2. It is seen from the Table 2 that the value of k signi®cantly depends on experimental conditions, material characteristics, material preparation (especially brining) and the material grown in dierent agro-climatic conditions.
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225
Table 1 Results of non-linear regression analysis for four parameter models of Arrhenius-type and power model for thin-layer drying of onion slices ((a) for the exponential model, MR c exp(ÿkt); (b) for the exponential model, MR exp(ÿkt)) Model
Arrhenius (a) (b)
Power (a) (b)
Parameters a0 (minÿ1 )
a1
a2
a3
47.57 38.85
0.31 0.32
ÿ0.20 ÿ0.20
3034 2961
b0 (minÿ1 )
b1
b2
b3
4.96 ´ 10ÿ6 5.96 ´ 10ÿ6
0.31 0.32
ÿ0.20 ÿ0.19
1.71 1.67
Fig. 9. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent temperatures for 0.5 m/s V and 15% RH ((h) 50°C, (+) 60°C, (s) 70°C, (*) 80°C, (A) predicted).
r2
v2
0.9882 0.9878
1.0173 ´ 10ÿ7 1.0165 ´ 10ÿ7
0.9845 0.9846
1.3326 ´ 10ÿ7 1.2785 ´ 10ÿ7
Fig. 11. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent absolute humidity for 70°C and 0.5 m/s V ((s) 0.0195 kg/kg, (+) 0.03 kg/kg, (h) 0.041 kg/kg, (A) predicted).
An experimental thin-layer drying system was developed and used to establish thin-layer drying behaviour of brined onion slices under wide range of drying conditions similar to those generally employed in commercial onion dehydration. It can be said that the single term exponential model (with c 1.00) adequately describes the drying behaviour of brined onion slices. The correlation of the drying constant, k with the drying air parameters (drying air temperature, ¯ow rate and absolute humidity) for Arrhenius-type and power model have also been established. Acknowledgements Fig. 10. Thin-layer drying curve of onion for experimental and predicted values using model 3 at dierent air ¯ow velocity for 70°C and 10% RH ((h) 0.25 m/s, (+) 0.5 m/s, (s) 0.75 m/s, (*) 1.00 m/s, (A) predicted).
P.N. Sarsavadia gratefully acknowledges to the vicechancellor, Gujarat Agricultural University, Sardar Krushi Nagar (Gujarat) India, for deputation granted to him.
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Table 2 Compiled values of drying rate constant, k with their experimental condition along with the present study on thin-layer drying of onions Source
Saravacos and Charm (1962) Mazza and LeMaguer (1980) Kiranoudis et al. (1992) Rapusas and Driscoll (1995) Present study a
Experimental conditions
k (minÿ1 )
Remark (variety)
sliced (ÿ) sliced (yellow globe) shredded (ÿ) sliced (white globe) sliced (Agfound white)
Range
T (°C)
H (kg/kg)
V (m/s)
Mo (% db)
L (m)
Min Max Min Max Min Max Min Max Min Max
62
0.0180
2.00
ÿ
0.0040
0.00600
40 65 60 81 42 90 50 80
ÿ
0.29 0.55 2.50 5.10 0.60 1.40 0.25 1.00
670a
0.0015
ÿ ÿ 385 452 612 641
0.0050 0.0150 0.0020 0.0080 0.0050
0.01050 0.01878 0.00800a 0.10000 0.00459 0.15430 0.00605 0.01838
0.0063 0.0374 0.0093 0.0440 0.0075 0.0640
Value obtained from the graph.
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