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Drying kinetics of plant products: Dependence on chemical composition
Journal of Food Engineering 117 (2013) 378–382
Contents lists available at SciVerse ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Drying kinetics of plant products: Dependence on chemical composition A.S. Kholmanskiy a,b,⇑, A.Z. Tilov a,b, E.Yu. Sorokina c a
Institute of Electrification of Agriculture, 1st Veshnyakovsky Drive, 2, VIESH, 109456 Moscow, Russian Federation Moscow State University of Engineering Ecology, Staraya Basmannaya St., 21/4, 105066 Moscow, Russian Federation c Institute of Petrochemical Synthesis (named after A.V.Topchiyev) RAS, Leninsky Avenue, h. 29, 119991, GPS-1 Moscow, Russian Federation b
a r t i c l e
i n f o
Article history: Received 6 January 2013 Received in revised form 7 March 2013 Accepted 12 March 2013 Available online 21 March 2013 Keywords: Drying Soaking Diffusion Membrane Activation energy Plant products
a b s t r a c t Kinetics of drying and soaking of fruits and vegetables (apples, pears, grapes, apricots, carrots, tomatoes, peppers, garlic, onions, peas, spinach, pumpkins, mushrooms, oats, perennial ryegrass, and beans) were investigated. The rate constants and the activation energies of drying/soaking were calculated with the use of the initial and final portions of the corresponding kinetic curves. The dependence of the drying kinetics upon the chemical composition of the material was explained with the help of the diffusion model. Within it the plant tissue was modeled by a diffusion membrane and Fick’s law was utilized. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Various technologies of drying/soaking are used widely in the food industry. Reversible dehydration of plant products is applied extensively for the conservation and for fast food production (dried fruit mixes, soups, etc.). In the engineering design of drying appliances an important question is that of energy saving and of the possibility to use natural resources (such as the energy of the sun, the wind, see, for example, (El-Beltagy et al., 2007; Bal et al., 2010). The drying kinetics of the plant food products depends on temperature, pressure (Chua and Chou, 2004) and on the sample size, but is hardly sensitive to the air flow velocity and to its humidity (Krokida et al., 2003). The main requirements to the drying technologies are the preservation of the nutritional quality and of the molecular cell structure of the dried product. Under such conditions the processes of drying and soaking are reversible to some extent. The mechanism of water transport in tissues will resemble that of water transfer in living plants (Polevoy, 1989). For the majority of plant products the chemical composition is known, while for some of them the microstructure of the tissue is defined as well – like for apples and pears (Verboven et al., 2008) and for carrots (Smith et al., 2007). The microstructure of the plant tissue is ⇑ Corresponding author at: Institute of Electrification of Agriculture, 1st Veshnyakovsky Drive, 2, VIESH, 109456 Moscow, Russian Federation. Tel.: +7 4986850852. E-mail addresses: [email protected] (A.S. Kholmanskiy), [email protected] (E.Yu. Sorokina). 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.03.017
formed by cells, intercellular spaces, capillaries and pores (Polevoy, 1989; Alzamora et al., 2005). During drying and soaking in air at atmospheric pressure, the macrostructures of plant products as a whole can be regarded as diffusion membranes (Alzamora et al., 2005). It should be noted that in the studies and, in particular, in the mathematical models of drying kinetics the differences in the chemical composition of various plant products are not taken into account. The goal of this study is to relate the drying/soaking kinetics to the chemical composition of plant products. To achieve that we calculated the drying constants and the activation energies for 18 plant products. In our calculations we utilized those portions of the kinetic curves where the diffusion of water is subject to Fick’s law, and the change of water content in the tissue can be approximated by an exponent. 2. Mathematical model We calculated the kinetics of soaking and drying using the initial portions of the drying kinetic curves and the end portions of the soaking curves. At these stages the cellular structure of the plant products has not suffered from irreversible changes. As the water content in plant products (Mw) can exceed 90% (Polevoy, 1989; Krokida et al., 2003), the change in weight of the sample during drying and soaking can be presented by a first-order kinetic equation:
dMw =dt ¼ k ðM w þ M 0 Þ k Mw :
ð1Þ
A.S. Kholmanskiy et al. / Journal of Food Engineering 117 (2013) 378–382
379
Nomenclature C D E, E+ Eav J K k, k+ L M M0 Mw Pi, P i Pj PR
heat capacity of water (J kg1 K1) diffusion coefficient (mm2 s1) activation energies for drying/soaking (kJ Mol1) average activation energy (kJ Mol1) water flow density (g mm2 s1) substance distribution coefficient (dimensionless) drying/soaking constants (s1) sample thickness (mm) total weight of the sample (g) weight of dehydrated product (g) water content (g) membrane permeability (mm1 s1) tissue fragment permeability (mm1 s1) entire sample permeability (mm1 s1)
Q, Q⁄ R R2 T
l q
qin, qex
Subscripts i, j membrane, tissue elements’ numbers in, ex internal, external R sum of all the elements
Here M0 is the dry mass of the product. The inequality M0 Mw holds at the initial stage of the kinetic drying curve (minus sign in Eq. (1)) and at the final stage of soaking (plus sign in Eq. (1)). The solution of Eq. (1) is the exponent:
M w ¼ const exp ðktÞ:
ð2Þ
Approximating the corresponding ranges of kinetic curves by function (2), one can determine the rate constants for drying (k) and for soaking (k+) processes. The rate of water diffusion in plant tissue depends upon the interaction energy of water molecules with the dissolved substances that are part of the plant tissue. These interactions determine basically the effective activation energy of the drying (E) and soaking (E+) processes. Those enter the Arrhenius equation for k and k+:
k ¼ const expðE=RTÞ;
ð3Þ 1
thermal energy (J) gas constant (J Mol1 K1) coefficient of determination, dimensionless (0 6 R2 6 1) temperature (K) molecular mass of water (g Mol1) boiling heat (J kg1) water density in the center of the sample and on its surface (g mm3)
1
where R is the gas constant equal to 8.31 J Mol K . The values of the rate constants k and k+ we defined from the kinetic curves at various temperatures. Then we calculated the activation energies E and E+ from the relations: ln k/1/T and ln k+/1/T. In a similar way we determined the values of E from the initial portions of the kinetic curves, presented in references El-Sebaii et al., 2002; Krokida et al., 2003; Meisami-asl and Rafiee, 2009. These plots we split into a sufficient number of time intervals (up to 10) and carried out the calculations for these points. The reliability of the approximations used (R2) was in the range 0.945–0.999. The relative error of the calculated values of k and E did not exceed 10%. The calculations, approximations and plots were all constructed in the software Microsoft Office Excel. 3. Materials and methods We studied the drying kinetics of carrots, seeds (oat seeds, lawn grass Ryegrass seeds, white haricot beans), and fruit (apples ‘‘Beliy Naliv’’, pears ‘‘Dushess’’, apricots, seedless grapes ‘‘Kish-Mish’’). For seeds we examined also the kinetics of soaking. To make the comparison more representative and to enlarge the range of the products’ chemical properties under study we utilized also the drying curves, published in the literature for pepper, onion, garlic, spinach, pumpkin, tomato, carrot, mushroom (Krokida et al., 2003), apple (Meisami-asl and Rafiee, 2009), and grapes (El-Sebaii et al., 2002). The sort, grade and chemical composition of the products are provided in Table 1. The main contribution to the interaction energy of water molecules with plant tissue comes from the hydrophilic centers of the following substances – proteins, sugar, starch, organic acids, and fi-
ber. Their total share in 100 g of the edible portion of the product was calculated with the use of the data from reference Chemical composition of foodstuff, 1987. These hydrophilic shares are provided in Table 1. The weight (M) of samples of seeds, fruit and carrots was about 10 g each, measured with electronic laboratory scales Adventurer Pro (RV153). The samples of apples, pears, apricots and carrots were prepared by cutting them in cubes approximately 3 mm in size. Grapes were used complete. The samples were distributed evenly in Petri plastic dishes. Petri dishes with samples of fruit and carrots were placed in an oven TVZ-25 and kept at fixed temperature (30, 40, 50, 60, and 70 °C). The accuracy of temperature stabilization in the chamber in the steady state was within the range ±0.3 °C. The kinetic curves were plotted through points, obtained by weighing the samples at regular time intervals (30 or 60 min). The time of measurement did not exceed 10 s. Seeds for soaking were placed in beaker heat-resistant glass (capacity 100 ml) and filled with tap water (50 ml), which had been settled previously for a day. Then the glasses were covered with aluminum foil. Prior to weighing the seeds, we removed water from their surface with the help of blotting paper. The corresponding kinetic curves of drying and soaking were presented in Kholmanskiy et al. (2012a) and Kholmanskiy et al. (2012b). In order to check the proposed methodology of calculation of values E and k we compared the results obtained in the processing of the kinetic curves for drying carrots (Krokida et al., 2003), apples (Meisami-asl and Rafiee, 2009), and grapes (El-Sebaii et al., 2002), with those obtained by us (Kholmanskiy et al., 2012a). These calculations produced close values for the activation energy of carrots and grapes, but different values for apples (see Table 1). The difference in E for apples, obviously is due to the difference of the sorts, utilized in Kholmanskiy et al. (2012a) and Meisami-asl and Rafiee (2009). Note that similar differences in the values of E are observed for different types of pepper (Table 1). 4. Results and discussion The types of fruit/vegetables, their chemical composition (hydrophilic fraction), and the values of the activation energies E, E+ and rate constants k, k+ are specified in Table 1. The analysis of E and k for the drying process of various plant products reveals an essential dependence of the activation energy E upon not only the type of the product, but also upon its grade. We calculated the values of k from the available kinetic curves for drying apples (Meisami-asl and Rafiee, 2009) and carrots (Krokida et al., 2003) with samples of different thickness. It turned out that k is proportional to 1/L (Fig. 1). The calculation of E from the curves of drying
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Table 1 Chemical composition of vegetables and fruit, kinetic characteristics and activation energy of drying. HPa-fraction
Temperature (°C)
k 104 (s1)
E, (E+) (kJ Mol1)
91 91 92 90 90 91 88
5.3 5.8 6.0 6.5 8.1 8.1 10
Pear Onions Apple
85 86 87
11.0 11.4 11.6
11 12 13
Apricot Garlic Grapes
86 80 80
11.8 12.6 17.0
14 15 16 17 18
Green peas Yellow pepper Oats Grass ryegrass Haricot
80 90 13.5 -«14.0
19.9 68.3 -«71.5
65–85 65–85 65–85 65–85 65–85 65–85 30–50 65–85 23–66 65–85 40–70 23–66 40–75 65–85 50–75 27–42 65–85 65–85 10–47 20–47 24–40
5.5 6.3 2.4 4.7 2.7 2.4 1.2 2.7 0.6 2.7 0.9 0.9 0.3 4.0 0.3 0.1 3.5 3.0 1.4 1.3 0.6
22 41 53 44 25 37 52 51 53 51 35 55 42 29 51 53 66 53 60 (30) 60 (30) 83 (55)
No.
Products
1 2 3 4 5 6 7
Field mushroom Spinach Tomato Pumpkin Red pepper Green pepper Carrots
8 9 10
Water share %
[1] [1] [1] [1] [1] [1] [1] [2] [1] [3] [2] [2] [1] [4] [1] [1] [2] [2] [2]
1 – Krokida et al. (2003); 2 – Kholmanskiy et al. (2012a); 3 – Meisami-asl and Rafiee (2009); 4 – El-Sebaii et al. (2002). a Fraction of hydrophilic substances (protein, sugar, starch, organic acids, cellulose) in 100 g of an edible part of the product, from Chemical composition of foodstuff, (1987).
Fig. 1. Schemes of the internal structure and the direction of diffusive water flows (J) in grapes (a), and in carrot roots (b) (the scheme from Polevoy (1989); qin and qex are the local densities of water inside and outside the product.
Table 2 Activation energy (E) for samples of apple of different thickness (L) at various airflow velocities (V), data from Meisami-asl and Rafiee (2009). V (m/s)
0.5 1.0 2.0
E (kJ Mol1) L = 2 mm
L = 4 mm
L = 6 mm
37 34 33
36 30 33
35 38 35
apples (Meisami-asl and Rafiee, 2009) for samples with different thickness L and for different air flow velocities revealed no dependence of E on L and on air velocity (Table 2). The dependence of k and E on the hydrophilic share in 14 plant products is provided in Fig. 2. It reveals the trend of increase of E and decrease of k with the increase of the hydrophilic share.
Fig. 2. The scheme of water diffusion through an element of the capillarymembrane system that represents two paths of diffusion – along cellular walls and the conducting system of sequential membranes with permeabilities P i , and through the sequential system of cellular membranes with permeabilities Pi.
In general, the seeds or plant products consist of a homogeneous parenchyma and its boundary layer (Polevoy, 1989; Alzamora et al., 2005). The latter may affect considerably the kinetics
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of drying and soaking of seeds and whole grapes only. The data on the microstructure of the cellular tissue of carrots (Smith et al., 2007) and fruit – apple, pear (Verboven et al., 2008) allow one to model the plants’ tissue by a capillary-membrane system (Alzamora et al., 2005), sated with water, that gets more dense in the boundary layer (Fig. 3). Then the plant tissue can be presented by a conducting system that includes subsystems, connected in parallel, each of them built up of consecutive membranes with different diffusion permeabilities Pi (Fig. 4). The permeabilities of one such element (Pj) and of the entire system (PR) are:
Pj ¼
X 1 1
PR ¼
Pi X
þ
X 1 1 Pi
P j ¼ DK=L:
ð4Þ
ð5Þ
Here L is the thickness of the sample (see Figs. 3 and 4), K is the substance distribution coefficient, Pi and Pi are the permeabilities of the cellular membranes, intercellular walls and capillaries, and D is the diffusion coefficient of water. Within this diffusion model, the water flow density J can be expressed by Fick’s law, which comprises the total permeability of the sample PR and the drop in the local densities of water in the center of the sample (qin) and on its surface (qex):
J ¼ Pr ðqin qex Þ
ð6Þ
The significant difference between E and E+ can be attributed to the lack of the evaporation stage in the course of soaking, which would require additional energy. The value of E+ obviously reflects the energetics of diffusion through the seed coat and through the parenchyma, which consists mostly of starch. The more dense shell and the larger share of hydrophilic centers in beans, in comparison to oat seeds and ryegrass seeds explain the larger values of E and E+ in beans (see Table 1). The diffusion model of the drying process allows one to provide an estimate of the thermal energy required for the drying of the plant product, for example, to 25% water content. The initial water content typically is 85% on average. Thus the weight of the evaporated water is 0.6 of the initial product weight. The activation energy varies in the range from 25 to 66 kJ Mol1 (see Table 2). The average amount of thermal energy Q, required for drying of a plant product, for example, with mass m = 1 kg and with an average activation energy Eav = 45 kJ Mol1 is:
Q ¼ ð0:6 m=lÞ Eav ;
ð7Þ
where l is the molecular mass of water (18 g Mol1). Thus, for drying of 1 kg of a product or evaporation of 0.6 kg of water according to Eq. (7) the following energy is required:
Q ¼ ð600=18Þ 45 103 ¼ 1:5 106 J: Another rough estimate of Q can be obtained (interaction of water with plant tissue neglected) by assuming that all the energy goes to the heating of the product with mass m = 1 kg from
Since the value of k is determined by PR, Eq. (5) explains the linear dependence of k on 1/L (Fig. 1). The dependence of k on temperature comes from the direct relationship of PR with the diffusion coefficient D. The value of D is proportional to the temperature and is inversely proportional to the dynamic viscosity, which, in turn, depends exponentially on the energy of intermolecular interactions (Kholmanskiy, 2006), and thus on the hydrophilic share. Therefore, with the increase of the hydrophilic share there is a tendency for k to decrease and for E to increase (Fig. 2).
(a)
Fig. 3. Dependence of the activation energy E – (a) and of the rate constants k – (b) of the drying process of fruit and vegetables on the total share of hydrophilic substances (HP-fraction) in their structure. Numbers of products (1–14) correspond to their numbering in Table 1.
(b) Fig. 4. The dependence of k on 1/L, for drying of carrots (a), and apple (b).
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To = 20 °C to Ti = 70 °C, and then to the evaporation of 0.6 kg of water at this temperature. With the specific heat of evaporation q = 2.3 106 J/kg and with the heat capacity of water C = 4.2 103 J/(kg K), the required amount of thermal energy is estimated as:
Q ¼ 0:85 m C ðT i T o Þ þ 0:6 m q ¼ 0:85 4:2 103 50 þ 0:6 1 2:3 106 ¼ 1:6 106 J:
ð8Þ
The values of E for the fruit and vegetables under study differ considerably from Eav, therefore the values of Q for them will also differ significantly from Q. The variations of E are determined largely by the interaction of water with the plant tissue, which is function of their chemical composition. Obviously, in the design of drying technologies the chemical composition of plant products should be accounted for in order to optimize the drying process. 5. Conclusions The effect of the chemical composition and of the sample size of plant products upon the rate constant and upon the activation energy for drying and soaking has been studied. The kinetic parameters have been calculated through the approximation of the initial and final sections of the corresponding kinetic curves by exponents. Correlations between the kinetic characteristics of the drying process and the thickness of the sample along with the share of hydrophilic components have been established. These correlations are consistent with the diffusion model of the drying process. The dependence of the drying activation energy on the chemical composition of the product can be used for the optimization of the technological parameters of industrial dryers.
References Alzamora, Stella M. et al., 2005. Novel functional foods from vegetable matrices impregnated with biologically active compounds. Journal of Food Engineering 67, 205–214. Bal, L.M., Satya, S., Naik, S.N., 2010. Solar dryer with thermal energy storage systems for drying agricultural food products: a review. Renewable and Sustainable Energy Reviews 14, 2298–2314. Chemical composition of foodstuff, 1987. Book 1: tables of the content of the main food substances and energy value of foodstuff. Skurikhin, I.M., Volgarev, M.N.M. (Eds.), 224 p. Chua, K.J., Chou, S.K., 2004. On the experimental study of a pressure regulatory system for bioproducts dehydration. Journal of Food Engineering 62 (2), 151– 158. El-Beltagy, A., Gamea, G.R., Amer Essa, A.H., 2007. Solar drying characteristics of strawberry. Journal of Food Engineering 78, 456–464. El-Sebaii, A.A. et al., 2002. Empirical correlations for drying kinetics of some fruits and vegetables. Energy 27, 845–859. Kholmanskiy, A.S., 2006. Features of thermodynamic properties of water. Reports of Russian Academy of Agrarian Sciences 2, 63–66. Kholmanskiy, A.S., Tilov, A.Z., Tyukhov, I.I., 2012a. Research of kinetics of drying of vegetable foodstuff. Messenger of Russian Academy of Agrarian Sciences 2, 15– 17. Kholmanskiy, A.S., Tilov, A.Z., Sorokina, E. Yu. 2012. Physical and chemical modeling of processes of drying of vegetables and fruit. Modern problems of, science and education, 5. Krokida, M.K. et al., 2003. Drying kinetics of some vegetables. Journal of Food Engineering 59, 391–403. Meisami-asl, E., Rafiee, S., 2009. Mathematical Modeling of Kinetics of Thin-layer Drying of Apple (var. Golab). Agricultural Engineering International: the CIGR Ejournal. Manuscript 1185, September, 2009. Polevoy, V.V., 1989. Physiology of plants. M: The higher school. 464 p. Smith, B.G., James, B., Ho, C.A.L., 2007. Microstructural characteristics of dried carrot pieces and real time observations during their exposure to moisture. International Journal of Food Engineering 3 (4) (Art. 7). Verboven, P. et al., 2008. Three-dimensional gas exchange pathways in pome fruit characterized by synchrotron X-ray computed tomography. Plant Physiology 147, 518–527.
Contents lists available at SciVerse ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Drying kinetics of plant products: Dependence on chemical composition A.S. Kholmanskiy a,b,⇑, A.Z. Tilov a,b, E.Yu. Sorokina c a
Institute of Electrification of Agriculture, 1st Veshnyakovsky Drive, 2, VIESH, 109456 Moscow, Russian Federation Moscow State University of Engineering Ecology, Staraya Basmannaya St., 21/4, 105066 Moscow, Russian Federation c Institute of Petrochemical Synthesis (named after A.V.Topchiyev) RAS, Leninsky Avenue, h. 29, 119991, GPS-1 Moscow, Russian Federation b
a r t i c l e
i n f o
Article history: Received 6 January 2013 Received in revised form 7 March 2013 Accepted 12 March 2013 Available online 21 March 2013 Keywords: Drying Soaking Diffusion Membrane Activation energy Plant products
a b s t r a c t Kinetics of drying and soaking of fruits and vegetables (apples, pears, grapes, apricots, carrots, tomatoes, peppers, garlic, onions, peas, spinach, pumpkins, mushrooms, oats, perennial ryegrass, and beans) were investigated. The rate constants and the activation energies of drying/soaking were calculated with the use of the initial and final portions of the corresponding kinetic curves. The dependence of the drying kinetics upon the chemical composition of the material was explained with the help of the diffusion model. Within it the plant tissue was modeled by a diffusion membrane and Fick’s law was utilized. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Various technologies of drying/soaking are used widely in the food industry. Reversible dehydration of plant products is applied extensively for the conservation and for fast food production (dried fruit mixes, soups, etc.). In the engineering design of drying appliances an important question is that of energy saving and of the possibility to use natural resources (such as the energy of the sun, the wind, see, for example, (El-Beltagy et al., 2007; Bal et al., 2010). The drying kinetics of the plant food products depends on temperature, pressure (Chua and Chou, 2004) and on the sample size, but is hardly sensitive to the air flow velocity and to its humidity (Krokida et al., 2003). The main requirements to the drying technologies are the preservation of the nutritional quality and of the molecular cell structure of the dried product. Under such conditions the processes of drying and soaking are reversible to some extent. The mechanism of water transport in tissues will resemble that of water transfer in living plants (Polevoy, 1989). For the majority of plant products the chemical composition is known, while for some of them the microstructure of the tissue is defined as well – like for apples and pears (Verboven et al., 2008) and for carrots (Smith et al., 2007). The microstructure of the plant tissue is ⇑ Corresponding author at: Institute of Electrification of Agriculture, 1st Veshnyakovsky Drive, 2, VIESH, 109456 Moscow, Russian Federation. Tel.: +7 4986850852. E-mail addresses: [email protected] (A.S. Kholmanskiy), [email protected] (E.Yu. Sorokina). 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.03.017
formed by cells, intercellular spaces, capillaries and pores (Polevoy, 1989; Alzamora et al., 2005). During drying and soaking in air at atmospheric pressure, the macrostructures of plant products as a whole can be regarded as diffusion membranes (Alzamora et al., 2005). It should be noted that in the studies and, in particular, in the mathematical models of drying kinetics the differences in the chemical composition of various plant products are not taken into account. The goal of this study is to relate the drying/soaking kinetics to the chemical composition of plant products. To achieve that we calculated the drying constants and the activation energies for 18 plant products. In our calculations we utilized those portions of the kinetic curves where the diffusion of water is subject to Fick’s law, and the change of water content in the tissue can be approximated by an exponent. 2. Mathematical model We calculated the kinetics of soaking and drying using the initial portions of the drying kinetic curves and the end portions of the soaking curves. At these stages the cellular structure of the plant products has not suffered from irreversible changes. As the water content in plant products (Mw) can exceed 90% (Polevoy, 1989; Krokida et al., 2003), the change in weight of the sample during drying and soaking can be presented by a first-order kinetic equation:
dMw =dt ¼ k ðM w þ M 0 Þ k Mw :
ð1Þ
A.S. Kholmanskiy et al. / Journal of Food Engineering 117 (2013) 378–382
379
Nomenclature C D E, E+ Eav J K k, k+ L M M0 Mw Pi, P i Pj PR
heat capacity of water (J kg1 K1) diffusion coefficient (mm2 s1) activation energies for drying/soaking (kJ Mol1) average activation energy (kJ Mol1) water flow density (g mm2 s1) substance distribution coefficient (dimensionless) drying/soaking constants (s1) sample thickness (mm) total weight of the sample (g) weight of dehydrated product (g) water content (g) membrane permeability (mm1 s1) tissue fragment permeability (mm1 s1) entire sample permeability (mm1 s1)
Q, Q⁄ R R2 T
l q
qin, qex
Subscripts i, j membrane, tissue elements’ numbers in, ex internal, external R sum of all the elements
Here M0 is the dry mass of the product. The inequality M0 Mw holds at the initial stage of the kinetic drying curve (minus sign in Eq. (1)) and at the final stage of soaking (plus sign in Eq. (1)). The solution of Eq. (1) is the exponent:
M w ¼ const exp ðktÞ:
ð2Þ
Approximating the corresponding ranges of kinetic curves by function (2), one can determine the rate constants for drying (k) and for soaking (k+) processes. The rate of water diffusion in plant tissue depends upon the interaction energy of water molecules with the dissolved substances that are part of the plant tissue. These interactions determine basically the effective activation energy of the drying (E) and soaking (E+) processes. Those enter the Arrhenius equation for k and k+:
k ¼ const expðE=RTÞ;
ð3Þ 1
thermal energy (J) gas constant (J Mol1 K1) coefficient of determination, dimensionless (0 6 R2 6 1) temperature (K) molecular mass of water (g Mol1) boiling heat (J kg1) water density in the center of the sample and on its surface (g mm3)
1
where R is the gas constant equal to 8.31 J Mol K . The values of the rate constants k and k+ we defined from the kinetic curves at various temperatures. Then we calculated the activation energies E and E+ from the relations: ln k/1/T and ln k+/1/T. In a similar way we determined the values of E from the initial portions of the kinetic curves, presented in references El-Sebaii et al., 2002; Krokida et al., 2003; Meisami-asl and Rafiee, 2009. These plots we split into a sufficient number of time intervals (up to 10) and carried out the calculations for these points. The reliability of the approximations used (R2) was in the range 0.945–0.999. The relative error of the calculated values of k and E did not exceed 10%. The calculations, approximations and plots were all constructed in the software Microsoft Office Excel. 3. Materials and methods We studied the drying kinetics of carrots, seeds (oat seeds, lawn grass Ryegrass seeds, white haricot beans), and fruit (apples ‘‘Beliy Naliv’’, pears ‘‘Dushess’’, apricots, seedless grapes ‘‘Kish-Mish’’). For seeds we examined also the kinetics of soaking. To make the comparison more representative and to enlarge the range of the products’ chemical properties under study we utilized also the drying curves, published in the literature for pepper, onion, garlic, spinach, pumpkin, tomato, carrot, mushroom (Krokida et al., 2003), apple (Meisami-asl and Rafiee, 2009), and grapes (El-Sebaii et al., 2002). The sort, grade and chemical composition of the products are provided in Table 1. The main contribution to the interaction energy of water molecules with plant tissue comes from the hydrophilic centers of the following substances – proteins, sugar, starch, organic acids, and fi-
ber. Their total share in 100 g of the edible portion of the product was calculated with the use of the data from reference Chemical composition of foodstuff, 1987. These hydrophilic shares are provided in Table 1. The weight (M) of samples of seeds, fruit and carrots was about 10 g each, measured with electronic laboratory scales Adventurer Pro (RV153). The samples of apples, pears, apricots and carrots were prepared by cutting them in cubes approximately 3 mm in size. Grapes were used complete. The samples were distributed evenly in Petri plastic dishes. Petri dishes with samples of fruit and carrots were placed in an oven TVZ-25 and kept at fixed temperature (30, 40, 50, 60, and 70 °C). The accuracy of temperature stabilization in the chamber in the steady state was within the range ±0.3 °C. The kinetic curves were plotted through points, obtained by weighing the samples at regular time intervals (30 or 60 min). The time of measurement did not exceed 10 s. Seeds for soaking were placed in beaker heat-resistant glass (capacity 100 ml) and filled with tap water (50 ml), which had been settled previously for a day. Then the glasses were covered with aluminum foil. Prior to weighing the seeds, we removed water from their surface with the help of blotting paper. The corresponding kinetic curves of drying and soaking were presented in Kholmanskiy et al. (2012a) and Kholmanskiy et al. (2012b). In order to check the proposed methodology of calculation of values E and k we compared the results obtained in the processing of the kinetic curves for drying carrots (Krokida et al., 2003), apples (Meisami-asl and Rafiee, 2009), and grapes (El-Sebaii et al., 2002), with those obtained by us (Kholmanskiy et al., 2012a). These calculations produced close values for the activation energy of carrots and grapes, but different values for apples (see Table 1). The difference in E for apples, obviously is due to the difference of the sorts, utilized in Kholmanskiy et al. (2012a) and Meisami-asl and Rafiee (2009). Note that similar differences in the values of E are observed for different types of pepper (Table 1). 4. Results and discussion The types of fruit/vegetables, their chemical composition (hydrophilic fraction), and the values of the activation energies E, E+ and rate constants k, k+ are specified in Table 1. The analysis of E and k for the drying process of various plant products reveals an essential dependence of the activation energy E upon not only the type of the product, but also upon its grade. We calculated the values of k from the available kinetic curves for drying apples (Meisami-asl and Rafiee, 2009) and carrots (Krokida et al., 2003) with samples of different thickness. It turned out that k is proportional to 1/L (Fig. 1). The calculation of E from the curves of drying
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Table 1 Chemical composition of vegetables and fruit, kinetic characteristics and activation energy of drying. HPa-fraction
Temperature (°C)
k 104 (s1)
E, (E+) (kJ Mol1)
91 91 92 90 90 91 88
5.3 5.8 6.0 6.5 8.1 8.1 10
Pear Onions Apple
85 86 87
11.0 11.4 11.6
11 12 13
Apricot Garlic Grapes
86 80 80
11.8 12.6 17.0
14 15 16 17 18
Green peas Yellow pepper Oats Grass ryegrass Haricot
80 90 13.5 -«14.0
19.9 68.3 -«71.5
65–85 65–85 65–85 65–85 65–85 65–85 30–50 65–85 23–66 65–85 40–70 23–66 40–75 65–85 50–75 27–42 65–85 65–85 10–47 20–47 24–40
5.5 6.3 2.4 4.7 2.7 2.4 1.2 2.7 0.6 2.7 0.9 0.9 0.3 4.0 0.3 0.1 3.5 3.0 1.4 1.3 0.6
22 41 53 44 25 37 52 51 53 51 35 55 42 29 51 53 66 53 60 (30) 60 (30) 83 (55)
No.
Products
1 2 3 4 5 6 7
Field mushroom Spinach Tomato Pumpkin Red pepper Green pepper Carrots
8 9 10
Water share %
[1] [1] [1] [1] [1] [1] [1] [2] [1] [3] [2] [2] [1] [4] [1] [1] [2] [2] [2]
1 – Krokida et al. (2003); 2 – Kholmanskiy et al. (2012a); 3 – Meisami-asl and Rafiee (2009); 4 – El-Sebaii et al. (2002). a Fraction of hydrophilic substances (protein, sugar, starch, organic acids, cellulose) in 100 g of an edible part of the product, from Chemical composition of foodstuff, (1987).
Fig. 1. Schemes of the internal structure and the direction of diffusive water flows (J) in grapes (a), and in carrot roots (b) (the scheme from Polevoy (1989); qin and qex are the local densities of water inside and outside the product.
Table 2 Activation energy (E) for samples of apple of different thickness (L) at various airflow velocities (V), data from Meisami-asl and Rafiee (2009). V (m/s)
0.5 1.0 2.0
E (kJ Mol1) L = 2 mm
L = 4 mm
L = 6 mm
37 34 33
36 30 33
35 38 35
apples (Meisami-asl and Rafiee, 2009) for samples with different thickness L and for different air flow velocities revealed no dependence of E on L and on air velocity (Table 2). The dependence of k and E on the hydrophilic share in 14 plant products is provided in Fig. 2. It reveals the trend of increase of E and decrease of k with the increase of the hydrophilic share.
Fig. 2. The scheme of water diffusion through an element of the capillarymembrane system that represents two paths of diffusion – along cellular walls and the conducting system of sequential membranes with permeabilities P i , and through the sequential system of cellular membranes with permeabilities Pi.
In general, the seeds or plant products consist of a homogeneous parenchyma and its boundary layer (Polevoy, 1989; Alzamora et al., 2005). The latter may affect considerably the kinetics
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of drying and soaking of seeds and whole grapes only. The data on the microstructure of the cellular tissue of carrots (Smith et al., 2007) and fruit – apple, pear (Verboven et al., 2008) allow one to model the plants’ tissue by a capillary-membrane system (Alzamora et al., 2005), sated with water, that gets more dense in the boundary layer (Fig. 3). Then the plant tissue can be presented by a conducting system that includes subsystems, connected in parallel, each of them built up of consecutive membranes with different diffusion permeabilities Pi (Fig. 4). The permeabilities of one such element (Pj) and of the entire system (PR) are:
Pj ¼
X 1 1
PR ¼
Pi X
þ
X 1 1 Pi
P j ¼ DK=L:
ð4Þ
ð5Þ
Here L is the thickness of the sample (see Figs. 3 and 4), K is the substance distribution coefficient, Pi and Pi are the permeabilities of the cellular membranes, intercellular walls and capillaries, and D is the diffusion coefficient of water. Within this diffusion model, the water flow density J can be expressed by Fick’s law, which comprises the total permeability of the sample PR and the drop in the local densities of water in the center of the sample (qin) and on its surface (qex):
J ¼ Pr ðqin qex Þ
ð6Þ
The significant difference between E and E+ can be attributed to the lack of the evaporation stage in the course of soaking, which would require additional energy. The value of E+ obviously reflects the energetics of diffusion through the seed coat and through the parenchyma, which consists mostly of starch. The more dense shell and the larger share of hydrophilic centers in beans, in comparison to oat seeds and ryegrass seeds explain the larger values of E and E+ in beans (see Table 1). The diffusion model of the drying process allows one to provide an estimate of the thermal energy required for the drying of the plant product, for example, to 25% water content. The initial water content typically is 85% on average. Thus the weight of the evaporated water is 0.6 of the initial product weight. The activation energy varies in the range from 25 to 66 kJ Mol1 (see Table 2). The average amount of thermal energy Q, required for drying of a plant product, for example, with mass m = 1 kg and with an average activation energy Eav = 45 kJ Mol1 is:
Q ¼ ð0:6 m=lÞ Eav ;
ð7Þ
where l is the molecular mass of water (18 g Mol1). Thus, for drying of 1 kg of a product or evaporation of 0.6 kg of water according to Eq. (7) the following energy is required:
Q ¼ ð600=18Þ 45 103 ¼ 1:5 106 J: Another rough estimate of Q can be obtained (interaction of water with plant tissue neglected) by assuming that all the energy goes to the heating of the product with mass m = 1 kg from
Since the value of k is determined by PR, Eq. (5) explains the linear dependence of k on 1/L (Fig. 1). The dependence of k on temperature comes from the direct relationship of PR with the diffusion coefficient D. The value of D is proportional to the temperature and is inversely proportional to the dynamic viscosity, which, in turn, depends exponentially on the energy of intermolecular interactions (Kholmanskiy, 2006), and thus on the hydrophilic share. Therefore, with the increase of the hydrophilic share there is a tendency for k to decrease and for E to increase (Fig. 2).
(a)
Fig. 3. Dependence of the activation energy E – (a) and of the rate constants k – (b) of the drying process of fruit and vegetables on the total share of hydrophilic substances (HP-fraction) in their structure. Numbers of products (1–14) correspond to their numbering in Table 1.
(b) Fig. 4. The dependence of k on 1/L, for drying of carrots (a), and apple (b).
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To = 20 °C to Ti = 70 °C, and then to the evaporation of 0.6 kg of water at this temperature. With the specific heat of evaporation q = 2.3 106 J/kg and with the heat capacity of water C = 4.2 103 J/(kg K), the required amount of thermal energy is estimated as:
Q ¼ 0:85 m C ðT i T o Þ þ 0:6 m q ¼ 0:85 4:2 103 50 þ 0:6 1 2:3 106 ¼ 1:6 106 J:
ð8Þ
The values of E for the fruit and vegetables under study differ considerably from Eav, therefore the values of Q for them will also differ significantly from Q. The variations of E are determined largely by the interaction of water with the plant tissue, which is function of their chemical composition. Obviously, in the design of drying technologies the chemical composition of plant products should be accounted for in order to optimize the drying process. 5. Conclusions The effect of the chemical composition and of the sample size of plant products upon the rate constant and upon the activation energy for drying and soaking has been studied. The kinetic parameters have been calculated through the approximation of the initial and final sections of the corresponding kinetic curves by exponents. Correlations between the kinetic characteristics of the drying process and the thickness of the sample along with the share of hydrophilic components have been established. These correlations are consistent with the diffusion model of the drying process. The dependence of the drying activation energy on the chemical composition of the product can be used for the optimization of the technological parameters of industrial dryers.
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