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Determination of characteristic properties of mulatto beans (Phaseolus vulgaris L.) during convective drying
Journal of Agriculture and Food Research 1 (2019) 100003
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Determination of characteristic properties of mulatto beans (Phaseolus vulgaris L.) during convective drying Hugo M. Lisboa *, Hanndson Araujo, Gustavo Paiva, Suelma Oriente, Matheus Pasquali, Maria Elita Duarte, Mario E.R.M. Cavalcanti Mata Unidade Academica de Engenharia de Alimentos, Universidade Federal de Campina Grande, Av. Aprigio Veloso, 882, 58429, Campina Grande, Paraiba, Brazil
A R T I C L E I N F O Keywords: Mulatto beans Drying Effective diffusivity Thermodynamic properties
A B S T R A C T
Mulatto beans (Phaseolus vulgaris L.) require proper drying for safe transport and storage. To support the drying process design, the objective of this work was to determine the mass transfer and thermodynamic properties of mulatto bean. Mulatto beans were dried under different convective conditions from an initial moisture content of 25% (w.b.) until its equilibrium drying. Using fundamental and empirical models, and considering the bean as a sphere, drying constants and the effective diffusivity of the moisture inside the product was determined at each temperature. Then, using an Arrhenius type equation, effective diffusivity values for each temperature were modeled, and the activation energy was determined along with other thermodynamic properties. Results revealed that effective diffusivity presented values typical of non-porous protein/starchy foods and varied from 4.11 1011 for 40 C and 8.72 1011 m2s1 for 70 C. The activation energy confirmed that effective diffusivity is highly dependent on temperature with values ranging from 21.13 to 22.23 kJ mol1, indicating liquid diffusion within the food material. Enthalpy, entropy, and Gibbs free energy also indicate that the process is endothermic and non-spontaneous. From a practical point of view, it is concluded that mulatto beans have a diffusion-controlled drying requiring thin layers of material for effective drying.
1. Introduction Drying is considered the most energy-intensive process and accounting to up to 15% of all industrial energy usage [1]. Inadequate management of crops and drying process often lead to infestations during storage, causing loss of crop and extensive waste [2]. Moreover, grain drying has the purpose of not only conserving the product but also increasing storage time and reducing costs, adding value to the product. In order for the drying process to be carried out quickly, safely, and economically, it is fundamental to know and monitor the physical phenomena during the drying of the product [3]. Mathematical simulations can be used to understand the drying requirements of a given product better. With this information, optimal design and commercial viability can be readily assessed. Subsequently, simulations based on the drying of successive thin layers of the product, using a mathematical model that satisfactorily represents moisture loss, can be helpful for industrial drying designs [4]. With this method, the use of substantial amounts of grains in trial and error experiments is avoided [5,6].
Moreover, drying can affect the physical and chemical properties of agricultural products [7,8]. Thus, it is of fundamental importance to know the effects of the drying on grain quality. As a result, alterations to those properties affect the operation of mass and heat transfer. Depending on the material being dried, moisture moves from inside the product to the surface accordingly to different transport phenomena. In porous capillary products, such as most products of agricultural origin, the possible transport mechanisms of moisture inside the product are liquid diffusion, capillary diffusion, surface diffusion, hydrodynamic flow, vapor diffusion and, thermal diffusion [9]. In addition to the theoretical model of Fick, other semi-theoretical and empirical models were proposed by several researchers to model drying phenomena [10]. The intent is to facilitate the operational management of drying representation of biological products such as grains and seeds. Chen and Morey, tested four models on 18 crops, finding that modified Henderson and Chung-Pfost equations are useful models for starchy grains and fibrous materials, while modified Halsey is a useful model for high oil and protein and modified Oswin is a good model for corn-based products [11]. Jian and Jayas also used several
* Corresponding author. E-mail address: [email protected] (H.M. Lisboa). https://doi.org/10.1016/j.jafr.2019.100003 Received 27 September 2019; Received in revised form 23 October 2019; Accepted 6 November 2019 2666-1543/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
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Journal of Agriculture and Food Research 1 (2019) 100003
hygrometer model MTH-1362W. All grain weightings were performed on a semi-analytical scale with a precision of 3 decimal places Bioprecisa model JH2102. The equilibrium moisture content for each temperature was determined when there was no more variation of the weight of the samples in three successive readings of 30 min. Variation of the masses was calculated considering the moisture content on a wet basis on a dry basis and establishing the ratio of the moisture content of the samples for each temperature in the time intervals considered. The drying curves of the mulatto bean were plotted with the dimensionless parameter of moisture content ratio (RX):
semi-theoretical and empirical models to characterize isotherms of red kidney beans finding Chung-Pfost and GAB as better models [12]. The liquid diffusion model allows determining the primary thermodynamic properties that result from the drying process. Thermodynamic properties of foods, including enthalpy, entropy and, Gibbs free energy, are essential for the design and optimization of drying operations. Moreover, thermodynamic properties provide an understanding of sorption mechanisms and food-water interactions [13]. The enthalpy gives us the energy variation of the interaction of the water molecules with the other constituents of the product during the drying processes. Entropy defines the degree of order or disorder existing in the water-product system. Finally, Gibbs free energy can indicate how much the water is bound to the product. It also allows determining if the drying process is characterized as spontaneous or non-spontaneous. Common beans are one of the most consumed foods worldwide, having high amounts of protein for a low price [14]. The grains of mulatto beans are usually harvested with high moisture content. Thus, exposure to environmental conditions causes grains to lose quality due to high water activity. In the post-harvest period, the beans have their moisture content reduced from 25% to 12% (w.b.) using convective drying. Considering the lack of studies on mulatto beans drying processes and thermodynamic properties, the objective of this work was to study the drying kinetics of mulatto beans submitted to different drying temperatures (40, 50, 60 and 70 C). Additionally, the effective diffusivity, activation energy and, thermodynamic properties (enthalpy, entropy and, Gibbs free energy) were determined, as well as the physical characteristics such as length, width, thickness, and volume for the different drying conditions.
RX ¼
2.4. Data modeling The experimental data on the drying of mulatto bean grains were adjusted using non-linear regression models using the Quasi-Newton method using the Statistica 7.0 software. The empirical, semiempirical, and theoretical mathematical models often used to represent the drying of agricultural products are shown in Table 1. For the fundamental Fick Model, up to six terms of the series were used. Where t is the drying time (min); k, k0, and k1 are drying constants; a, a1, a2, a3, b, n, n1, n2 are coefficients of the models and r is the product radius, m2. The coefficient of determination (R2) and the mean square deviation (MSD) was used as selection criteria in order to obtain the model that best represents the observed data.
2.1. Materials
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P RXexp RXpre MSD ¼ N
Mulatto beans (Phaseolus vulgaris L.) were collected at a local farm with a moisture content of 25.0% on a wet basis (w.b.). Moisture content was determined by placing some amount of beans in an oven at 105 3 C until the weight was constant.
(9)
Where RXexp is the ratio of moisture content obtained experimentally, RXpre is the ratio of the moisture content predicted by the mathematical model, and n is the number of observations throughout the experiment. A simplified geometry of the grain assuming a spherical model was used for the effective diffusivity determinations [15]. Thus, constant values were assigned for volume, temperatures, and initial moisture content on its surface. The effective diffusivity (Def) was obtained through the
2.2. Mulatto beans measurements The calculation to obtain the radius of equivalence to a sphere was performed by measuring the three orthogonal axes of 100 randomly chosen mulatto bean grains. These measurements were performed with the aid of a digital caliper, STANLEY model 78-440S, with a resolution of 0.01 mm. Mulatto beans radius (req) was determined by equation (1) considering the volume of the ellipsoid (Velip) as a sphere: req
(2)
In equation (2), RX is the ratio of moisture content (dimensionless), Xe is the equilibrium moisture content, decimal (dry basis); Xdb ¼ moisture content, decimal (dry basis) and Xdb,initial is the initial moisture content, decimal (dry basis);
2. Materials and methods
rffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 ¼ Velip ; 4π
Xdb Xe Xdb initial Xe
Table 1 Non-linear regression models used to predict the drying phenomenon of agricultural products.
(1)
2.3. Mulatto beans drying Drying tests were performed using a fixed bed experimental dryer with temperature and drying air velocity controls. The airflow was provided by an axial fan that led the air to the plenum, where it flowed between four screened and removable trays containing the samples of the mulatto bean grains. During the drying process, trays with mulatto bean samples were weighed periodically every 5 min for each temperature. The drying air velocity was set to 1 m s1 and measured with a portable digital anemometer INSTRUTEMP, model ITTHAL-300. This velocity was chosen to avoid external resistance to moisture transfer. The dryer was adjusted to operate at temperatures of 40, 50, 60 and 70 C. The relative humidity of the drying air corresponding to the drying temperatures were, respectively, 23%, 14%, 8%, and 5%. The mean ambient temperature was 26 C, and the relative humidity was 50%. These conditions were determined by a Minipa Digital thermo-
Model Designation
Model Equation
Page
RX ¼ expð k t n Þ
Henderson & Pabis Henderson
RX ¼ a expð k tÞ
Fick
Midilli CavalcantiMata
2
RX ¼ a expð k0 tÞ þ b expð k1 tÞ π2 6 4π 2 RX ¼ exp 2 D t n þ 2 exp 2 D t þ 4π r r 2 9π 2 3 16π 2 exp D t þ þ exp Dt þ 3π 2 8π 2 r2 r2 6 25π 2 1 36π 2 exp 2 D t þ 2 exp 2 D t 2 25π 6π r r RX ¼ a expð k t n Þ þ b t RX ¼ a1 expð k1 t n1 Þ þ a2 expð k1 t n2 Þ þ a3
(eq. 3) (eq. 4) (eq. 5) (eq. 6)
(eq. 7) (eq. 8)
H.M. Lisboa et al.
Journal of Agriculture and Food Research 1 (2019) 100003
7.35 to 4.53 is obtained when the drying temperature increases. As expected, these values are inversely proportional to the drying temperature, a fact also observed by Ref. [12] when studying red kidney beans.
following expression: RX ¼
∞ 6 X 1 exp n2 At 2 n n¼1
(10)
π2
where: A¼
π
3.2. Mathematical modeling of the drying process
2
r2
Table 3 presents the parameters for Page, Henderson & Pabis, Henderson, Midilli, and Cavalcanti Mata models, adjusted to the drying kinetics of mulatto beans at temperatures of 40 to 70 C. These models were chosen because are widely used by the ASABE – American Society of Agricultural and Biological Engineers. All mathematical models adjusted to the experimental data presented coefficients of determination (R2) higher than 98.18% and MSD values below 0.0011. This result indicates that the equations represent well the drying phenomenon. Similar values were obtained by Ref. [17] when dried the Adzuki Bean, obtaining values of (R2) greater than 98%, mentioning an adequate representation for the studied phenomenon. However, it can be observed that the Page, Henderson, Midilli, and Cavalcanti Mata models have coefficients higher than 99.4%, with an emphasis on the Cavalcanti-Mata model where the MSD is inferior to the others, indicating a better fit to the experimental data. Analyzing Fig. 1, the drying constants (k) for the Page, Henderson & Pabis, Henderson, Midilli, and Cavalcanti-Mata models increase in absolute value with the increase of drying air temperature. This is an expected result since the drying constant represents the effect of external drying conditions and tends to increase with increasing drying air temperature. The coefficient (n) of the Cavalcanti Mata, Page, and Midilli models also presented a linear trend of their values with the drying temperatures. For this coefficient, it is known that n ¼ 1 represents the first-order kinetics, while n ¼ 0 would represent a constantrate drying [18]. Experimental data shows that moisture content decreases the most in the first hour. At this first stage of drying, the moisture at the surface of the beans is first evaporated. This result is consistent with a drying principle where the external conditions control the initial stage. After that initial stage, moisture migration from the interior of the beans to the surface is the controlling factor of the drying process [19]. It was also observed that the increase of the temperature of the drying air promotes a higher rate of moisture removal from the product, evidencing, therefore, the increase of the drying rate, a fact already expected and also verified in other works [20]. The average time required to complete the drying process was 1300, 1000, 880, and 640 min for, respectively, temperatures of 40, 50, 60, and 70 C. As expected, the drying time decreases with increasing drying air temperature. Moreover, the Cavalcanti-Mata model represents better experimental data. This decision is based on the fact that this model has coefficients of determination (R2) above 99.8%. However, the coefficient of determination, when used alone, it is not a good criterion for the selection of highly parameterized non-linear mathematical models [21]. Therefore, MSD values were also considered. Since the Cavalcanti-Mata model has the lowest MSD value, this confirms that this model has a good representation of the drying kinetics of the mulatto bean for the studied temperature range from 40 to 70 C.
(11)
Def
and Def ¼ A
r2
(12)
π2
Where, Def is effective diffusivity, mm2. s1, r is the radius of the sphere equivalent to the grain, m; n is the number of terms, and t is the drying time, s. To evaluate the influence of temperature on the diffusion coefficient, the Arrhenius equation was used: Ea 0 Def ¼ Do exp RT
(13)
where, D0 0 is the pre-exponential factor, mm2 s1; Ea is the activation energy, kJ mol1; R ¼ universal gas constant, 8.314 J mol1 K1 and T is the absolute temperature, K. The determination of the activation energy allowed the calculation of the different thermodynamic properties, such as enthalpy, entropy, and Gibbs free energy, using the method described by Ref. [16]), according to the following equations: ΔH ¼ Ea R T
(14)
kb lnðTÞ ΔS ¼ R lnðDo Þ ln kp
(15)
ΔG ¼ ΔH T ΔS
(16)
Where, ΔH is the enthalpy, J mol1; ΔS is the entropy, J mol1 K1, and ΔG ¼ Gibbs free energy, J mol1. Kb is the Boltzmann's constant, 1.38 10–23 J K1, and hp is the Planck's constant, 6.626 10–34 J s1. The coefficient Ln (D0) of the entropy expression (ΔS) can be obtained by linearizing the Arrhenius equation. The expression used was: E1 lnDef ¼ lnDo : RT
(17)
3. Results and discussion 3.1. Equilibrium moisture content Under a given drying setup, the equilibrium moisture content is the moisture content at which the material neither gains or loses moisture. This stabilization occurs because equilibrium is reached when the rate of evaporation equals the rate of condensation. This result is important for drying processes because when the equilibrium moisture content is reached, no further drying is possible. Table 2 shows the mean values of the equilibrium moisture content (Xeq) for the drying temperatures of 40, 50, 60, and 70 C. A decrease in equilibrium moisture content from
3.3. Moisture effective diffusivity Table 4 presents the parameters of the Fick model for the six terms of the series, highlighting the effective diffusivity determination. When fitting Fick model by varying the number of terms from 1 to 6, for mulatto bean dryings at temperatures from 40 to 70 C, it is observed that the coefficients of determination (R2) vary from 80.08% for the 1st term of the series to 99.58% for the 6th terms of the series (Table 4). Concerning the MSD values, the variation was 0.0112 to 0.0002, respectively. Therefore, it is observed that increasing the number of
Table 2 Equilibrium moisture content (Xeq) as a function of drying temperatures. Drying Temperature ( C)
%RH
Equilibrium moisture content (%)
40 50 60 70
23.0 14.0 8.0 5.0
7.35 0.02 5.67 0.05 4.88 0.04 4.53 0.05
3
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Journal of Agriculture and Food Research 1 (2019) 100003
Table 3 Coefficients of the six models analyzed. coefficients of determination (R2) and mean square deviation (MSD). of the drying of the mulatto beans. for the temperatures (40–70 C). Temperature. K
Parameters
Page 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Henderson & Pabis 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C)
k (min –n) 0.0310 0.0361 0.0373 0.0381 a 0.8361 0.8441 0.8532 0.8886
Henderson
a
k0 (min1)
b
0.7394 0.7338 0.7509 0.8021 a 0.9875 0.9767 0.9890 1.0046
0.0027 0.0038 0.0047 0.0066 k (min –n) 0.0408 0.0421 0.0433 0.0446
0.2382 0.2498 0.2391 0.1935 n 0.5670 0.5951 0.6226 0.6443
313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Midilli 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Cavalcanti Mata 313 323 333 343
(40 C) (50 C) (60 C) (70 C)
R2 (%) 99.40 99.53 99.62 99.71 R2 (%) 98.20 98.18 98.39 98.96
MSD 0.0011 0.0011 0.0010 0.0008 MSD 0.0008 0.0009 0.0009 0.0008
k1 (min1)
R2 (%)
MSD
0.0550 0.0642 0.0802 0.0966 b (min1) 0.000076 0.000104 0.000072 0.000146
99.85 99.91 99.94 99.95 R2 (%) 99.96 99.90 99.95 99.83
0.0001 0.0001 0.0001 0.00001 MSD 0.0001 0.0009 0.0001 0.0001
n 0.6392 0.6515 0.6677 0.6958 k (min1) 0.0032 0.0046 0.0056 0.0076
–n1
a1
k1 (min
0.6021 0.5838 0.5613 0.5845
0.03790 0.0433 0.0479 0.0547
)
n1
a2
n2
a3
R2 (%)
MSD
0.5352 0.5642 0.5742 0.5833
0.6020 0.5547 0.5631 0.5790
0.5352 0.5642 0.5742 0.5829
0.2110 0.1428 0.1186 0.1209
99.98 99.98 99.96 99.80
0.00001 0.00001 0.00001 0.00001
Fig. 1. Drying constants of (i) Page, Midilli and Cavalcanti-Mata, (ii) Henderson & Pabis, Henderson, models.
terms of the Fick model, better fitting, is obtained. Using the Fick model with six terms (results not presented), using non-linear regression, and using Equations (10) and (11), the effective diffusion was determined for the drying process considering the product has a spherical geometry, with a mean equivalent radius of 3.3 mm. The effective diffusion determination is the analytical solution for Fick's second law [22]. Disregarding the volumetric grain contraction and knowing the moisture content boundary condition on the grain surface. Thus, considering Fick's model first term, the effective diffusivity varied as a function of the temperature from 3.64 1011 m2s1 at 40 C to 7.99 1011 m2s1 at 70 C. When using the same model but with six terms, similar values are obtained, respectively from, 4.11 1011 to 8.72 1011 m2s1. According to Ref. [23] work, the
obtained values are in the range of food with high starch content. Also, accordingly to Ref. [9], the obtained values are considered low and typical of protein/starchy non-porous food. Moreover, the increasing values of effective diffusivity with increasing temperature can be attributed to the fact that water molecules are more loosely bound to the food matrix at higher temperatures, thus requiring less energy for diffusion. From a practical point of view, our results indicate that mulatto beans require thin layers for optimal drying. 3.4. Activation energy Thermodynamically, assuming a free volume theory, the activation energy is defined as the energy barrier that a molecule has to overcome 4
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Journal of Agriculture and Food Research 1 (2019) 100003
Table 4 Effective Diffusivity, coefficients of determination (R2) and mean square deviation as a function of the number of terms of the Fick model. at four temperatures (40 C. 50 C. 60 C and 70 C) for drying kinetics of mulatto bean grains. T ( C)
One term
Two terms
Three terms
Deff mm2 min1
R2
MSD
Deff mm2 min1
R2
MSD
Deff mm2 min1
R2
MSD
40 50 60 70 Ea (kJ mol1)
0.002185 0.003092 0.003729 0.004792 22.232
83.77 83.58 83.44 80.08 99.19
0.0086 0.0091 0.0094 0.0112 0.1427
0.002384 0.003365 0.004037 0.005150 21.741
96.39 96.12 95.93 94.32 99.11
0.0029 0.0032 0.0033 0.0046 0.1583
0.002436 0.003437 0.004114 0.005213 21.415
98.56 98.38 98.24 97.16 99.05
0.0013 0.0015 0.0017 0.0027 0.1643
T( C)
Four terms Deff mm2 min1
R2
MSD
Five terms Deff mm2 min1
R2
MSD
Six terms Deff mm2 min1
R2
MSD
0.002455 0.003461 0.004138 0.005229 21.263
99.19 99.08 98.97 98.08 99.02
0.0007 0.0009 0.0011 0.0019 0.1662
0.002464 0.003470 0.004148 0.005232 21.173
99.45 99.38 99.29 98.48 99.03
0.0004 0.0006 0.0007 0.0015 0.1661
0.002468 0.003474 0.004151 0.005233 21.130
99.58 99.53 99.45 98.69 99.02
0.0002 0.0004 0.0005 0.0013 0.1663
40 50 60 70 Ea (kJ mol1)
to move from one position to another [24]. Thus, it can be related to the migration of water molecules from inside the product to the surface. Therefore, considering drying processes, the lower the activation energy, the higher the speed with which the water will be removed from the grains [25]. We found that activation energy values calculated considering the various terms of the Fick Model decreased from 22.23 kJ mol1 to 21.13 kJ mol1 when the number of terms increased from one to six. This result suggests that with the increasing number of terms, a more characteristic equation of the process is obtained. As a result, the process reveals more energy efficiency. The activation energy for moisture diffusion on mulatto beans has high values suggesting that effective diffusivity is a highly dependent temperature. From a practical point of view, this means that moisture diffuses as a liquid inside the non-porous mulatto beans [26].
Table 5 Thermodynamic properties obtained by drying kinetics of mulatto beans at different temperature and moisture content of 25% wet basis. Temperature
Enthalpy (ΔH)
Entropy (ΔS)
Gibbs Free Energy (ΔG)
( C) 40 50 60 70
J mol1 18 528.5 18 445.4 18 362.2 18 279.1
J mol1 K1 116.2706 116.5321 116.7856 117.0316
J mol1 54 921.23 56 085.25 57 251.84 58 420.93
K 313 323 333 343
Table 5 shows that Gibb's free energy increased with increasing temperature, and its values were positive for the entire temperature range studied. This result indicates that drying and absorption in the current study conditions were not spontaneous. According to Ref. [31], the positive value of the Gibbs free energy is characteristic of an endergonic reaction, in which it requires the addition of energy from the medium in which the product is involved for the reaction to occur. Therefore, this result is consistent since the desorption process is not spontaneous [27].
3.5. Thermodynamic properties The thermodynamic properties enthalpy, entropy, and Gibbs free energy of moisture on mulatto bean grains at different temperatures are presented in Table 5. Analyzing Table 5, it can be observed that the enthalpy decreases with increasing temperature of drying air, from 18.53 kJ mol1 for 40 C to 18.28 kJ mol1 for 70 C. This behavior is related to the increase of the partial pressure of water vapor in the grains due to the increase of drying air temperature. Thus, diffusion velocity of moisture from the interior to the surface increases, resulting in loss of water from the product by desorption. The lower enthalpy value for higher drying temperatures indicates that the amount of energy required to remove the water attached to the product during drying is also lower. Moreover, according to Ref. [27], the positive differential enthalpy values indicate that in the process, heat absorption occurs, therefore it is an endothermic process. Also from Table 5, entropy values are lower for higher drying temperatures, varying from 116.27 J mol1 K1 for 40 C to 117.03 J mol1 K1 at 70 C. Entropy is a thermodynamic quantity associated with the degree of disorder of the system. Thus, with an increase in temperature, water molecules become more excited, resulting in a decrease of order between the water-grain system. Therefore, it is expected that the entropy decreases with increasing temperature. Otherwise, decreasing temperature entails less excitation of water molecules and increases the degree of order between the watergrain system, so entropy increases with decreasing temperature [16]. According to Ref. [28], negative entropy values may be attributed to the existence of structural modifications on the adsorbent. Since moisture is being removed, it is possible to suggest that similar structure modifications are occurring. Negative entropy values have also been reported for beans [29] and sweet potato [30] both starchy foods.
4. Conclusions In this work, drying curves were studied for mulatto bean grains submitted to different drying temperatures (40–70 C). It was determined the effective diffusivity of the product, the activation energy, using the Fick model, varying the series from one to six terms, besides Page, Henderson and Pabis, Henderson, Midilli and Cavalcanti-Mata models. It is found that the loss of the moisture content occurred more intensively at higher temperatures, thus reducing the drying time and making the drying curve more pronounced. The drying constants increase with increasing temperature for all models studied, and the model that best represents the experimental data was the CavalcantiMata model because it presents the highest coefficient of determination and the lowest mean squared deviation. The effective diffusion increases with the temperature rise from 40 to 70 C, varying from 4.11 1011 to 8.72 1011 m2s1. The activation energy of the mulatto bean varied from 22.23 to 21.130 kJ mol1 depending on the number of terms used in the Fick model. In the drying process of mulatto beans, the enthalpy and entropy are positive and negative, respectively, decreasing with increasing temperature and thus indicating that the process is endothermic. Finally, Gibbs free energy increases with increasing temperature, indicating that the process does not occur spontaneously. Declaration of competing interest The authors declare no conflict of interest. 5
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Journal of Agriculture and Food Research 1 (2019) 100003
Acknowledgment
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The authors would like to acknowledge CAPES and CNPq for grant 311341/2017-9. References [1] R.O. Lamidi, et al., Recent advances in sustainable drying of agricultural produce: a review, Appl. Energy 233 (2019) 367–385. [2] M.A. Karim, M. Hawlader, Mathematical modelling and experimental investigation of tropical fruits drying, Int. J. Heat Mass Transf. 48 (23–24) (2005) 4914–4925. [3] J. Srikiatden, J.S. Roberts, Moisture transfer in solid food materials: a review of mechanisms, models, and measurements, Int. J. Food Prop. 10 (4) (2007) 739–777. [4] A. Castro, E. Mayorga, F. Moreno, Mathematical modelling of convective drying of fruits: a review, J. Food Eng. 107 (2017), https://doi.org/10.1016/ j.fbp.2017.09.006. [5] H.M. Lisboa, M.E. Duarte, M.E. Cavalcanti-Mata, Modeling of food drying processes in industrial spray dryers, Food Bioprod. Process. 107 (2018) 49–60. [6] A. Nascimento, et al., Construction of a design space for goat milk powder production using moisture sorption isotherms, J. Food Process. Eng. (2019) e13228. [7] F. Sarpong, et al., The kinetics and thermodynamics study of bioactive compounds and antioxidant degradation of dried banana (Musa ssp.) slices using controlled humidity convective air drying, J. Food Meas. Char. (2018) 1–12. [8] D. Dantas, et al., Influence of spray drying conditions on the properties of avocado powder drink, Food Chem. 266 (2018) 284–291. [9] G.D. Saravacos, Z.B. Maroulis, Transport Properties of Foods, CRC Press, 2001. [10] N. Karakaplan, et al., Kinetic and artificial neural network modeling techniques to predict the drying kinetics of Mentha spicata L, J. Food Proc. Pres. (2019) e14142. [11] C.-C. Chen, R.V. Morey, Comparison of four EMC/ERH equations, Transactions of the ASAE 32 (3) (1989) 983–0990. [12] F. Jian, D.S. Jayas, Characterization of isotherms and thin-layer drying of red kidney beans, part I, choosing appropriate empirical and semitheoretical models, Dry. Technol. (2018) 1–11. [13] A. Al-Muhtaseb, W. McMinn, T. Magee, Moisture sorption isotherm characteristics of food products: a review, Food Bioprod. Process. 80 (2) (2002) 118–128. [14] A. Baptista, et al., Characterization of protein and fat composition of seeds from common beans (Phaseolus vulgaris L.), cowpea (Vigna unguiculata L. Walp) and Bambara groundnuts (Vigna subterranea L. Verdc) from Mozambique, J. Food Meas. Char. 11 (2) (2017) 442–450.
6
Contents lists available at ScienceDirect
Journal of Agriculture and Food Research journal homepage: www.journals.elsevier.com/journal-of-agriculture-and-food-research/
Determination of characteristic properties of mulatto beans (Phaseolus vulgaris L.) during convective drying Hugo M. Lisboa *, Hanndson Araujo, Gustavo Paiva, Suelma Oriente, Matheus Pasquali, Maria Elita Duarte, Mario E.R.M. Cavalcanti Mata Unidade Academica de Engenharia de Alimentos, Universidade Federal de Campina Grande, Av. Aprigio Veloso, 882, 58429, Campina Grande, Paraiba, Brazil
A R T I C L E I N F O Keywords: Mulatto beans Drying Effective diffusivity Thermodynamic properties
A B S T R A C T
Mulatto beans (Phaseolus vulgaris L.) require proper drying for safe transport and storage. To support the drying process design, the objective of this work was to determine the mass transfer and thermodynamic properties of mulatto bean. Mulatto beans were dried under different convective conditions from an initial moisture content of 25% (w.b.) until its equilibrium drying. Using fundamental and empirical models, and considering the bean as a sphere, drying constants and the effective diffusivity of the moisture inside the product was determined at each temperature. Then, using an Arrhenius type equation, effective diffusivity values for each temperature were modeled, and the activation energy was determined along with other thermodynamic properties. Results revealed that effective diffusivity presented values typical of non-porous protein/starchy foods and varied from 4.11 1011 for 40 C and 8.72 1011 m2s1 for 70 C. The activation energy confirmed that effective diffusivity is highly dependent on temperature with values ranging from 21.13 to 22.23 kJ mol1, indicating liquid diffusion within the food material. Enthalpy, entropy, and Gibbs free energy also indicate that the process is endothermic and non-spontaneous. From a practical point of view, it is concluded that mulatto beans have a diffusion-controlled drying requiring thin layers of material for effective drying.
1. Introduction Drying is considered the most energy-intensive process and accounting to up to 15% of all industrial energy usage [1]. Inadequate management of crops and drying process often lead to infestations during storage, causing loss of crop and extensive waste [2]. Moreover, grain drying has the purpose of not only conserving the product but also increasing storage time and reducing costs, adding value to the product. In order for the drying process to be carried out quickly, safely, and economically, it is fundamental to know and monitor the physical phenomena during the drying of the product [3]. Mathematical simulations can be used to understand the drying requirements of a given product better. With this information, optimal design and commercial viability can be readily assessed. Subsequently, simulations based on the drying of successive thin layers of the product, using a mathematical model that satisfactorily represents moisture loss, can be helpful for industrial drying designs [4]. With this method, the use of substantial amounts of grains in trial and error experiments is avoided [5,6].
Moreover, drying can affect the physical and chemical properties of agricultural products [7,8]. Thus, it is of fundamental importance to know the effects of the drying on grain quality. As a result, alterations to those properties affect the operation of mass and heat transfer. Depending on the material being dried, moisture moves from inside the product to the surface accordingly to different transport phenomena. In porous capillary products, such as most products of agricultural origin, the possible transport mechanisms of moisture inside the product are liquid diffusion, capillary diffusion, surface diffusion, hydrodynamic flow, vapor diffusion and, thermal diffusion [9]. In addition to the theoretical model of Fick, other semi-theoretical and empirical models were proposed by several researchers to model drying phenomena [10]. The intent is to facilitate the operational management of drying representation of biological products such as grains and seeds. Chen and Morey, tested four models on 18 crops, finding that modified Henderson and Chung-Pfost equations are useful models for starchy grains and fibrous materials, while modified Halsey is a useful model for high oil and protein and modified Oswin is a good model for corn-based products [11]. Jian and Jayas also used several
* Corresponding author. E-mail address: [email protected] (H.M. Lisboa). https://doi.org/10.1016/j.jafr.2019.100003 Received 27 September 2019; Received in revised form 23 October 2019; Accepted 6 November 2019 2666-1543/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
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Journal of Agriculture and Food Research 1 (2019) 100003
hygrometer model MTH-1362W. All grain weightings were performed on a semi-analytical scale with a precision of 3 decimal places Bioprecisa model JH2102. The equilibrium moisture content for each temperature was determined when there was no more variation of the weight of the samples in three successive readings of 30 min. Variation of the masses was calculated considering the moisture content on a wet basis on a dry basis and establishing the ratio of the moisture content of the samples for each temperature in the time intervals considered. The drying curves of the mulatto bean were plotted with the dimensionless parameter of moisture content ratio (RX):
semi-theoretical and empirical models to characterize isotherms of red kidney beans finding Chung-Pfost and GAB as better models [12]. The liquid diffusion model allows determining the primary thermodynamic properties that result from the drying process. Thermodynamic properties of foods, including enthalpy, entropy and, Gibbs free energy, are essential for the design and optimization of drying operations. Moreover, thermodynamic properties provide an understanding of sorption mechanisms and food-water interactions [13]. The enthalpy gives us the energy variation of the interaction of the water molecules with the other constituents of the product during the drying processes. Entropy defines the degree of order or disorder existing in the water-product system. Finally, Gibbs free energy can indicate how much the water is bound to the product. It also allows determining if the drying process is characterized as spontaneous or non-spontaneous. Common beans are one of the most consumed foods worldwide, having high amounts of protein for a low price [14]. The grains of mulatto beans are usually harvested with high moisture content. Thus, exposure to environmental conditions causes grains to lose quality due to high water activity. In the post-harvest period, the beans have their moisture content reduced from 25% to 12% (w.b.) using convective drying. Considering the lack of studies on mulatto beans drying processes and thermodynamic properties, the objective of this work was to study the drying kinetics of mulatto beans submitted to different drying temperatures (40, 50, 60 and 70 C). Additionally, the effective diffusivity, activation energy and, thermodynamic properties (enthalpy, entropy and, Gibbs free energy) were determined, as well as the physical characteristics such as length, width, thickness, and volume for the different drying conditions.
RX ¼
2.4. Data modeling The experimental data on the drying of mulatto bean grains were adjusted using non-linear regression models using the Quasi-Newton method using the Statistica 7.0 software. The empirical, semiempirical, and theoretical mathematical models often used to represent the drying of agricultural products are shown in Table 1. For the fundamental Fick Model, up to six terms of the series were used. Where t is the drying time (min); k, k0, and k1 are drying constants; a, a1, a2, a3, b, n, n1, n2 are coefficients of the models and r is the product radius, m2. The coefficient of determination (R2) and the mean square deviation (MSD) was used as selection criteria in order to obtain the model that best represents the observed data.
2.1. Materials
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P RXexp RXpre MSD ¼ N
Mulatto beans (Phaseolus vulgaris L.) were collected at a local farm with a moisture content of 25.0% on a wet basis (w.b.). Moisture content was determined by placing some amount of beans in an oven at 105 3 C until the weight was constant.
(9)
Where RXexp is the ratio of moisture content obtained experimentally, RXpre is the ratio of the moisture content predicted by the mathematical model, and n is the number of observations throughout the experiment. A simplified geometry of the grain assuming a spherical model was used for the effective diffusivity determinations [15]. Thus, constant values were assigned for volume, temperatures, and initial moisture content on its surface. The effective diffusivity (Def) was obtained through the
2.2. Mulatto beans measurements The calculation to obtain the radius of equivalence to a sphere was performed by measuring the three orthogonal axes of 100 randomly chosen mulatto bean grains. These measurements were performed with the aid of a digital caliper, STANLEY model 78-440S, with a resolution of 0.01 mm. Mulatto beans radius (req) was determined by equation (1) considering the volume of the ellipsoid (Velip) as a sphere: req
(2)
In equation (2), RX is the ratio of moisture content (dimensionless), Xe is the equilibrium moisture content, decimal (dry basis); Xdb ¼ moisture content, decimal (dry basis) and Xdb,initial is the initial moisture content, decimal (dry basis);
2. Materials and methods
rffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 ¼ Velip ; 4π
Xdb Xe Xdb initial Xe
Table 1 Non-linear regression models used to predict the drying phenomenon of agricultural products.
(1)
2.3. Mulatto beans drying Drying tests were performed using a fixed bed experimental dryer with temperature and drying air velocity controls. The airflow was provided by an axial fan that led the air to the plenum, where it flowed between four screened and removable trays containing the samples of the mulatto bean grains. During the drying process, trays with mulatto bean samples were weighed periodically every 5 min for each temperature. The drying air velocity was set to 1 m s1 and measured with a portable digital anemometer INSTRUTEMP, model ITTHAL-300. This velocity was chosen to avoid external resistance to moisture transfer. The dryer was adjusted to operate at temperatures of 40, 50, 60 and 70 C. The relative humidity of the drying air corresponding to the drying temperatures were, respectively, 23%, 14%, 8%, and 5%. The mean ambient temperature was 26 C, and the relative humidity was 50%. These conditions were determined by a Minipa Digital thermo-
Model Designation
Model Equation
Page
RX ¼ expð k t n Þ
Henderson & Pabis Henderson
RX ¼ a expð k tÞ
Fick
Midilli CavalcantiMata
2
RX ¼ a expð k0 tÞ þ b expð k1 tÞ π2 6 4π 2 RX ¼ exp 2 D t n þ 2 exp 2 D t þ 4π r r 2 9π 2 3 16π 2 exp D t þ þ exp Dt þ 3π 2 8π 2 r2 r2 6 25π 2 1 36π 2 exp 2 D t þ 2 exp 2 D t 2 25π 6π r r RX ¼ a expð k t n Þ þ b t RX ¼ a1 expð k1 t n1 Þ þ a2 expð k1 t n2 Þ þ a3
(eq. 3) (eq. 4) (eq. 5) (eq. 6)
(eq. 7) (eq. 8)
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Journal of Agriculture and Food Research 1 (2019) 100003
7.35 to 4.53 is obtained when the drying temperature increases. As expected, these values are inversely proportional to the drying temperature, a fact also observed by Ref. [12] when studying red kidney beans.
following expression: RX ¼
∞ 6 X 1 exp n2 At 2 n n¼1
(10)
π2
where: A¼
π
3.2. Mathematical modeling of the drying process
2
r2
Table 3 presents the parameters for Page, Henderson & Pabis, Henderson, Midilli, and Cavalcanti Mata models, adjusted to the drying kinetics of mulatto beans at temperatures of 40 to 70 C. These models were chosen because are widely used by the ASABE – American Society of Agricultural and Biological Engineers. All mathematical models adjusted to the experimental data presented coefficients of determination (R2) higher than 98.18% and MSD values below 0.0011. This result indicates that the equations represent well the drying phenomenon. Similar values were obtained by Ref. [17] when dried the Adzuki Bean, obtaining values of (R2) greater than 98%, mentioning an adequate representation for the studied phenomenon. However, it can be observed that the Page, Henderson, Midilli, and Cavalcanti Mata models have coefficients higher than 99.4%, with an emphasis on the Cavalcanti-Mata model where the MSD is inferior to the others, indicating a better fit to the experimental data. Analyzing Fig. 1, the drying constants (k) for the Page, Henderson & Pabis, Henderson, Midilli, and Cavalcanti-Mata models increase in absolute value with the increase of drying air temperature. This is an expected result since the drying constant represents the effect of external drying conditions and tends to increase with increasing drying air temperature. The coefficient (n) of the Cavalcanti Mata, Page, and Midilli models also presented a linear trend of their values with the drying temperatures. For this coefficient, it is known that n ¼ 1 represents the first-order kinetics, while n ¼ 0 would represent a constantrate drying [18]. Experimental data shows that moisture content decreases the most in the first hour. At this first stage of drying, the moisture at the surface of the beans is first evaporated. This result is consistent with a drying principle where the external conditions control the initial stage. After that initial stage, moisture migration from the interior of the beans to the surface is the controlling factor of the drying process [19]. It was also observed that the increase of the temperature of the drying air promotes a higher rate of moisture removal from the product, evidencing, therefore, the increase of the drying rate, a fact already expected and also verified in other works [20]. The average time required to complete the drying process was 1300, 1000, 880, and 640 min for, respectively, temperatures of 40, 50, 60, and 70 C. As expected, the drying time decreases with increasing drying air temperature. Moreover, the Cavalcanti-Mata model represents better experimental data. This decision is based on the fact that this model has coefficients of determination (R2) above 99.8%. However, the coefficient of determination, when used alone, it is not a good criterion for the selection of highly parameterized non-linear mathematical models [21]. Therefore, MSD values were also considered. Since the Cavalcanti-Mata model has the lowest MSD value, this confirms that this model has a good representation of the drying kinetics of the mulatto bean for the studied temperature range from 40 to 70 C.
(11)
Def
and Def ¼ A
r2
(12)
π2
Where, Def is effective diffusivity, mm2. s1, r is the radius of the sphere equivalent to the grain, m; n is the number of terms, and t is the drying time, s. To evaluate the influence of temperature on the diffusion coefficient, the Arrhenius equation was used: Ea 0 Def ¼ Do exp RT
(13)
where, D0 0 is the pre-exponential factor, mm2 s1; Ea is the activation energy, kJ mol1; R ¼ universal gas constant, 8.314 J mol1 K1 and T is the absolute temperature, K. The determination of the activation energy allowed the calculation of the different thermodynamic properties, such as enthalpy, entropy, and Gibbs free energy, using the method described by Ref. [16]), according to the following equations: ΔH ¼ Ea R T
(14)
kb lnðTÞ ΔS ¼ R lnðDo Þ ln kp
(15)
ΔG ¼ ΔH T ΔS
(16)
Where, ΔH is the enthalpy, J mol1; ΔS is the entropy, J mol1 K1, and ΔG ¼ Gibbs free energy, J mol1. Kb is the Boltzmann's constant, 1.38 10–23 J K1, and hp is the Planck's constant, 6.626 10–34 J s1. The coefficient Ln (D0) of the entropy expression (ΔS) can be obtained by linearizing the Arrhenius equation. The expression used was: E1 lnDef ¼ lnDo : RT
(17)
3. Results and discussion 3.1. Equilibrium moisture content Under a given drying setup, the equilibrium moisture content is the moisture content at which the material neither gains or loses moisture. This stabilization occurs because equilibrium is reached when the rate of evaporation equals the rate of condensation. This result is important for drying processes because when the equilibrium moisture content is reached, no further drying is possible. Table 2 shows the mean values of the equilibrium moisture content (Xeq) for the drying temperatures of 40, 50, 60, and 70 C. A decrease in equilibrium moisture content from
3.3. Moisture effective diffusivity Table 4 presents the parameters of the Fick model for the six terms of the series, highlighting the effective diffusivity determination. When fitting Fick model by varying the number of terms from 1 to 6, for mulatto bean dryings at temperatures from 40 to 70 C, it is observed that the coefficients of determination (R2) vary from 80.08% for the 1st term of the series to 99.58% for the 6th terms of the series (Table 4). Concerning the MSD values, the variation was 0.0112 to 0.0002, respectively. Therefore, it is observed that increasing the number of
Table 2 Equilibrium moisture content (Xeq) as a function of drying temperatures. Drying Temperature ( C)
%RH
Equilibrium moisture content (%)
40 50 60 70
23.0 14.0 8.0 5.0
7.35 0.02 5.67 0.05 4.88 0.04 4.53 0.05
3
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Journal of Agriculture and Food Research 1 (2019) 100003
Table 3 Coefficients of the six models analyzed. coefficients of determination (R2) and mean square deviation (MSD). of the drying of the mulatto beans. for the temperatures (40–70 C). Temperature. K
Parameters
Page 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Henderson & Pabis 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C)
k (min –n) 0.0310 0.0361 0.0373 0.0381 a 0.8361 0.8441 0.8532 0.8886
Henderson
a
k0 (min1)
b
0.7394 0.7338 0.7509 0.8021 a 0.9875 0.9767 0.9890 1.0046
0.0027 0.0038 0.0047 0.0066 k (min –n) 0.0408 0.0421 0.0433 0.0446
0.2382 0.2498 0.2391 0.1935 n 0.5670 0.5951 0.6226 0.6443
313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Midilli 313 (40 C) 323 (50 C) 333 (60 C) 343 (70 C) Cavalcanti Mata 313 323 333 343
(40 C) (50 C) (60 C) (70 C)
R2 (%) 99.40 99.53 99.62 99.71 R2 (%) 98.20 98.18 98.39 98.96
MSD 0.0011 0.0011 0.0010 0.0008 MSD 0.0008 0.0009 0.0009 0.0008
k1 (min1)
R2 (%)
MSD
0.0550 0.0642 0.0802 0.0966 b (min1) 0.000076 0.000104 0.000072 0.000146
99.85 99.91 99.94 99.95 R2 (%) 99.96 99.90 99.95 99.83
0.0001 0.0001 0.0001 0.00001 MSD 0.0001 0.0009 0.0001 0.0001
n 0.6392 0.6515 0.6677 0.6958 k (min1) 0.0032 0.0046 0.0056 0.0076
–n1
a1
k1 (min
0.6021 0.5838 0.5613 0.5845
0.03790 0.0433 0.0479 0.0547
)
n1
a2
n2
a3
R2 (%)
MSD
0.5352 0.5642 0.5742 0.5833
0.6020 0.5547 0.5631 0.5790
0.5352 0.5642 0.5742 0.5829
0.2110 0.1428 0.1186 0.1209
99.98 99.98 99.96 99.80
0.00001 0.00001 0.00001 0.00001
Fig. 1. Drying constants of (i) Page, Midilli and Cavalcanti-Mata, (ii) Henderson & Pabis, Henderson, models.
terms of the Fick model, better fitting, is obtained. Using the Fick model with six terms (results not presented), using non-linear regression, and using Equations (10) and (11), the effective diffusion was determined for the drying process considering the product has a spherical geometry, with a mean equivalent radius of 3.3 mm. The effective diffusion determination is the analytical solution for Fick's second law [22]. Disregarding the volumetric grain contraction and knowing the moisture content boundary condition on the grain surface. Thus, considering Fick's model first term, the effective diffusivity varied as a function of the temperature from 3.64 1011 m2s1 at 40 C to 7.99 1011 m2s1 at 70 C. When using the same model but with six terms, similar values are obtained, respectively from, 4.11 1011 to 8.72 1011 m2s1. According to Ref. [23] work, the
obtained values are in the range of food with high starch content. Also, accordingly to Ref. [9], the obtained values are considered low and typical of protein/starchy non-porous food. Moreover, the increasing values of effective diffusivity with increasing temperature can be attributed to the fact that water molecules are more loosely bound to the food matrix at higher temperatures, thus requiring less energy for diffusion. From a practical point of view, our results indicate that mulatto beans require thin layers for optimal drying. 3.4. Activation energy Thermodynamically, assuming a free volume theory, the activation energy is defined as the energy barrier that a molecule has to overcome 4
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Journal of Agriculture and Food Research 1 (2019) 100003
Table 4 Effective Diffusivity, coefficients of determination (R2) and mean square deviation as a function of the number of terms of the Fick model. at four temperatures (40 C. 50 C. 60 C and 70 C) for drying kinetics of mulatto bean grains. T ( C)
One term
Two terms
Three terms
Deff mm2 min1
R2
MSD
Deff mm2 min1
R2
MSD
Deff mm2 min1
R2
MSD
40 50 60 70 Ea (kJ mol1)
0.002185 0.003092 0.003729 0.004792 22.232
83.77 83.58 83.44 80.08 99.19
0.0086 0.0091 0.0094 0.0112 0.1427
0.002384 0.003365 0.004037 0.005150 21.741
96.39 96.12 95.93 94.32 99.11
0.0029 0.0032 0.0033 0.0046 0.1583
0.002436 0.003437 0.004114 0.005213 21.415
98.56 98.38 98.24 97.16 99.05
0.0013 0.0015 0.0017 0.0027 0.1643
T( C)
Four terms Deff mm2 min1
R2
MSD
Five terms Deff mm2 min1
R2
MSD
Six terms Deff mm2 min1
R2
MSD
0.002455 0.003461 0.004138 0.005229 21.263
99.19 99.08 98.97 98.08 99.02
0.0007 0.0009 0.0011 0.0019 0.1662
0.002464 0.003470 0.004148 0.005232 21.173
99.45 99.38 99.29 98.48 99.03
0.0004 0.0006 0.0007 0.0015 0.1661
0.002468 0.003474 0.004151 0.005233 21.130
99.58 99.53 99.45 98.69 99.02
0.0002 0.0004 0.0005 0.0013 0.1663
40 50 60 70 Ea (kJ mol1)
to move from one position to another [24]. Thus, it can be related to the migration of water molecules from inside the product to the surface. Therefore, considering drying processes, the lower the activation energy, the higher the speed with which the water will be removed from the grains [25]. We found that activation energy values calculated considering the various terms of the Fick Model decreased from 22.23 kJ mol1 to 21.13 kJ mol1 when the number of terms increased from one to six. This result suggests that with the increasing number of terms, a more characteristic equation of the process is obtained. As a result, the process reveals more energy efficiency. The activation energy for moisture diffusion on mulatto beans has high values suggesting that effective diffusivity is a highly dependent temperature. From a practical point of view, this means that moisture diffuses as a liquid inside the non-porous mulatto beans [26].
Table 5 Thermodynamic properties obtained by drying kinetics of mulatto beans at different temperature and moisture content of 25% wet basis. Temperature
Enthalpy (ΔH)
Entropy (ΔS)
Gibbs Free Energy (ΔG)
( C) 40 50 60 70
J mol1 18 528.5 18 445.4 18 362.2 18 279.1
J mol1 K1 116.2706 116.5321 116.7856 117.0316
J mol1 54 921.23 56 085.25 57 251.84 58 420.93
K 313 323 333 343
Table 5 shows that Gibb's free energy increased with increasing temperature, and its values were positive for the entire temperature range studied. This result indicates that drying and absorption in the current study conditions were not spontaneous. According to Ref. [31], the positive value of the Gibbs free energy is characteristic of an endergonic reaction, in which it requires the addition of energy from the medium in which the product is involved for the reaction to occur. Therefore, this result is consistent since the desorption process is not spontaneous [27].
3.5. Thermodynamic properties The thermodynamic properties enthalpy, entropy, and Gibbs free energy of moisture on mulatto bean grains at different temperatures are presented in Table 5. Analyzing Table 5, it can be observed that the enthalpy decreases with increasing temperature of drying air, from 18.53 kJ mol1 for 40 C to 18.28 kJ mol1 for 70 C. This behavior is related to the increase of the partial pressure of water vapor in the grains due to the increase of drying air temperature. Thus, diffusion velocity of moisture from the interior to the surface increases, resulting in loss of water from the product by desorption. The lower enthalpy value for higher drying temperatures indicates that the amount of energy required to remove the water attached to the product during drying is also lower. Moreover, according to Ref. [27], the positive differential enthalpy values indicate that in the process, heat absorption occurs, therefore it is an endothermic process. Also from Table 5, entropy values are lower for higher drying temperatures, varying from 116.27 J mol1 K1 for 40 C to 117.03 J mol1 K1 at 70 C. Entropy is a thermodynamic quantity associated with the degree of disorder of the system. Thus, with an increase in temperature, water molecules become more excited, resulting in a decrease of order between the water-grain system. Therefore, it is expected that the entropy decreases with increasing temperature. Otherwise, decreasing temperature entails less excitation of water molecules and increases the degree of order between the watergrain system, so entropy increases with decreasing temperature [16]. According to Ref. [28], negative entropy values may be attributed to the existence of structural modifications on the adsorbent. Since moisture is being removed, it is possible to suggest that similar structure modifications are occurring. Negative entropy values have also been reported for beans [29] and sweet potato [30] both starchy foods.
4. Conclusions In this work, drying curves were studied for mulatto bean grains submitted to different drying temperatures (40–70 C). It was determined the effective diffusivity of the product, the activation energy, using the Fick model, varying the series from one to six terms, besides Page, Henderson and Pabis, Henderson, Midilli and Cavalcanti-Mata models. It is found that the loss of the moisture content occurred more intensively at higher temperatures, thus reducing the drying time and making the drying curve more pronounced. The drying constants increase with increasing temperature for all models studied, and the model that best represents the experimental data was the CavalcantiMata model because it presents the highest coefficient of determination and the lowest mean squared deviation. The effective diffusion increases with the temperature rise from 40 to 70 C, varying from 4.11 1011 to 8.72 1011 m2s1. The activation energy of the mulatto bean varied from 22.23 to 21.130 kJ mol1 depending on the number of terms used in the Fick model. In the drying process of mulatto beans, the enthalpy and entropy are positive and negative, respectively, decreasing with increasing temperature and thus indicating that the process is endothermic. Finally, Gibbs free energy increases with increasing temperature, indicating that the process does not occur spontaneously. Declaration of competing interest The authors declare no conflict of interest. 5
H.M. Lisboa et al.
Journal of Agriculture and Food Research 1 (2019) 100003
Acknowledgment
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