Hydrodynamic characteristics and its associated thermodynamic and textural variation of three common Malawian beans varieties ( Boma , Sugar and Mandondo ) during soaking were evaluated at four temperature regimes (25° C, 35°C, 45°C and 55°C). The equilibrium water uptake of 127 % ± 5% was reached in 10, 6, and 4 hours respectively, for 25° C, 35°C and 45°C. Not much variation was observed between 45°C and 55°C except for sugar beans where equilibrium water uptake was reached within two hours of soaking at 55°C. Three models namely Peleg, two - parameter Mitscherlich model and viscoelastic model were used to evaluate the comparative predicting capabilities of the bean hydrodynamic characteristics. All models predicted the water absorption accurately (R^{2} > 0.903, RMSE < 4.95). In addition, the viscoelastic model gave a good prediction for the two water absorption phases. The impact of temperature and time on moisture transfer rate and bean hardness showed the activation kinetic parameters to be between 25 - 65 kJ/mol. Sugar beans w ere found to be the least hard. At room temperature, its hardness reduced by 58% within 2 hours of soaking. At higher temperature (55° C) hardness values were reduced to 12.5 % , 11.1 % and 15.0% within the first hour for Boma, Sugar and Mandondo beans, respectively.
Common beans (Phaseolus vulgaris) are included in pulses that make a significant contribution to human and animal food supply. Globally, bean legumes make important contribution to the diets and nutrition. They are known to be important sources of starch and fibre, minerals and bioactive compounds and health benefits [
Water uptake during soaking influences the product’s textural and nutritional qualities [
Although, the hydrodynamics of beans has been considered as a diffusion process, and the liquid water transport has been modeled using Fick’s law, other researchers [
Therefore, the objectives of this work were to 1) model the hydrodynamic characteristics of three Malawian bean varieties using the Peleg, the two-parameter Mitscherlich model and the recently proposed viscoelastic two-phase model; 2) evaluate the thermodynamics variations during soaking of common beans; 3) assess the textural changes during soaking.
Three varieties of common beans namely Boma, Sugar and Mandondo harvested from the Kameme and Lufita communities in the Chitipa district of Malawi were used for this work. The beans were harvested during the 2016 harvest season. Prior to the experiments, the seeds were cleaned by removing foreign materials such as dried pods, stones, dirt, and broken bean seeds. Seeds with length 10.5 ± 0.5 mm were used in this work for consistency and to eliminate the influence of seed size on water absorption. Initial moisture content of samples was determined using the ASAE S352.2 DEC 97.
Hydrodynamic experiments were conducted using randomly selected seeds of each variety to obtain 4 ± 0.1 g. The seeds were soaked in 20 ml distilled water at different temperatures (25˚C, 35˚C, 45˚C and 55˚C). The selected temperatures were below the starch gelatinization temperature. Prior to the experiment, the distilled water and its container were maintained at the desired temperature. For temperatures above room temperature, a water bath was used to establish the thermal equilibrium. Soaking were than for 15, 30, 60, 120, 240, 360, 480, 600, and 720 min. Preliminary experiments showed negligible water absorption variations after 600 min. At the end of each experimental run, the water was drained and the surface water on the samples dried using a paper towel. The weight of the samples was then determined. Experiments were conducted in triplicates.
The water absorption capacity was evaluated using Equation (1) [
W a = W f − W i W i × 100 (1)
where W a is the water absorption (d.b. %), W f is the final weight of seeds after soaking (g) and W i is the initial weight of seeds prior to soaking (g).
The Dumas combustion method in accordance with AOAC method 968.06 [
Hydrodynamics of legumes have widely been modelled with theoretical and empirical models. Due to the relative ease of use, the latter is preferred. The Peleg equation and its modifications are the most used empirical models for hydrodynamic characteristics. In this work, in addition to the Peleg model, three other hydrodynamic models namely viscoelastic model, the Weibull model and the two-parameter Mitscherlich model were all fitted to the experimental data.
The Peleg model [
R = d M d t = K 1 ( K 1 + K 2 t ) 2 (2)
In its linearized form, the water absorption capacity is given by Equation (3)
t M t − M o = K 1 + K 2 t (3)
where, t is the soaking time in min, M t is the moisture content (d.b) at time t (%), M o is the initial moisture content (d.b), K 1 is the Peleg rate constant, min/% m.c. (d.b), and K 2 is the Peleg capacity constant 1/% m.c. (d.b).
The equilibrium moisture content, M e (d.b) was determined using Equation (4) [
M e = M o + 1 K 2 (4)
The viscoelastic model is based on the fact that water absorption characteristics are time dependent just like other viscoelastic properties of food. Therefore, the two-phase water absorption characteristics of common beans can be model using Equation (5)
M t − M o = M r e t ( 1 − e − t / T r e l ) + K r e l t (5)
where K r e l is the rate of water absorption in the relaxation phase (%/min.), M r e t is the total retarded moisture content and T r e t is the retardation time, referring to the time required by the seed moisture content to reach 63% of M r e t .
The Mitscherlich model [
W t = γ − α β t (6)
where, W t is the weight after soaking for time t (hours), γ is the asymptote, α is the increase in weight and β is a curve parameter related to the rate of weight change over the period t = 0 to t = ∞ .
In its modified form, the weight gain is modeled and the asymptote, γ is eliminated. The water absorption capacity can now be predicted with a two parameter Mitscherlich model given by Equation (7) [
W a = α ( 1 − β t ) (7)
where, W a is the water absorption (d.b %) after soaking for t (min).
The models were evaluated using the coefficient of determination (R^{2}) and the root mean square error (RMSE). The expression for estimation of the R^{2} and RMSE are given by Equation (8) and Equation (9) as:
R 2 = ∑ i = 1 n ( M exp , i − M e x p , a v e ) 2 − ∑ i = 1 n ( M exp , i − M p r e , i ) 2 ∑ i = 1 n ( M exp , i − M e x p , a v e ) 2 (8)
RMSE = ∑ i = 1 n ( M exp , i − M p r e , i ) 2 N (9)
Thermodynamic variations during soaking can be determined by estimating the dependence of the Peleg model coefficient on the water temperature. This dependence is expressed in the Arrhenius equation shown in Equation (10):
1 K = K r e f , f exp [ − E a R ( 1 T − 1 T r e f ) ] (10)
where, K r e f , is the coefficient of hydration at reference temperature; E a is the activation energy expressed in KJmol^{−}^{1}; R, is the universal gas constant (8.314 KJmol^{−}^{1}∙K^{−}^{1}); T, the experimental temperature (K) and T r e f is the reference temperature (K). The reference temperature was chosen as the average of the experimental temperatures to lessen the co-linearity of K r e f and activation energy [
ln ( 1 K ) = ln K r e f , f + ( E a R ) ( 1 T − 1 T r e f ) (11)
A plot of ln ( 1 K ) against ( 1 T − 1 T r e f ) gives a linear graph with ( E a R ) as slope. The activation energy E a is then determined form the slope. From the estimated E a other thermodynamics parameters can be determined. The enthalpy, entropy and Gibbs free energy of activation can be estimated from Equations (12)-(14), respectively [
H = E a − R T (12)
Δ S = R ( ln K r e f − ln K B h p − ln T ) (13)
Δ G = Δ H − T Δ S (14)
where, R is the universal gas constant; ln K r e f is the ordinate intersection of the linearized plot to obtain the activation energy (Equation (11)) KB is the Boltzmann constant (1.38 × 10^{−}^{23} J∙K^{−}^{1}); h p , is the Planck’s constant (6.626 × 10^{−}^{34} J∙s); and T is the absolute temperature.
Changes in hardness of dry and soaked beans (as a function of time and temperature) were determined using a TA-HD Plus texture analyzer (Stable Micro Systems Ltd, Surrey, UK), a return-to-start (RTS), measuring force under compression using a 2-mm cylindrical stain less-steel probe (P2). The selected probe is widely used for bean hardness due to its ability to impact the tegument which helps differentiate similar samples [
Bean hardness was defined as the peak force of the texture curve corresponding to the required force to deform the seed. Due to significant variation of individual bean hardness [
The chemical composition of the varieties used in the study is shown in
Sample Name | Protein (%) | Ash (%) | Moisture (%) | Fat (%) | Carbohydrate (%) | Gross Energy (kJ/100 g) |
---|---|---|---|---|---|---|
Boma | 24.81 ± 0.69 | 3.55 ± 0.32 | 9.89 ± 0.01 | 1.53 ± 0.00 | 60.22 | 1477.68 |
Sugar beans | 27.67 ± 0.99 | 3.21 ± 0.15 | 8.55 ± 0.08 | 1.21 ± 0.00 | 59.36 | 1499.02 |
Mandondo | 24.91 ± 0.32 | 3.04 ± 0.12 | 10.30 ± 0.01 | 1.29 ± 0.00 | 60.46 | 1474.31 |
Source: Authors’ experimental results.
that the main mechanism controlling the rate of water absorption in seeds is diffusion through the endosperm regardless of the process condition. During hydration, water is absorbed by the seed coat, then diffused into the interior and cotyledon [
The effect of variety on water absorption can be seen by comparing the plots. Hydrodynamic behavior of Sugar beans differs significantly from Boma and Mandondo beans. It showed even a much faster water uptake within the first 200 mins of soaking.
The results also showed that equilibrium water uptake was similar for all varieties even at different temperatures, however, the time to reach that point varied significantly for different soaking water temperature. This may be attributed to the increase in water permeability as the temperature rises. On the average, the equilibrium water uptake was reached in 10, 6, and 4 hours, respectively for water temperature at 25˚C, 35˚C and 45˚C. Not much variation was seen between 45˚C and 55˚C except for sugar beans where equilibrium water uptake was reached within two hours of soaking at 55˚C.
The experimental data were fitted to the Peleg model (Equation (3)). Using a non-linear regression analysis, the model constants were determined and presented in
Variety | Temperature | K_{1} (min/% MC (d.b) | K_{2} (min/% MC (d.b) | R^{2} | RMSE |
---|---|---|---|---|---|
Boma Beans | 25 | 5.006 | 0.034 | 0.903 | 3.15 |
35 | 2.619 | 0.031 | 0.999 | 0.25 | |
45 | 0.982 | 0.030 | 0.997 | 0.36 | |
55 | 0.706 | 0.029 | 0.996 | 0.43 | |
Sugar Beans | 25 | 3.844 | 0.035 | 0.945 | 2.40 |
35 | 1.832 | 0.033 | 0.979 | 1.39 | |
45 | 0.580 | 0.031 | 0.997 | 0.44 | |
55 | 0.390 | 0.029 | 0.997 | 0.46 | |
Mandondo beans | 25 | 1.829 | 0.032 | 0.979 | 1.28 |
35 | 1.665 | 0.031 | 0.983 | 1.30 | |
45 | 1.368 | 0.028 | 0.981 | 1.16 | |
55 | 0.669 | 0.027 | 0.996 | 0.55 |
K_{1} is the Peleg rate constant and K_{2} is the Peleg capacity constant.
at temperatures above 40˚C. Several factors including temperature, soaking duration, presence and concentration of salt have been attributed to higher mass flow rates during soaking [
Similarly, K_{2} which represents the maximum water absorption capacity followed a decreasing trend as water temperature increased. This was expected due to the inverse relationship with the water absorption capacity as reported by other researchers [
The two parameter Mitscherlich model was fitted to the experimental data and the results displayed in
In contrast to raw experimental data which indicated that regardless of the soaking temperature, the equilibrium water uptake was similar for all varieties, the two parameter Mitscherlich model showed that the maximum hydration among the varieties at room temperature, α differs significantly (p < 0.05). This may be due to an underestimation of maximum hydration at lower temperature. This is also reflected in the high RMSE values at room temperature.
Variety | Temperature | α | β | R^{2} | RMSE |
---|---|---|---|---|---|
Boma beans | 25 | 102.5 | 0.999 | 0.945 | 2.53 |
35 | 110.8 | 0.994 | 0.991 | 1.88 | |
45 | 115.9 | 0.992 | 0.972 | 2.25 | |
55 | 117.2 | 0.984 | 0.988 | 4.52 | |
Sugar beans | 25 | 104.7 | 0.995 | 0.985 | 4.91 |
35 | 108.1 | 0.989 | 0.990 | 4.21 | |
45 | 110.5 | 0.985 | 0.995 | 3.19 | |
55 | 111.4 | 0.976 | 0.987 | 4.39 | |
Mandondo | 25 | 109.0 | 0.996 | 0.987 | 4.78 |
35 | 111.1 | 0.994 | 0.992 | 3.77 | |
45 | 117.5 | 0.993 | 0.995 | 3.15 | |
55 | 119.4 | 0.990 | 0.990 | 4.57 |
Variety | Temperature | M_{o} % (d.b) | M_{rel} % (d.b) | T_{rel} min | K_{rel} % (d.b)/min | R^{2} | RMSE |
---|---|---|---|---|---|---|---|
Boma Beans | 25 | 9.96 | 49.2 | 177.94 | 0.029 | 0.987 | 2.420 |
35 | 9.96 | 74.5 | 145.99 | 0.025 | 0.966 | 0.551 | |
45 | 9.96 | 82.6 | 102.15 | 0.010 | 0.984 | 0.527 | |
55 | 9.96 | 90.3 | 55.40 | 0.005 | 0.991 | 0.123 | |
Sugar Beans | 25 | 10.21 | 58.1 | 128.21 | 0.107 | 0.976 | 1.660 |
35 | 10.21 | 75.8 | 91.32 | 0.030 | 0.986 | 0.988 | |
45 | 10.21 | 81.2 | 39.01 | 0.013 | 0.989 | 0.368 | |
55 | 10.21 | 85.6 | 22.29 | 0.012 | 0.989 | 0.120 | |
Mandondo Beans | 25 | 9.69 | 62.1 | 149.45 | 0.029 | 0.994 | 0.490 |
35 | 9.69 | 75.0 | 137.93 | 0.019 | 0.990 | 0.679 | |
45 | 9.69 | 80.3 | 109.69 | 0.011 | 0.979 | 0.274 | |
55 | 9.69 | 99.5 | 50.25 | 0.004 | 0.987 | 0.201 |
temperature. At higher temperature (55˚C) this time reduced to a third for Boma and Mandondo beans and only 17% for Sugar beans. This implies commercial hydration process for sugar beans can be achieved rapidly (less than 25 mins) during processing by increasing water temperature to 55˚C.
A comparison of the three models used for this work is shown in
behavior of Boma beans than others, while the Viscoelastic model predict Mandondo beans better than the others.
Temperature dependence of the initial rate of water absorption has been modeled with the Arrhenius equation expressed in Equation (10). The kinetic parameters are reported in the
Changes in thermodynamic properties during common bean hydration are displayed in
Textural variations determined as the changes in bean hardness as a function of time and temperature are shown in
Variety | E_{a}(kj/mol) | R^{2} | K_{ref} |
---|---|---|---|
Boma Beans | 55.84 | 0.974 | 0.592 |
Sugar beans | 65.25 | 0.975 | 0.919 |
Mandondo beans | 25.78 | 0.801 | 0.784 |
hardness pattern can be observed for the beans at different soaking temperatures. These phases which were especially pronounced during soaking at room temperature represent an initial slow softening during the first 30 mins, a subsequent rapid softening then a much slower final softening phase. As can be seen from
hydrodynamic characteristics (Section 3.2), which was significantly different from Boma and Mandondo as well as the two parameter Mitscherlich model which indicated that the first phase of water absorption for Sugar beans occurred within 128 mins of soaking. The thermodynamic results which revealed that Sugar beans showed the highest enthalpy change and the greatest energy variation due to bean-water interaction during hydration also seem to support this assertion.
The effect of soaking water temperature on bean hardness, shown in
In this present study, the hydrodynamic characteristics of three Malawian common beans varieties were investigated. Hydration temperature and time had a significant influence (p < 0.05) on the hydration kinetics of the selected common bean varieties. The time required to reach equilibrium water uptake was determined as 10 ± 1.08 hours for all bean samples. This equilibrium time reduces to 6 and 4 hours when beans are soaked at 35˚C and 45˚C. Soaking above 45˚C did not significantly reduce the equilibrium water uptake except in Sugar beans. The hydrodynamic characteristics were modeled using Peleg model, two-parameter Mitscherlich model and the viscoelastic model. All the models accurately described the water absorption characteristics of the common bean varieties at the selected soaking temperatures. Furthermore, the initial rapid early water absorption was successfully modeled to be between 49.2% and 99.5% with the viscoelastic model for the studied varieties. The impact of temperature and time on moisture transfer rate was determined with Arrhenius relation. The activation energies were found to be within 25 - 65 kJ/mol. Thermodynamic properties such as enthalpy and entropy change decreased with increasing temperature while Gibbs energy increased with increasing soaking water temperature. Changes in bean hardness were found to be significantly influenced by soaking time and temperature. While it takes 360 mins to reduce bean hardness to less than 20% at room temperature, the same level of hardness reduction can be achieved in 60 mins during soaking at 55˚C.
The authors gratefully acknowledge the International Fund for Agricultural Development (IFAD) for providing financial assistance through IFAD project grant 2000000974.
The authors declare no conflicts of interest regarding the publication of this paper.
Kwofie, E.M., Mba, O.I. and Ngadi, M. (2019) Hydrodynamic Modelling, Thermodynamic and Textural Variations during Common Beans Soaking. Advances in Chemical Engineering and Science, 9, 27-43. https://doi.org/10.4236/aces.2019.91003