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) [10] [19]

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 [20] was used to determine the total nitrogen content of bean powders. The crude protein was then estimated using a conversion factor of 6.25. Moisture content of pulverized samples was measured using the hot air oven method AOAC Method 925.09 [20] . Crude fat was determined by petroleum ether extraction method (AOAC method 963.15) using automated solvent extractor (VelpScientific, Usmate, Italy). The energy value (in kilojoules) of the bean seeds was estimated by multiplying the values of protein (%), fat (%) and carbohydrate (%) by the factors 16.7, 37.7 and 16.7, respectively [21] .

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.

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 [10] [24] . In the linearized form Equation (10) becomes:

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 [10] [25] .

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 [26] . A 50-kg load cell was used for the experiment. Soaked beans were compressed axially to 75% of their original height applying a cross head speed of 1.0 mm/s and a pre-test and post-test speed of 1 mm/s [27] .

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 [24] ten (10) bean seeds were chosen to represent each treatment. For consistency, the orientations of the seeds on the analyzer platform were kept uniform.

The chemical composition of the varieties used in the study is shown in Table 1. The average protein, fat and carbohydrate contents of all samples were 25.8, 1.34 and 60.01%, respectively. The gross energy varied between 1474 and 1499 kJ/100 g. Analysis of variance of among the different chemical components shows that only the protein content was significantly different (p < 0.01) among the selected cultivars. However, a mean comparison using Tukey-Kramer HSD show protein content of Boma beans and Mandondo were not significantly different (p > 0.05). Sugar beans on the other hand were significantly higher than the other beans (p < 0.01). The protein content (24.1% - 28.7%) of the selected varieties was similar to those reported by Joshi, Adhikari [12] . They were however, higher than some common beans powders reported in the literature [28] [29] and other legumes such as chickpeas, peas [29] and lentils but lower than others like Faba beans [30] .

Figure 1 shows a plot of the hydrodynamic characteristics of the studied cultivars at different soaking times and water temperature. It can be seen from these plots that water uptake was faster in the initial stages (first 240 min.) for all temperatures. Although, it has been demonstrated by other researchers [31] [32]

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 [33] . It was evident from the results obtained that the influence of temperature was substantial. For instance, after soaking Boma beans for four hours at room temperature, only 21.8% water uptake was recorded compared to 89.2% when soaked at 35˚C. Certainly, the rate of hydration increases with rising temperature which may be attributed to the changes in resistance to gain diffusion. Several studies [32] [34] [35] have supported the argument that a significant shortening of the processing time is the result of accelerating the water absorption with higher temperature.

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.

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 Table 5 below. The magnitude of the activation energyE_a, was within the range of values typical of grains and legumes, 11.1 - 136.5 kJ/mol [22] [39] .

Changes in thermodynamic properties during common bean hydration are displayed in Figure 3. The result reveals that the enthalpy and entropy change decreased with increasing temperature, but the Gibbs free energy showed a positive correlation with temperature. Sugar beans had the maximum change in enthalpy and entropy at all the experimental temperatures and the lowest Gibbs free energy among the varieties studied. The enthalpy which is the heat dissipated by the hydration process at constant pressure is the binding energy or intermolecular force established between both the solvent and the adsorbent surface as well as the solvent and the absorbed molecules. Therefore, with the relatively high activation energy of the Sugar beans the enthalpy change shown in Figure 3(a) can be expected. This change demonstrated the measure of energy variation taking place because of water molecules and bean interaction during hydration.

Textural variations determined as the changes in bean hardness as a function of time and temperature are shown in Figure 4 and Figure 5. Three phases of

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 Figure 4(a), Sugar beans showed the least hardness of the three varieties with a maximum force of 13.5 in its dry state compared to 15.1 and 18.1 kg for Boma and Mandondo, respectively. After two hours of soaking, hardness of sugar beans reduced by 42%. This seems to corroborate the results from the

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 Figure 5 revealed that soaking above room temperature significantly impacted hardness. Although, this difference reduces markedly above 35˚C. Nonetheless, after 360 mins of soaking bean hardness is similar irrespective of the water temperature.