Kinetics of Cooking Presoaked and Unsoaked Dry Legumes: Analysis of Softening Rate of Soybeans and Red Kidney Beans

Abstract

The kinetics of hardness changes in soybeans and red kidney beans during cooking were analyzed in presoaked and unsoaked samples. Unsoaked test samples were heated to 10–99.5 °C, and changes in water absorption and hardness were measured. These rates were compared to those of control samples that had been presoaked before cooking. Based on the slope of the line from the first-order plot, softening of dry legumes to reach the optimum edible state occurred through reactions that included “softening due to water absorption” and “softening due to heating”. A two-step reaction was also involved in the “softening due to heating” of soybeans and red kidney beans after reaching hardness of 30 N, which was the lower limit of “softening due to water absorption”. Furthermore, we predicted the precise cooking time with temperature changes by determining the softening rate constants at an arbitrary temperature from the Arrhenius equation.

Introduction

Mature dry legumes with moisture content (w.b.) of approximately 10–15% are commonly soaked in water to allow water absorption before cooking or processing. In general, the main purposes of soaking are to shorten the length of the subsequent heating time and to evenly soften the bean tissue (Abu-Ghannam and McKenna, 1997; Kon, 1979). Bean tissue partially swells during soaking due to water absorption, resulting in decreased hardness (Murakami et al., 2008). The water absorption rate of beans depends on soaking temperature, with soaking at temperatures higher than room temperature facilitating water absorption (Nakamura et al., 1979). However, soaking at 50–70 °C causes hardening of vegetables, fruits, and beans (Bartolome and Hoff, 1972; Fuchigami et al., 2002; Kasai et al., 1994; Koriyama et al., 2017). We previously reported that compared to beans soaked at 20 °C, those soaked at 50 or 60 °C exhibited greater hardening during heating in boiling water (Koriyama et al., 2017). Therefore, the presoak treatment that is essential for the proper cooking of dry legumes can cause either softening or hardening in the subsequent heating process, depending on the soaking temperature.

The kinetics of water absorption and changes in hardness of beans during cooking been widely examined. Several studies evaluated only the water absorption rate in the soaking step (Kubota 1979a, 1979b) or the softening rate in the heating step after soaking (Anzaldúa-Morales et al., 1996; Quast and Da Silva, 1977). Both water absorption and heating are thought to affect the hardness of dried beans during cooking. However, no studies have clarified the continuous softening behavior from dry bean to a softness suitable for consumption by simultaneously analyzing “water absorption” and “softening” during the cooking of beans.

Here, we examined “softening due to water absorption” and “softening due to heating” during cooking by kinetics analysis. Water absorption and softening were examined simultaneously in beans that were incubated over a wide temperature range of 10–99.5 °C without presoaking (unsoaked beans). Softening rates were measured and compared to those of control samples that had been soaked and then heated, as during ordinary cooking. We used soybeans and red kidney beans, which differ in chemical composition, and evaluated the relationships between these characteristics and the softening behavior of beans.

Materials and Methods

Samples    Two types of legumes were used as sample beans. Soybeans (non-starchy; Glycine max L. Merrill, Yukihomare, Tokachi, Hokkaido) and red kidney beans (starchy; Phaseolus vulgaris L., Taishokintoki, Tokachi, Hokkaido) were purchased immediately after harvest in 2015 (Futami Seika, Kushiro City, Hokkaido, Japan). The samples were stored in sealed plastic bags in a cold chamber at 4 °C until the experiments. Broken or immature beans were removed by visual inspection before use.

Cooking conditions    Based on the general cooking method for beans of “cooking after soaking in water overnight”, both soybeans and red kidney beans were soaked in a 20-fold (w/w) volume of distilled water per bean sample at 20 °C for 8 h (presoaking). To examine the effects of cooking temperature on bean hardness, changes in bean hardness were measured in presoaked and unsoaked beans during cooking (Fig. 1). Unsoaked raw beans were heated at specified constant temperatures between 10 and 99.5 °C for 0–24 h, while presoaked beans, which is representative of the normal cooking method, were heated at specified constant temperatures between 50 and 99.5 °C for 0–3 h.

Fig. 1.

Schematic overview of the experiment.

For cooking, bean samples were placed in a beaker containing a 20-fold volume (w/w) of distilled water and were held isothermally at the specified temperature. For treatments at 10 and 20 °C, samples were cooled in an incubator (IN600, Yamato, Santa Clara, CA, USA); for treatments at 30–90 °C, samples were held in a thermostatic water bath (Isotemp model 228, Fisher Scientific, Waltham, MA, USA); and for treatments at 99.5 °C, the sample was heated on an electric cooking stove (HP634, HP635, Toshiba, Tokyo, Japan). Temperature was controlled within ±1 °C of the specified temperature over the experimental period.

Water absorption percentages    Beans were weighed on an electric balance before and after soaking, and the water absorption ratio (W) was determined using the following equation:   

where W₀ and W₁ denote the initial bean weight (g) and bean weight after soaking (g) at the specified temperature/time, respectively. Five to ten beans were used for each measurement, and the experiment was repeated three times.

Changes in hardness    To determine the softening rate of beans during cooking, changes in hardness were measured. A texture analyzer (TA.XT. Plus; Stable Micro Systems, Ltd., Surrey, UK) was used for the measurement, and the maximum load value was regarded as hardness (Szczesniak et al., 1963). Measurement conditions were as follows: load cell, 30 kg; probe, φ 3 mm cylindrical shape; probe speed, 1 mm/s; and compression ratio, 80%. Five to ten beans were used for hardness measurement in each experiment, and the results were averaged. The experiment was repeated three times.

Kinetic analysis    To determine the softening rate at each temperature, we defined the softening ratio x (Kasai and Shimada, 1985) as a dimensionless value for changes in hardness as follows:   

where y₀, y_e, and y represent the initial hardness, equilibrium hardness, and hardness (N) at time t, respectively. The equilibrium hardness value is the value at which hardness can be regarded as essentially constant over 10–20 min while heating at 99.5 °C. Based on experimentally determined values, 1.5 and 1.0 N were the equilibrium hardness values for soybeans and red kidney beans, respectively.

Assuming approximation to a first-order velocity equation, the rate of softening percentage (x) defined by equation 2 can be expressed as   

At t = 0, x = 0, equation 3 can be modified to yield   

where k is the rate constant for softening (min⁻¹) and t is the soaking time (min).

The temperature dependencies of the water absorption rate and softening rate were determined using the Arrhenius equation (equation 5) after first obtaining k at each temperature from the slope of the linear regression fit to the first-order reaction plots and then plotting the logarithmic values of the rate constants against the reciprocal values of temperature:   

where A is the frequency factor (min⁻¹), E is the apparent activation energy (J/mol), R is the gas constant (8.314 J/mol·K), and T is the absolute temperature (K). E and A were calculated over the temperature range in which data were concordant with the Arrhenius equation.

Results and Discussion

Effect of temperature on water absorption rate    We first measured changes over time in the water absorption at 10–99.5 °C for beans soaked at a constant temperature to determine the relationship between water absorption percentage and temperature (Fig. 2). In soybeans, the water absorption percentage sharply increased during the initial stage of soaking, while subsequent change was slower. In red kidney beans, an initial rapid increase in the water absorption percentage was followed by slower changes at ≥30 °C, while water absorption in the initial phase was slightly delayed at 10 °C and 20 °C. For both beans, temperature-dependent differences were clear in the range of 10–50 °C; water absorption was more accelerated as temperature increased. However, temperature-dependent differences were smaller at ≥60 °C, presumably because tissue changes precede water absorption when dried beans are rapidly heated above a certain temperature.

Fig. 2.

Changes in water absorption rate of soybeans and red kidney beans during incubation at constant temperatures between 10 °C to 99.5 °C.

Changes in hardness during cooking without presoaking    Time-dependent changes in hardness of beans without presoaking were measured during incubation at 10–99.5 °C. When dry legumes are directly heated without presoaking as in this experiment, softening due to water absorption and softening due to heating likely occur simultaneously in a temperature-dependent manner. The results are shown separately for 10–50 °C in Fig. 3A and 60–99.5 °C in Fig. 3B.

Fig. 3.

Changes in hardness of soybeans and red kidney beans during incubation at constant temperatures between 10 °C to 99.5 °C. Sample beans were directly treated (un-soaked). [A]: 10–50 °C, [B]: 60–99.5 °C.

At all temperatures tested, both soybeans and red kidney beans rapidly softened after starting the soak. As shown in Fig. 3A for the low temperature range of 10–50 °C, minimal changes in hardness were observed for both bean types after reaching about 30 N, even when the soaking treatment was continued. Compared to the water absorption percentages shown in Fig. 2, the duration required for the hardness to reach an apparent equilibrium was shorter than for water absorption at all temperatures in the range of 10–50 °C. At 20 °C, for example, the time required for hardness to reach an apparent equilibrium was 4 h for soybeans and 8 h for red kidney beans, while water absorption percentage required 8 h and more than 16 h for soybeans and red kidney beans, respectively. These results indicate that beans continue to absorb water even after hardness reaches equilibrium and there is a limit to the softening due to water absorption.

In general, softening during the cooking process is referred to as “softening due to heating,” which is accompanied by β-elimination of pectin and other reactions. However, beans with low water content also soften through water absorption. Softening due to water absorption is thought to induce swelling of tissue, reducing the compression resistance when load is applied to beans compared to before soaking. Because β-elimination of pectin by heat hardly occurs at ≤50 °C (Albersheim et al., 1960), softening observed during soaking at 10–50 °C represents “softening due to water absorption”. Additionally, beans softened to approximately 30 N through water absorption, while the hardness levels before soaking were ≥100 and ≥200 N for soybeans and red kidney beans, respectively. Because an appropriate level of hardness for cooked beans is approximately 3 N (Murakami et al., 2008), the extent of “softening due to water absorption alone” relative to the hardness of beans before soaking appears to be sufficiently large to achieve an appropriate level of hardness by subsequent heating treatment. Furthermore, the apparently equilibrated hardness at 30 N suggests that dried beans have a lower limit of “softening due to water absorption”, which is constant (around 30 N) regardless of the type of bean, such as starchy versus non-starchy beans.

At ≥60 °C for soybeans and red kidney beans (Fig. 3B), there was almost no difference in the softening tendency at different temperatures from the start of incubation until the hardness reached approximately 30 N. At 60 and 70 °C, the softening curve increased slightly at around 30 N, after which it remained substantially flat. At higher temperatures of 80–99.5 °C, the beans softened as the temperature increased after reaching 30 N. In this experiment, a rapid change in hardness to approximately 30 N in the first half of the experiment was observed for both beans. The hardness of 30 N is the lower limit of “softening due to water absorption” shown in Fig. 3A. Therefore, even when soybeans and red kidney beans are incubated at ≥60 °C without presoaking, “softening due to water absorption” predominantly occurred irrespective of temperature until reaching about 30 N, and “hardening/softening due to heating” occurs after reaching 30 N. This is supported by the fact that the temperature effects were greater in softening in the latter half of the heating when the hardness was ≤30 N.

Changes in hardness of pre-soaked beans during cooking    For comparison, beans after presoaking were incubated at constant temperature between 50 and 99.5 °C, and changes in hardness over time were measured. As shown in Fig. 4, both types of beans had hardness before incubation of approximately 30 N, which is the level at which “softening due to water absorption” reaches equilibrium during the presoaking step.

Fig. 4.

Changes in hardness of soybeans and red kidney beans during cooking at constant temperatures between 50 °C and 99.5 °C. Sample beans were treated after presoaking at 20 °C for 8 h.

Soybeans incubated at 50 and 60 °C and red kidney beans incubated at 60 and 70 °C transiently became harder after heating. Particularly, soybeans showed marked hardening at 50 °C and clearer differences among the temperatures than red kidney beans. In contrast, red kidney beans showed minimal changes in hardness at 50 °C. These results agree with those of a previous report (Koriyama et al., 2017) showing that soybeans and red kidney beans most readily harden at 50 and 60 °C, respectively. In addition, beans without presoaking hardened after reaching 30 N, whereas beans with presoaking hardened immediately after starting the heating treatment. This indicates that hardening of dry beans occurs after water content reaches a certain level. At ≥80 °C, both types of beans softened more rapidly as temperature was increased.

Proposed model for softening of dry legumes during cooking    The results described thus far show that softening of dry legumes during cooking occurs in steps; in the shift from the state of dried beans to a level of hardness near 30 N, water immersion has a great impact, and “softening due to water absorption” is considered to occur preferentially. After reaching 30 N, the impact of heating increases and “hardening/softening due to heating” is considered to occur preferentially. This “softening due to heating” mainly involves β-elimination of pectin, which is considered to occur during soaking or at a certain water content level. Thus, we propose a model for softening that occurs in the shift from the state of dried beans to the optimum edible state.

As shown in Fig. 5, “softening due to water absorption” and “softening due to heating” occur in steps during the softening of dry beans to the optimum edible state. The model shows that “softening due to water absorption” and “softening due to heating” also occur in steps when water absorption and heating are simultaneously performed at 99.5 °C without presoaking. For H₀ as the state of dried beans, H_e as the hardness in the optimum edible state, and H_w as the lower limit of “softening due to water absorption”, H₀ was approximately 115 N for soybeans and 205 N for red kidney beans and He and Hw for both beans were 3 and 30 N, respectively. Thus, we determined the rate constant of softening for each process.

Fig. 5.

Softening model during soaking and cooking of dry legumes.

H₀: Initial hardness of beans in raw state

H_w: Lower limit of softening by water absorption

H_e: Optimum edible state

Softening rate    We conducted kinetic analysis of the softening behavior of dry legumes incubated at 10–99.5 °C without presoaking, and we used the first-order rate equation to quantitatively evaluate “softening due to water absorption” and “softening due to heating”. The rates of change in x were obtained from the measured values of hardness, and the logarithmic values were plotted against heating time as first-order kinetics.

As shown in Fig. 6, the rate of “softening due to water absorption”, linear relationships were obtained in the 10–50 °C range in the first-order plots for both soybeans and red kidney beans. As shown in Fig. 7, even at 60 °C or higher, where both “softening due to water absorption” and “softening due to heating” are considered to occur, the first-order plots were regarded as nearly straight lines up to approximately 30 N. For incubation at ≥80 °C (Fig. 7), the first-order plots for both beans were not represented by straight lines, but rather by curves comprising two or three straight lines. In these first-order plots, the slope of the straight line changed at approximately 30 N, as shown by the dotted line, reflecting the lower limit of softening due to water absorption at all temperatures. The straight line of “softening due to heating” after reaching 30 N at all temperatures in both beans changed in the shaded portion, and hardness at this point was approximately 10 N. Therefore, when soybeans and red kidney beans were incubated at ≥80 °Cwithout presoaking, “softening due to water absorption” was predominant until approximately 30 N, regardless of temperature. Once “softening due to water absorption” was complete, softening due to the effect of temperature predominated, which was likely accompanied by “hardening due to heating”.

Fig. 6.

First-order plot of the rate of “softening due to water absorption” in soybean and red kidney beans incubated at 10–50 °C.

Sample beans were directly treated (un-soaked). x: softening ratio.

Fig. 7.

First-order plot of the rate of “softening due to water absorption” and “softening due to heating” in the un-soaked soybean and red kidney beans incubated at 60–99.5 °C. Sample beans were directly treated (un-soaked). x: softening ratio.

Therefore, softening kinetic data of beans heated at 80–99.5 °C after presoaking, which represents “softening due to heating”, was plotted as first-order kinetics for comparison. As shown in Fig. 8, the slope of the line of the softening rate of “softening due to heating” of both bean types changed in the shaded portion in the figures, corresponding to hardness of approximately 10 N, as in the case of heating without presoaking (Fig. 7). Previous reports showed that softening of presoaked soybeans during heating consists of two first-order kinetics with different mechanisms; the first half is a change in pectin, while the second half is changes in materials other than pectin (Gandhi and Bourne, 1991; Huang and Bourne, 1983). Based on these findings, a two-step reaction is likely involved in “softening due to heating” of soybeans and red kidney beans after reaching a certain water content until adequate hardness is achieved.

Fig. 8.

First-order plot of the rate of “softening due to heating” in the presoaked soybean and red kidney beans incubated at 80–99.5 °C.

All sample beans were treated after presoaking at 20 °C for 8 h. x: softening ratio.

Based on these results, softening during the cooking of dry legumes was shown to involve stepwise changes. Specifically, during the shift from the state of dry beans to a level of softness near 30 N, the presence of water had a major impact, and “softening due to water absorption” occurred as the preferential reaction. After reaching 30 N, the impact of heating increased, and “hardening/softening due to heating” occurred preferentially. This “softening due to heating” mainly involves β-elimination of pectin, which is considered to occur during soaking at ≥80 °C or at a certain water content level. Therefore, the trend to 30 N was defined as k_w, which is the rate constant of “softening due to water absorption”; for the rate constant of “softening due to heating”, the slope in the first half from 30 N to approximately 10 N was set as k_s1, while the latter half from 10 to 3 N was set as k_s2.

Temperature dependence of softening rates    To clarify the relationship with temperature, the rate constants for softening were obtained from the slope of each straight line in Figs. 6–8, and the logarithmic values were plotted against the reciprocals of the temperature to construct an Arrhenius plot.

As shown in Fig. 9, the rate constant, k_w, describes “softening due to water absorption” and shows a good fit with the Arrhenius equation in the temperature range of 10–60 °C for both soybeans and red kidney beans; however, the temperature-dependence was smaller above 60 °C. For both types of beans, changes in the rate constant for “softening due to water absorption” were smaller at ≥60 °C, which is presumably because changes such as heat denaturation of proteins and gelatinization of starch occurred in dried beans heated at ≥60 °Cfrom the first half of the softening period, and these changes were the rate-limiting steps of “softening due to water absorption”. This finding is supported by differential scanning calorimetry results obtained in a previous study showing endothermic peaks at 71 and 92 °C for soybeans and 75 and 85 °C for red kidney beans (Koriyama et al., 2017).

Fig. 9.

Arrhenius plot of the softening rate constant k_w for soybeans and red kidney beans temperature at 10–99.5 °C.

k_w (min⁻¹) means the rate constant of “softening by water absorption”.

As shown in Fig. 10, the rate constant, k_s1, describes “softening due to heating” and shows a good fit with the Arrhenius equation in the temperature range of 80–99.5 °C for both soybeans and red kidney beans with or without presoaking. For both types of beans, the slope of the Arrhenius plot with presoaking was steeper than that without presoaking. Additionally, the k_s1 value with presoaking was larger than that without presoaking at ≥80 °C. These findings indicate that for both soybeans and red kidney beans, the softening rate upon boiling is greater when heating is carried out after presoaking compared to that without presoaking, providing quantitative support for the effectiveness of soaking in the typical cooking process.

Fig. 10.

Arrhenius plot of softening rate constant k_s1 for soybeans and red kidney beans temperature at 80–99.5 °C.

k_s1 (min⁻¹) means the rate constant of “softening due to heating.”

▴: Softening rate constant of un-soaked beans after reaching 30 N softness.

△: Softening rate constant of beans after pre-soaking.

From the slope of the line of each Arrhenius plot, the apparent activation energy E and frequency factor A of k_w, k_s1, and k_s2 were calculated. As shown in Table 1, the apparent activation energy E of k_s1 of presoaked soybeans was 1.6-fold higher than that of unsoaked soybeans. For red kidney beans, this value was 1.8-fold higher. Thus, when cooking soybeans or red kidney beans at a high temperature, softening by heating after presoaking is easier than when heating without presoaking. In general, “softening of vegetable due to heating” is caused by β-elimination of pectin and elution of the degradation of pectin (Fuchigami, 1983). Albersherm (1960) reported that 6.3% of the glycosidic bounds in pectin solution were cleaved when heated at 95 °C, and 1.6% were cleaved when heated at 80 °C. This suggests that the change in pectin is temperature-dependent and occurs in the state of pectin solution. In this study, the distribution of water in the beans without presoaking was uneven during cooking compared to that in presoaked beans. This can be inferred from the results shown in Fig. 2 in which the water absorption percentage of the presoaked beans before heating reached an equilibrium value (soybean: 120%, red kidney beans: 95%), whereas that of unsoaked beans was 50%–60% when the hardness reached approximately 30 N. Thus, β-elimination of pectin is more likely to occur when the water content of beans is sufficient, indicating that the temperature dependence is larger compared to in the insufficient case.

Table 1. Apparent activation energy (E) and frequency factor (A) on un-soaked and presoaked samples.

		Soybean			Red kidney bean
		Temperature range (°C)	E (kJ/mol)	A (min−1)	Temperature range (°C)	E (kJ/mol)	A (min−1)
Un-soaked	kw	10–60	37	4.7×104	10–60	51	1.6×107
		60–99.5	11	2.6	60–99.5	10	2.2
	ks1	80–99.5	76	1.4×109	80–99.5	90	2.1×1011
	ks2		147	6.7×1018		105	1.5×1013
Presoaked	ks1	80–99.5	122	9.8×1015	80–99.5	163	8.8×1021
	ks2		101	3.7×1012		236	1.7×1032

Un-soaked samples were directly treated without soaking treatment.

Presoaked samples were treated after soaking at 20 °C for 8 h.

k_w: rate constant of “softening by water absorption.”

k_s1, k_s2: rate constant of “softening by cooking.”

Furthermore, we found that the degree of presoaking had a larger effect on red kidney beans than on soybeans. In starchy beans, water absorption during presoaking made it easier for starch to swell and gelatinize, which may contribute to softening. These findings indicate that the effect of presoaking treatment in normal cooking is reflected in the rate constant of softening.

Predicted and measured lengths of cooking time    Finally, we predicted the change in hardness of soybeans and red kidney beans as the temperature changed by calculating the apparent activation energy E and frequency factor A as shown in Table 1. Cooking conditions involved heating from 20 to 99.5 °C, followed by continued boiling.

First, the water temperature change was measured and the rate constants of “softening by water absorption” and “softening by heating” corresponding to each temperature change were calculated. Next, the changes in the softening ratio were obtained from Eq. 6. The softening ratio x is expressed by the following equation, which is derived from equation Eq. 3.

  

The kt value in Eq. 6 corresponds to the area under the k-t curve, which can be obtained by graphic integration using the trapezoidal formula (Kasai et al., 1985). Next, the softening curve can be obtained by converting hardness values from the softening ratio determined by the above equation above.

To compare the predicted value with the measured value, as in another experiment, the unsoaked beans were heated from 20 to 99.5 °C and boiling was continued until they reached the optimal edible hardness of 3 N. Subsamples of beans were removed at specified time points for hardness measurement. The predicted and measured values showed very good agreement for both soybeans and red kidney beans (Fig. 11). The time to reach 3 N obtained from the calculated values was 138 min for soybeans and 87 min for red kidney beans. These results demonstrate that the cooking time with temperature changes can be predicted by separately analyzing “softening due to water absorption” and “softening due to heating”.

Fig. 11.

Comparison between predicted and measured values of hardness during cooking with temperature changes.

Conclusions

When incubating soybeans and red kidney beans at 10–99.5 °C without presoaking, the softening process was found to be approximately divided into “softening due to water absorption” and “hardening/softening due to heating”, each of which occurred as a stepwise reaction. “Softening due to water absorption” showed a lower limit of approximately 30 N regardless of temperature. “Hardening/softening due to heating” was suggested to follow “softening due to water absorption”, as hardening due to heating occurred after a certain level of water content had been reached. Furthermore, we accurately predicted the cooking time required for dried beans to reach the optimum edible state by determining the rate constants over a wide temperature range and approximating the complex changes in hardness of beans during cooking using the first-order rate equation.

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