Notes
A method for estimating the equilibrium moisture content of spaghetti at any temperature by using the change in moisture content during non-isothermal cooking
2024 Volume 30 Issue 1 Pages 57-62
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2024 Volume 30 Issue 1 Pages 57-62
A novel method is proposed to estimate the equilibrium moisture content Xe at a specific temperature using the change over time in moisture content during cooking of spaghetti at different rates of temperature increase. In this method, the moisture content XvT→0 at infinitely slow heating is the equilibrium moisture content Xe at that temperature, based on the relationship between the average rate of temperature increase vt in reaching a certain temperature and the moisture content X. Xe estimated by the proposed method was almost consistent with the equilibrium moisture content estimated from the change in moisture content over time at a constant temperature, and the validity of the proposed method was verified.
The Italian word for dough (i.e., pasta) is generally used for Italian-style extruded foods such as spaghetti and lasagna. Pasta is a healthy food because it is relatively low in fat, high in carbohydrates, and rich in protein. The main ingredients of pasta are semolina, which is coarsely ground from durum wheat (Triticum durum), the hardest wheat, and water; it is a porous food composed primarily of starch and protein. Durum semolina is the ideal flour for pasta because of its hardness, strong yellow color, and nutty flavor (Wrigley et al., 2004).
Drying is one of the most effective ways to improve the shelf life of foods by reducing quality deterioration and microbial spoilage. Dried foods are usually rehydrated to improve taste and digestibility before use or consumption. Pasta is also usually distributed in a dried state for storage stability and transportation efficiency. Dried pasta is rehydrated by cooking before being consumed, but the mechanism of water transfer into the pores of dried pasta is a complex process (Saguy et al., 2005; Ogawa and Adachi, 2017).
There are many types of pasta made from durum semolina, among which long and cylindrical pasta is called spaghetti. Spaghetti is usually distributed in a dried state and is rehydrated or cooked before eating. Spaghetti is said to be most delicious when it has a core that is about the size of a hair in the center and is chewy (this state is called al dente). Although spaghetti is not cooked to its equilibrium moisture content Xe for the purpose of eating, Xe is one of the most important parameters in considering the rehydration process of dried spaghetti. The Xe at a given temperature is obtained by measuring the change in moisture content over time, describing it as a function of time using empirical and theoretical equations (García-Pascual et al., 2006), and estimating the value at a sufficiently long time. These functional equations include the exponential equation (Misra and Brooker, 1980), Peleg's model (Peleg, 1988), first-order kinetics (Chhinnan, 1984; Krokida and Philippopoulos, 2005), and the Weibull distribution function (Cunha et al., 1998). We estimated Xe by expressing the relationship between moisture content X at any given time t as a hyperbolic equation (Ogawa et al., 2011).
We hypothesized that the equilibrium moisture content at a given temperature could be estimated by obtaining the relationship between the average rate of temperature increase until a certain temperature is reached and the moisture content at that time by using the change over time in the moisture content when the temperature is increased at different rates. This relationship is then extrapolated to the case where the temperature is increased infinitely slowly, that is, where the rate of temperature increase is zero. In this study, the feasibility and validity of this method were examined.
Materials The spaghetti used was 1.6 mm diameter (recommended cooking time: 7 min) and was made by Nisshin Seifun Welna Inc. (Tokyo, Japan). Spaghetti was cut into approximately 4 cm lengths and used to measure the change over time in the moisture content.
Changes in temperature and moisture content during non-isothermal cooking A cylindrical stainless-steel vessel (outer diameter 122.8 mm, inner diameter 120.3 mm, height 120.2 mm) containing 1 L of distilled water (milli-Q water) was covered and heated by a mantle heater (P-102, Tokyo Garasu Kikai, Tokyo, Japan). The rate of increase in water temperature was adjusted by regulating the voltage applied to the mantle heater from 35 to 100 V using a power transformer (S-130-15, Yamabishi Denki, Tokushima, Japan). The mantle heater was wrapped with four layers of towels or cloth rags to reduce heat loss. A disk-shaped plastic plate was placed above the water surface in the cylindrical vessel at a distance from the water surface, and three cloth rags were placed above the plate to suppress heat loss from the top. The water in the cylindrical vessel was gently stirred by rotating a stirrer (length 40.8 mm, diameter 7.8 mm) at approximately 140 rpm using a magnetic stirrer (Magic Stirrer, M&S Instruments Inc., Osaka, Japan). A K-type thermocouple was fixed near the inner surface of the cylindrical vessel, and a digital thermometer (AD-5605H, A&D Corp., Tokyo, Japan) was used to measure the temperature.
To measure the rehydration behavior when heated at various voltages, more than 33 pieces of spaghetti samples were used. The initial water temperature was kept below 25 °C. Heating was started, and all spaghetti samples were put into the vessel when the water temperature reached 25 °C. The cooking time at this moment was set to be 0 min.
The time t was recorded each time the water temperature increased by 5 °C. Six rehydrated samples (spaghetti) were removed using a wire-mesh remover, and the surface water was lightly wiped off with a Kim towel and Kim wipes. Each of two samples was placed on a heat-resistant sheet (As One, Osaka, Japan) with an identification number and weighed (tare) using an electronic balance (TX423N, Shimadzu, Kyoto, Japan), and the weight of the tare was subtracted from this weight to obtain the weight of the rehydrated sample mw. The samples were dried in a dryer (DO-300FA, As One) at 130 °C for about 2 h and then weighed again, and the weight of the tare was subtracted to obtain the dry weight md. From these weights, the dry weight-based moisture content X at the rehydration time t was calculated by Eq. (1).
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Due to heat loss, the water temperature increased only up to 60°C when the voltage was 35 V. Similarly, the water temperature rose to 65 °C at 40 V, 70 °C at 45 V and 50 V, 75 °C at 55 V, 80 °C at 60 V and 65 V, and 85 °C at 70 V. At voltages above 75 V (75, 80, 85, 90, and 100 V), the water temperature rose to 90 °C.
Change over time in moisture content at a constant temperature A temperature controller (TXN-700, As One) was connected between the 100-V AC power supply and the transformer. As mentioned above, the water temperature in the cylindrical stainless-steel vessel was measured with a K-type thermocouple connected to the temperature controller, and the water temperature was adjusted to a constant value between 30 and 70 °C. Although a transformer was not necessarily required, the temperature was controlled ON-OFF, and the voltage applied to the mantle heater was adjusted while monitoring the temperature change to avoid overheating when the temperature was turned ON. When the water temperature reached a predetermined level, more than 39 pieces of spaghetti samples were placed into the vessel to begin rehydration. It is known that the moisture content of spaghetti X increases rapidly at the beginning of rehydration due to the penetration of water into minute cracks (Yoshino et al., 2013). Therefore, samples were taken out at 1-min intervals up to 5 min at the beginning of rehydration, and at 10, 15, 20, 30, 45, 60, 90, 120, 150, 180, 210, and 240 min thereafter, and dried at 130 °C for 2 h for three sets of two pieces each. As described above, the moisture content based on dry weight X was calculated by Eq. 1.
Water in a pot was heated to boiling point (100 °C) using an induction heater (KZ-PH33, Panasonic, Tokyo, Japan), and spaghetti samples were placed in the pot. The maximum cooking time was 180 min to allow for errors due to cooking loss.
Changes in temperature and moisture content during non-isothermal cooking Fig. 1(A) and (B) show examples of changes over time in water temperature and moisture content of spaghetti, respectively, when heated at various voltages. We proposed a method for estimating the gelatinization temperature of starch in noodles from the intersection of two curves (a straight line for the low-temperature region and a curve for the high-temperature region) connecting points of the moisture content against the water temperature (Hasegawa et al., 2012). The gelatinization temperature obtained by this method was given as a value between the onset and peak temperatures for gelatinization in differential scanning calorimetry (DSC) (Hasegawa et al., 2012).
Changes in (A) water temperature and (B) the moisture content of rehydrated spaghetti, X, during cooking at different voltages. The applied voltages were (a, △) 40, (b, ▲) 45, (c, O) 55, (d, ●) 60, (e, ◊) 70, (f, ◆) 80, (g, □) 90, and (h, ■) 100 V. The curves in (B) were drawn empirically.
The moisture content was plotted against temperature, and a straight line and a smooth curve were drawn for the low-and high-temperature regions using straight-edge and French rulers, respectively. The temperature at the intersection Tis was determined. The Tis was independent of the applied voltage and was 57.23 ± 0.82 °C (mean ± S.D.), except when the applied voltage was 35 or 40 V and the heating rate was extremely slow. When the water temperature was increased linearly with respect to time, the rate of temperature increase had no effect on Tis (Hasegawa et al., 2012). In the present study, the water temperature increased exponentially with time, but as before, the applied voltage (rate of temperature increase) had no effect on Tis. The Tis values obtained in this study were also in the middle of the onset and peak temperatures in DSC.
Estimation of equilibrium moisture content at any temperature The average rate of temperature increase, vT, was defined by Eq. (2) from the time tT taken for the water temperature to reach the predetermined temperature, T, from 25 °C.
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Fig. 2(A) shows examples of the relationship between the average rate of temperature increase, vT, and the moisture content, X. In Fig. 2(A), X increased rapidly as vT decreased, and it was difficult to determine the moisture content at vT→0 (moisture content when cooked infinitely slowly) by extrapolation of the plots. Therefore, we plotted the reciprocal of X (1/X) against vT and attempted to obtain the moisture content
at each temperature from 1/X when extrapolated to vT→0 [Fig. 2(B)]. Because arbitrariness could not be eliminated when
was estimated by connecting the plots with a French ruler,
was estimated using Eq. (3), which was the most appropriate among several tested functions to correlate 1/X and vT.
Relationships (A) between the moisture content, X, and the average rate of temperature increase, vT; and (B) between the reciprocal of X, 1/X, and vt for estimating the equilibrium moisture contents at (△) 40, (▲) 45, (○) 50, (●) 55, (◊) 60, (◆) 65, (□) 70, and (■) 80°C using the moisture contents measured during cooking at different voltages. The curves in (B) were drawn based on Eq. (3).
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where a and b are constants. The values of a, b, and Xe were estimated to minimize the sum of the residual squares of 1/X based on the measured values and 1/X calculated by Eq. (3) using the Solver function of Microsoft® Excel (Redmond, WA, USA). The curves in the figure were drawn using the estimated a, b, and Xe values.
Change over time in moisture content at a constant temperature To verify the validity of Xe estimated above, changes in the moisture content over time during isothermal rehydration at various temperatures were measured. Some examples are shown in Fig. 3. As mentioned above, many equations have been proposed to express the change over time in the moisture content at a constant temperature. In this study, the hyperbolic form of Eq. (4) was first applied (Ogawa et al., 2011).
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where α and β are constants. In addition, as mentioned above, water penetrates into cracks near the spaghetti surface immediately after the start of rehydration, resulting in a rapid increase in the moisture content (Yoshino et al., 2013). Therefore, using the polynomial approximation of Microsoft® Excel, the relationship between the moisture content X and the time t from 1 to 10 min was expressed as a quadratic equation, and the initial moisture content estimated by extrapolation to t → 0 was expressed as X0′. Furthermore, α and β were estimated using the Solver function of Microsoft® Excel in order to minimize the sum of the residual squares of the measured values of X at all cooking times t and the values calculated using Eq. (4). The solid curves in Fig. 3 were drawn using the estimated α, β, and X0′ values. The equilibrium moisture content Xe is given by Eq. (5).
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On the other hand, the rehydration rate of pasta (Krokida and Philippopous, 2005) and starch noodles (Adachi et al., 2021) has also been reported to be proportional to the difference between the equilibrium moisture content Xe and the moisture content X at an arbitrary time t, as expressed by Eq. (6).
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where k is the rate constant. By solving Eq. (6) under the initial condition of Eq. (7), we can obtain Eq. (8).
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Similar to the above, the parameters Xe and k were estimated using the Solver function of Microsoft® Excel in order to minimize the sum of residual squares between the measured value of X and the value calculated by Eq. (8). The broken curves in Fig. 3 were drawn using the Xe and k values estimated in this way.
Verification of the validity of the proposed method The temperature dependence of equilibrium moisture content is generally expressed by the van't Hoff equation (Eq. (9)).
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where ΔH is the change in the enthalpy of rehydration, T is the absolute temperature, and R is the gas constant. Fig. 4 shows the van't Hoff plots for the Xe values estimated by the three different methods. The Xe estimated by the linear driving force approximation [Eq. (8)] was somewhat smaller than the Xe values estimated by the other two methods in the high-temperature region. Although the effect of cooking loss became significant in the high-temperature region, no consideration of the effect could explain the difference in values obtained by the three methods. The ΔH estimated from Xe in the high-temperature region by the proposed method was 39.0 kJ/mol, which was a little larger than the ΔH value (25.1 kJ/mol), which was estimated from the Xe values at constant temperatures (Ogawa et al., 2011).
van't Hoff plots for the equilibrium moisture contents, Xe, estimated by (□) Eq. (4), (△) Eq. (8), and (○) the proposed method at various temperatures. The solid lines were drawn for Xe in the high- and low-temperature regions, and the broken line represents the temperature range where the gelatinization of starch occurred for the Xe estimated by the proposed method.
On the other hand, the Xe estimated by the proposed method was somewhat smaller than the Xe values estimated by the other two methods in the low-temperature region. Because the moisture content was small at low temperatures, errors are likely to have occurred. The ΔH estimated from the Xe values in the low-temperature region by the proposed method was 24.9 kJ/mol. The value was much larger than the ΔH value (1.44 kJ/mol) estimated from the Xe values at constant temperatures (Ogawa et al., 2011). Possible reasons why the values of ΔH in both the high- and low-temperature regions were different from those previously reported would be the difference in the durum flour used as the raw material, the difference in the spaghetti manufacturing conditions, and the difference in the method to estimate the Xe value. However, the Xe values obtained by the proposed method and the ΔH values estimated from the Xe values would be within a reasonable range in the high-temperature region. On the other hand, the large difference in ΔH values among the methods would be ascribed to difficulty in estimating precise Xe values because the moisture content was smaller in the temperature region lower than the gelatinization temperature of starch.
The discontinuity in plots of Xe to 1/T between high- and low-temperature regions is caused by starch gelatinization. The plots for Xe became discontinuous at around 57 °C for all three methods, which was between the onset and peak temperatures in DSC and reasonably reflected the gelatinization temperature of starch of the durum semolina. This fact would represent the validity of the proposed method for estimating the Xe value, especially in the temperature region higher than the gelatinization temperature of starch.
A method to estimate the equilibrium moisture content at any temperature by extrapolating the relationship between the average rate of temperature increase to a specific temperature and the moisture content at that temperature to the average rate of temperature increase to zero, that is, when heated infinitely slowly. The Xe estimated by the proposed method almost agreed with the equilibrium moisture content estimated from the change over time in the moisture content at a constant temperature in the temperature region higher than the gelatinization temperature of starch. Therefore, the equilibrium moisture content at any temperature, especially in the temperature region higher than the gelatinization temperature of starch, can be estimated by the proposed method.
Acknowledgements We thank Mr. Kohsaka for his technical assistance.
Conflict of interest There are no conflicts of interest to declare.
