The use of the orthogonal collocation method on the study of the drying kinetics of soybean seeds

The purpose of this paper is to present numerical solutions of a diffusion model by the orthogonal collocation method applied to soybean seeds when drying, when the effective diffusivity is moisture content dependent. The model used takes into account both internal and external mass transfer resistances. The simulated results were compared with experimental data of soybean drying in a thin layer. The results showed that the convective mass transfer resistance was negligible, for the experimental conditions. That being so, the hypothesis that the moisture at the solid surface instantly attains the equilibrium moisture of the grain is adequate for this case. A functional dependency of the effective diffusivity with the solid's moisture and with temperature was determined in this work.     

重量法研究大豆水分吸附速率和有效扩散系数

在5种温度（10³5℃）、3个湿度（RH 65%、86%及100%）组合环境中,以称重法测定了初始低水分（4.33%⁵.85%）、正常水分（11.74%¹2.65%）、高水分（17.58%¹7.89%）两个大豆品种\     

Moving Boundary Model For Simulating Moisture Movement In Grapes

A diffusional model for simulating grape dehydration with simultaneous shrinkage was developed using a finite difference method to solve differential equations for moisture transfer within a sphere. Volume decrease was assumed to be equivalent to the volume of moisture removed. An effective diffusivity coefficient was developed from drying data at air temperatures between 30 and 90°C and constant air velocity. Effective diffusivity varied with drying air temperature following the Arrhenius equation. Experimental data at two different diffusional periods in drying were adequately represented by this moving boundary diffusivity model. Drying kinetics at temperatures different from those used to develop the model and different grape sizes could be predicted.     

Application of effective diffusivity approach for the moisture content prediction of tortilla chips during baking

Fick's law of diffusion and an empirical model were used to describe moisture transport in tortilla chips during baking. An empirical model based on regression of moisture content in terms of baking time and temperature slightly over predicted the moisture content of samples. There was a good agreement (R²=0.93) between experimental results and predicted values with the empirical model. The model based on effective diffusivity approach also predicted the moisture content fairly good. Both liquid and vapor diffusion was effective in the transport of vapor. Liquid diffusion and vapor diffusion were dominant in the beginning and toward to end of baking, respectively. The average moisture diffusivity of samples was calculated using a nonlinear regression of moisture content data during baking. The range for the average effective diffusivity was 6.25×10⁻¹⁰-10.98×10⁻¹⁰ m²/s and the diffusivity coefficient increased with increasing temperature. There was an Arrhenius type relationship between effective diffusivity coefficient and baking temperature.     

Hot air drying of whole fruit Chinese jujube (Zizyphus jujuba Miller): thin-layer mathematical modelling

Chinese jujube fruits were dried at 50, 60 and 70 °C in an electric heat blast dryer. Verma model was superior to the others for explaining change of moisture ratio in Chinese jujube by comparing thirteen commonly used mathematical models, suggested by the lowest percent error (1.211%). A strong linear dependence between drying rate and drying time was suggested by high values of determination coefficient ( R ² > 0.97). Linear model (effective diffusivity model) was found to be excellent adequacy in describing relationship between effective diffusivity, D _eff, and dry-basis moisture content, M . The effects of drying air temperature on the coefficients of the model were determined by multiple regression method. Lower percent error (3.44%) proved that the effective diffusivity model has higher precision. Our study indicated that it is possible to describe moisture content, drying rate, effective diffusivity, with the models including the effect of drying air temperature on the model constants and coefficients.     

PREDICTING DRYING BEHAVIOR OF SPAGHETTI IN A CONTINUOUS INDUSTRIAL DRYER WITH THE MODELS DETERMINED IN A LAB SCALE BATCH SYSTEM

In the first stage of this study experimental data were obtained by using a lab scale batch type dryer, operating under various constant temperature/constant relative humidity combinations; then a mathematical model was determined for the effective diffusivity of moisture in spaghetti. In the second stage of the study the model obtained in the lab scale batch type dryer was used to calculate the moisture content of the spaghetti leaving continuous industrial scale dryer, and its success was tested by comparing with the experimentally determined moisture content of the product. The model was not found successful and corrected. Mathematical models based on experimental data obtained in a bench-top laboratory dryer underestimated the apparent equilibrium moisture content and over estimated the effective diffusivity of water in spaghetti in industrial scale continuous drying equipment. The structural differences in the product, extrapolation of the data beyond the range of the original experiments, variations in mode (batch versus continuous), surface-to-volume ratios, flow patterns, and geometry associated with each drying system were anticipated as the cause of the scale up problem.     

Sensitivity analysis of parameters affecting the drying behaviour of durum wheat pasta

In this work, a comprehensive model of pasta drying combining Neumann boundary conditions, differential shrinkage and with consideration of the constant drying rate period and falling drying rate period was investigated through sensitivity and uncertainty analysis. Results confirmed that shrinkage, moisture loss and drying rate during the constant drying rate period and external resistance to mass transfer did not have a significant impact on the predicted required drying time. The predicted required drying time was influenced predominantly by the effective moisture diffusion coefficient. A correlation to estimate the effective moisture diffusion coefficient was developed from published values and was used to predict the required drying time with an uncertainty of ±3.5 h at a 90% confidence interval. Since this magnitude of uncertainty is unreasonable for most industrial uses, accurate data collection of effective moisture diffusivity should be viewed as a major objective in pasta drying research.     

Specific Heat, Thermal Conductivity, Density, and Thermal Diffusivity of Mexican Tortillas Dough

A split-split unit experiment was conducted and analyzed to determine the specific heat, thermal conductivity, density, and thermal diffusivity of Mexican corn-based tortillas dough (MCTD) as a function of processing time, temperature, and moisture content (wb). The data indicated that thermal conductivity and thermal diffusivity were significantly influenced by processing time, and respective components of temperature and moisture content. Specific heat and density varied with levels of moisture content and temperature. Thermal conductivity, specific heat, density, and thermal diffusivity could each be predicted separately by a polynomial equation.     

Effect of Temperature and Relative Humidity on Drying Kinetics of Fresh Japanese Noodle (Udon)

The effects of temperature and relative humidity (RH) on the drying kinetics were investigated to identify the optimal drying conditions for Japanese noodle (udon). Drying of fresh udon was carried out under nine conditions involving three temperatures (20, 30 and 40°C) and three RHs (60, 70 and 80%) at a constant airflow. The apparent moisture diffusivities were determined using a diffusion model taking into account both the internal and external mass transfer resistances. The effect of RH on the apparent moisture diffusivity was found to be smaller than that of temperature, but could not be neglected. A modified Arrhenius-type equation of diffusivity involving a RH term was proposed and used for the calculation of moisture content with time. The proposed equation was found to be effective for representing the drying process of fresh udon.     

Mathematical Evaluation of Effective Moisture Diffusivity in Fresh Japanese Noodles (Udon) by Regular Regime Theory

The effect of moisture content and temperature on the effective moisture diffusivity was investigated to have the optimal drying condition of Japanese noodles (Udon) using regular regime theory. The drying of fresh Udon of different moisture contents was carried out under constant conditions of relative humidity and airflow at 20, 30, and 40 °C. The existence of regular regime periods for fresh noodles was experimentally verified. Effective moisture diffusivity obtained ranged from 2.1 × 10 ^-7 to 3.7 × 10 ^-7 cm² s^-1. The effect of temperature on effective moisture diffusivity was adequately modeled by the Arrhenius relationship, although the effect of moisture content was quite small.     

Hydration of grain kernels and its effect on drying

Different hydration methods have been considered and their effect on the drying characteristics of corn and amaranth grains have been studied at different drying temperatures and the results compared with those for the fresh materials. The effect of hydration on drying was found to depend on the type of grain. In general, for corn hydrated grain particles the moisture content was found to be in a looser condition than it was in the fresh grains, and hence, smaller effective diffusion coefficients where found for the latter. Such differences were found to increase with increasing drying temperature. Also a first-order irreversible kinetic model was applied to the drying data for hydrated and fresh corn and a reduction on the drying activation energy was observed by the humidification process. In contrast, for the relatively small amaranth grains, both hydrated and fresh particles showed similar drying characteristics. The results suggest that drying kinetics and transport properties obtained for rehydrated grains can overestimate drying rates for the corresponding freshly harvested material, especially at relatively high moisture contents and for relatively large grain particles like corn.     

Modeling of rice hydration using finite elements

Great effort has been devoted towards developing models that describe cooking processes. A difficulty towards developing such models arises from the fact that during cooking, the physical properties and quite often sample geometry are time dependent. In this work a finite element model describing cooking of rice and water uptake using a Fickian diffusion model was developed, assuming axisymmetric conditions. Effective diffusivity was considered a function of moisture content. The numerical model compared favorably with experimental results. The value of the effective water diffusivity was estimated to be in the order of 7 × 10⁻¹⁰ m²/s, by minimizing the error between experimental and numerically predicted results.The effect of grain size on the cooking was also investigated using the model. Cooking time, i.e. the time to reach about 70% moisture content (wet basis), appeared to be a strong function of the initial size distribution.     

Kinetic modelling of drying and conversion/degradation of isoflavones during infrared drying of soybean

Soy isoflavones, which are well-known for their health benefits, could be affected by the technique and condition that are used to dry soybean prior to its use. In this study the drying kinetics of soybean as well as the inter-conversion and degradation of soy isoflavones during gas-fired infrared combined with hot air vibrating drying (GFIR–HAVD) at various temperatures (50, 70, 130 and 150 °C) were investigated. Simple kinetic models for the evolutions of both moisture content and isoflavones were proposed and tested. The temperature dependency of the effective moisture diffusivity of soybean could be well described by the Arrhenius correlation with the activation energy of 13.88 kJ/mol. In terms of the evolutions of isoflavones the contents of 6″-O-malonylgenistin (MGI) and 6″-O-acetylgenistin (AGI) decreased, while genistin (GI) and genistein increased with an increase in the drying temperature and drying time. First-order kinetic models could be used to describe the changes of isoflavones. At all drying temperatures the conversion of MGI to GI exhibited the highest rate constant; this was followed by the conversion of AGI to GI. In addition, MGI had the highest degradation rate constant; this was followed, in descending order, by AGI, GI and GE. The activation energies of degradation were lower than those of inter-conversion among all forms of isoflavones.     

Moisture Diffusivity in Sponge Cake as Related to Porous Structure Evaluation and Moisture Content

ABSTRACT: Water diffusivity within sponge cake was determined at 5, 20, and 25 °C by identification from a water sorption kinetic and using a mathematical model based on Fick's 2nd law. Water diffusivity at 20 °C within sponge cake varied from 0.5 × 10^-10 m²/s to 7.5 × 10^-10 m²/s as a function of sponge cake moisture content. Influence of temperature on the concentration-dependent diffusivity was investigated. The activation energy was found to vary with sponge cake moisture content from 84 to 128 kj/mole. Effective diffusivity variations were correlated with the changes in microstructure of the material that was observed by using environmental scanning electron microscopy. The level of porosity in the material played a dominant role in determining the effective diffusivity.     

基于介电谱的醋酸酯水刺非织造布含水率估算

为估算醋酸酯水刺非织造布含水率,测试了不同体积分数与不同含水率醋酸酯非织造布的介电谱,分析了干燥醋酸酯非织造布的体积分数以及非织造布中水分的体积分数对其介电常数的影响,并建立了单位质量醋酸酯非织造布介电常数变化率与含水率的关系。实验结果显示:在干燥状态下醋酸酯的介电常数对电场频率不敏感,醋酸酯的体积分数与其介电常数都存在显著的线性关系;在非织造布-水两相集合体中水分的体积分数与其介电常数呈指数函数关系,在电场频率为1 Hz和1×10⁶ Hz时含水率与其介电常数之间为指数函数关系,试样的含水率与其单位质量介电常数变化率之间存在幂函数关系。     

Hydration Kinetics of Red Kidney Beans (Phaseolus vulgaris L.)

Soaking of dry red kidney beans was studied at 20, 30 40 and 60°C by the method of weight gain until equilibrium conditions were attained. Water absorbed during soaking was a function of both soaking time and temperature. Soaking at high temperatures increased the hydration rate constant and decreased soaking time to achieve equilibrium. Compared to unblanched beans, the application of a pre-blanching step considerably reduced hydration times of blanched beans. Due to the plasticity effect acquired upon blanching, blanched beans showed a significantly high hydration rate constant and exhibited a more constant equilibrium moisture content regardless of soaking temperature. Activation energy values (E_a) of the hydration process were 6.48 Kcal/mole for blanched and 14.25 for unblanched beans.     

Drying kinetics and quality changes during drying of red pepper

A mathematical model is proposed to simulate the process of drying of individual pieces of red pepper under constant external conditions and to predict changes in some nutritional and organoleptic attributes of the product. The model was solved numerically to obtain moisture content and temperature as well as ascorbic acid and carotenoids concentration in the product as a function of time. A good agreement between predictions and experimental data at different drying temperatures was obtained.Water sorption isotherms of red pepper were determined in the range 20-50 °C and represented by two different sorption equations. Drying kinetics were represented by a diffusive model, the effective moisture diffusivity ranging from 5.01 to 8.32×10⁻¹⁰ m²/s with an activation energy of 23.35 kJ/mol. Degradation kinetics for ascorbic acid and total carotenoids were measured in the range 50-70 °C and modelled as first-order reactions. The rate constants increased with temperature and product moisture content. Average activation energies for carotenoids and vitamin C degradation were 50.1 and 26.9 kJ/mol, respectively.     

基于主成分分析的豆粕物理特性评价

为对豆粕的物理特性进行分析及量化评价,本文以42个豆粕样品为试验材料,测定分析其水分、容重、热物理特性、摩擦特性及粉碎特性指标参数,并运用主成分分析法简化物理特性指标,构架评价体系,得到每种样品的综合得分。结果表明,样品各物理特性指标之间存在不同程度的相关性,其中比热与水分和热传导系数呈显著正相关,与热扩散系数、休止角和摩擦系数呈极显著负相关;热传导系数与热扩散系数呈显著正相关,与休止角和摩擦系数呈极显著负相关;热扩散系数与容重呈显著负相关;摩擦系数与水分呈显著正相关,与容重和休止角呈极显著正相关;平均粒径与水分呈显著正相关,与休止角呈显著负相关。通过主成分分析提取了前4个主成分,累积方差贡献率达到88.898%(85%),能够代表原来8个物理特性指标中的绝大部分的信息,并得到评价公式Z=0.363Z_1+0.234Z_2+0.150Z_3+0.142Z_4,计算出豆粕物理特性指标综合得分。     

Modelling the effect of temperature on the hydration kinetic of adzuki beans (Vigna angularis)

The Aw reduction is a widely used technique to preserve grains, which hydration kinetics needs to be studied in order to obtain optimized processes. This work evaluated the hydration kinetic of Adzuki beans, a widely consumed grain by the oriental culture, modelling its behaviour as function of temperature. The grains were soaked in water and the moisture over the time was evaluated at temperatures of 25–70 °C. The grain behaviour during water uptake showed an initial lag phase, with a low water absorption rate. Therefore, the hydration kinetic was evaluated using a sigmoidal model (R² > 0.99). When soaking temperature was increased the hydration rate increased and both the lag phase and the moisture at the equilibrium decreased. These behaviour were, then, modelled as function of the soaking temperature (R² > 0.99). The obtained results are potentially useful for future studies on product development, food properties and process design.     

Moisture diffusivity in pears: experimental determination and derivation of a mathematical prediction model

In the present work the dependence of moisture diffusivity on pear composition (in particular, water and sugar concentrations) was examined from the drying rate data measured experimentally. A model for predicting diffusivity that accounts for the effects of three variables (temperature, moisture content and sugar concentration) was then developed, and compared with the model presented by Zogzas and Maroulis (Drying Technology 1996;14:1543), which accounts only for the influence of temperature and moisture concentration. It was observed that the value for the activation energy predicted by the model that includes the influence of the sugar concentration is higher, showing that the amount of sugar present influences the diffusion of moisture through the pear. From the results obtained it was possible to conclude that at constant temperature the diffusivity is increased for higher water contents and lower sugar concentrations. Furthermore, it was possible to observe that higher temperatures have a much more pronounced influence on the diffusivity, compared with lower temperatures.