Diffusive Model with Shrinkage in the Thin-Layer Drying of Fish Muscles

Fish fillets present large variation in volume during drying, due to their high initial moisture content. A kinetical study on the drying of fish muscles in slabs shaped with constant air conditions at three temperature levels is presented. For the modeling of the drying process of these materials, a diffusive model can be used, assuming a one-dimensional volume change. A linear correlation was considered between the thickness of the material and its moisture content, where the linear shrinkage coefficient has been determined. The resulting dimensionless nonlinear partial differential equation was solved numerically by the finite differences technique.     

Effective Diffusivity and Evaporative Cooling in Convective Drying of Food Material

This article presents mathematical models to simulate coupled heat and mass transfer during convective drying of food materials using three different effective diffusivities: shrinkage dependent, temperature dependent, and the average of those two. Engineering simulation software COMSOL Multiphysics was utilized to simulate the model in 2D and 3D. The simulation results were compared with experimental data. It is found that the temperature-dependent effective diffusivity model predicts the moisture content more accurately at the initial stage of the drying, whereas the shrinkage-dependent effective diffusivity model is better for the final stage of the drying. The model with shrinkage-dependent effective diffusivity shows evaporative cooling phenomena at the initial stage of drying. This phenomenon was investigated and explained. Three-dimensional temperature and moisture profiles show that even when the surface is dry, the inside of the sample may still contain a large amount of moisture. Therefore, the drying process should be dealt with carefully; otherwise, microbial spoilage may start from the center of the dried food. A parametric investigation was conducted after validation of the model.     

Hot-Air Drying and Rehydration Characteristics of Red Kidney Bean Seeds

The effects of pretreatments such as citric acid and hot water blanching and air temperature on drying and rehydration characteristics of red kidney bean seeds were investigated. Drying experiments were carried out at four different drying air temperatures of 50°C, 60°C, 70°C, and 80°C. It was observed that drying and rehydration characteristics of bean seeds were greatly influenced by air temperatures and pretreatments. Four commonly used mathematical models were evaluated to predict the drying kinetics of bean seeds. The Weibull model described the drying behaviour of bean seeds at all temperatures better than the other models. The effective moisture diffusivities (D_eff) of bean seeds were determined using Fick's law of diffusion. The values of D_eff were between 1.25 × 10^?9 and 3.58 × 10^?9 m²/s. Activation energy was estimated by an Arrhenius-type equation and was determined as 24.62, 21.06, and 20.36 kJ/mol for citric acid, blanch, and control samples, respectively.     

Estimation of Effective Moisture Diffusivity of Okra for Microwave Drying

The effect of microwave output power and sample amount on effective moisture diffusivity were investigated using microwave drying technique on round okra (Hibiscus esculentus L.). The various microwave output powers ranging from 180 to 900 W were used for the determination of effective moisture diffusivity for constant sample amount of 100 g okra. To examine the effect of sample amount on effective moisture diffusivity, the samples in the range of 25-100 g were dried at constant microwave output power of 360 W. By increasing the microwave output powers and decreasing the sample amounts, the effective moisture diffusivity values ranged from 20.52 × 10^-10 to 86.17 × 10^-10 and 34.87 × 10^-10 to 11.91 × 10^-9 m²/s^-1, respectively. The modeling studies were performed to illustrate the relationship between the ratio of the microwave output power to sample amount and effective moisture diffusivity. The relationship between drying constant and effective moisture diffusivity was also estimated.     

Estimation of Effective Moisture Diffusivity of Okra for Microwave Drying

The effect of microwave output power and sample amount on effective moisture diffusivity were investigated using microwave drying technique on round okra (Hibiscus esculentus L.). The various microwave output powers ranging from 180 to 900 W were used for the determination of effective moisture diffusivity for constant sample amount of 100 g okra. To examine the effect of sample amount on effective moisture diffusivity, the samples in the range of 25–100 g were dried at constant microwave output power of 360 W. By increasing the microwave output powers and decreasing the sample amounts, the effective moisture diffusivity values ranged from 20.52 × 10^?10 to 86.17 × 10^?10 and 34.87 × 10^?10 to 11.91 × 10^?9 m²/s^?1, respectively. The modeling studies were performed to illustrate the relationship between the ratio of the microwave output power to sample amount and effective moisture diffusivity. The relationship between drying constant and effective moisture diffusivity was also estimated.     

Water Diffusivity and Drying Kinetics of Air Drying of Figs

The aim of this study is to evaluate experimentally the effective diffusion coefficient and the drying kinetics of whole unpeeled figs (Ficus carica L. var. tsapela) in terms of drying conditions. Estimation of the effective diffusion coefficient was carried out employing Fick's law for unsteady diffusion, which was solved analytically and numerically. In both methods, shrinkage effect was considered. The results from the two methods were compared and presented together with the limited results from the literature. The estimated effective diffusion coefficient values by both methods were fitted to a modified Arrhenius equation. Finally, a model predicting drying kinetics was developed. The model's coefficients were associated to the experimental conditions.     

Microwave Heat Treatment of Spinach: Drying Kinetics and Effective Moisture Diffusivity

The effect of microwave drying technique on moisture content, moisture ratio, drying rate, drying time, effective moisture diffusivity, and porosity of spinach (Spinacia oleracea L.) were investigated. By increasing the microwave output powers (180-900 W) and the sample amounts (25-100 g), the drying time decreased from 18 to 3.5 min and increased from 7.7 to 25 min, respectively. To determine the kinetic parameters, the drying data were fitted to various models based on the ratios of the differences between the initial and final moisture contents and equilibrium moisture content versus drying time. Among of the models proposed, Page's model gave a better fit for all drying conditions applied. The activation energy was calculated using an exponential expression based on Arrhenius equation. The relationship between the drying rate constant and effective moisture diffusivity was also estimated and gave a linear relationship.     

Microwave Heat Treatment of Spinach: Drying Kinetics and Effective Moisture Diffusivity

The effect of microwave drying technique on moisture content, moisture ratio, drying rate, drying time, effective moisture diffusivity, and porosity of spinach (Spinacia oleracea L.) were investigated. By increasing the microwave output powers (180–900 W) and the sample amounts (25–100 g), the drying time decreased from 18 to 3.5 min and increased from 7.7 to 25 min, respectively. To determine the kinetic parameters, the drying data were fitted to various models based on the ratios of the differences between the initial and final moisture contents and equilibrium moisture content versus drying time. Among of the models proposed, Page's model gave a better fit for all drying conditions applied. The activation energy was calculated using an exponential expression based on Arrhenius equation. The relationship between the drying rate constant and effective moisture diffusivity was also estimated and gave a linear relationship.     

Thin Layer Drying Models for Osmotically Pre-dried Young Coconut

Thin layer convection drying was performed on osmotically pre-dried young coconut, strips, both thin and thick. A drying air temperature range of 50-70°C and an airflow of 0.25 m s^-1 was used to dry samples soaked in three sugar solution concentrations (40, 50, and 60°B) during the osmotic drying phase, with the convection drying alone serving as control. An analysis of variance (ANOVA) revealed that sugar concentration and thickness significantly affected osmotic drying rates as shown by their final moisture contents. While the drying air temperature and slab thickness significantly affected the average drying rate and the sugar concentration was an insignificant factor during convective drying phase. Effective diffusivity of water during hot air drying varied from 1.71 to 5.51 × 10^-10 m²s^-1 over the temperature range investigated, with energy of activation equal to 1173.0 kJ/kg. Three mathematical models available in the literature were fitted to the experimental data, with the Page model giving better predictions than the single or double term exponential model. The temperature dependence of the diffusivity coefficients was satisfactorily described by a simple Arrhenius type relationship.     

Effective Diffusivities and Energy Consumption of Whole Fruit Chinese Jujube (Zizyphus jujuba Miller) in Microwave Drying

Microwave drying of whole fruit Chinese jujube was performed at 45, 90, and 135 W. Ten commonly used mathematical models of thin-layer drying were compared. The Midilli model was best in describing drying time dependency of product moisture ratios. The initial drying rate and drying rate constant are linearly proportional to microwave power level. An effective diffusivity model was presented and validated with the Renka-Cline algorithm. The model has very high predictive precision, suggested by the relative percentage error of 3.734% on average between the model and the Renka-Cline algorithm. The effective diffusivity was proved to be a linear function of microwave power level and a quadratic function of moisture content. Energy consumption in microwave drying of Chinese jujube decreased as microwave power increased from 45 to 135 W, but 90 W was adequate for high-quality products with less energy consumption.     

Effect of Osmotic Dehydration with Pulsed Vacuum on Hot-Air Drying Kinetics and Quality Attributes of Cherry Tomatoes

The effects of osmotic dehydration (OD) with or without pulsed vacuum (PV) on hot-air drying kinetics and quality attributes of cherry tomatoes were investigated. Both OD and PVOD pre-treatments were performed for 3 h at 50°C in 50 and 70^o Brix sucrose solutions with a solution-to-fruit mass ratio of 4:1, and PVOD was applied for 15 min before OD at atmospheric pressure. Samples were further dried at air temperature of 70°C. Effective moisture diffusivity (D _eff) of osmotically dehydrated samples increased gradually while the D_eff curve of fresh samples had a plateau stage during hot air drying. Lower glass transition temperature, T_g, values of osmotically dehydrated samples indicated that they needed a lower storage temperature. Both OD and PVOD pre-treatments had advantages in shortening drying cycles and improving quality of products. Compared with air drying, osmo-air drying decreased the total drying time, color change, and hardness of dried samples by 32.26%, 18.11%, and 88.21%, respectively, and increased volume ratio and vitamin C retention rate by 72.31% and 125.82%. As compared with OD, PVOD decreased color change and hardness by 28.48% and 45.17%, increased volume ratio and vitamin C retention rate by 27.41% and 17.77%, but there was no significant difference shown in drying time. Therefore, osmotic pre-treatment can shorten the total dehydration time, and improve the general quality of dried cherry tomatoes.     

Computer Vision for Real-Time Measurements of Shrinkage and Color Changes in Blueberry Convective Drying

The effect of temperature on blueberry drying rate, shrinkage, and color changes was evaluated from drying experiments for both high bush (Vaccinium corymbosum L.) and wild (Vaccinium angustifolium) blueberries. Drying temperature significantly affected texture and color of both varieties. Temperatures above 55°C caused a significant color change (ΔE > 25) within 30 min of the beginning of drying, followed by a significant drop in density from 1.02 to 0.38 g/cm³. In contrast, drying at temperatures below 50°C resulted in nonsignificant color changes and an eventual density increase to 1.26 g/cm³. It follows that blueberry color could be used as an early stage indicator of quality degradation in the process of drying.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

城市污泥与木屑混合薄层干燥实验及动力学分析

角度研究了比,添加木通过对纯污泥和添加木屑的污泥进行薄层干燥对比实验,分别从混合比例、薄层厚度、干燥温度、风速木屑添加对污泥干燥特性的影响,并引入薄层模型对其干燥过程进行模拟。结果表明：与纯污泥干燥相屑后污泥干燥速率明显加快,且木屑添加比例越大、薄层越薄、干燥温度越高干燥速率越快,风速对干燥速率的影响不大;Wang—singh模型能很好的描述两种污泥薄层干燥,利用费克第二扩散定律导出的无限平板公式求出纯污泥和添加木屑的污泥在温度120℃～170℃时的有效扩散系数分别为6．13×10-6m／s～1．11×10-5m／s、1．07×10-5m／s～1．67×10-5m／s;由阿伦尼乌斯方程分别求得活化能为Es=16．67kJ／mol、Es=12．97kJ／mol。     

Numerical Investigation of Case Hardening of Plant Tissue During Drying and Its Influence on the Cellular-Level Shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding of different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a mesh-free-based 2D numerical model developed by the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model the fluid mechanisms of plant cells, smoothed particle hydrodynamics (SPH), which is a popular mesh-free technique used to solve hydrodynamics problems, is used. The cell wall mechanisms are modeled using the discrete element method (DEM). The model is fundamentally more capable of simulating large deformations of multiphase materials compared to conventional grid-based modeling techniques such as finite element methods (FEM) or finite difference methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformation under case hardening, four different plant tissue varieties (apple, potato, carrot, and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling, compared to the case-hardened outer cell layers of the tissues. For a given dried tissue condition, the case-hardened cellular deformations are highly influenced by the unique characteristics of the different tissues, such as cell size, cell fluid turgor pressure, and cell wall properties.     

Fluid Flow Effect and Mechanical Interactions during Drying of a Deformable Food Model

The purpose of this work was to evaluate a mathematical representation for the drying of a spherical food model, including the fluid flow effect and mechanical interactions. Drying kinetics data were obtained under a laminar fluid flow and the mechanical properties were evaluated through compression tests. The drying model considers two-dimensional mass transfer and the mechanical model was formulated from elasticity theory. The solution made possible the understanding of the fluid flow effect on mass transfer and the relationship between drying stresses and physical degradation of the food models.