Mathematical Modeling of Withering Characteristics of Tea Leaves

The withering characteristics of tea leaves were examined for different temperatures. Tea leaves were withered at a temperature range of 20-45°C with a constant air velocity of 1.1 m/s. The experimental results illustrated the absence of constant-rate drying period and withering took place only in the falling-rate period. During the falling-rate period, at constant drying air flow rate, the drying rate increased and drying time decreased with the increase in drying air temperature. Drying models of Henderson and Pabis and Page were evaluated based on mean bias error (E_MB), root mean square error (E_RMS), correlation coefficient (R²), and the chi square (χ²). The Henderson and Pabis model was found to be a better model for describing the withering characteristics of tea leaves for each of the temperatures of 20, 25, 30, and 35°C. The values obtained from Page model were found to be more reasonable for temperatures of 40 and 45°C than the other model. Both the models closely fitted the withering data within a certain range of temperature. The Henderson and Pabis model gave better prediction and satisfactorily described the withering characteristics of tea leaves at temperatures lower than 40°C whereas the Page model fitted well at temperatures greater than 40°C.     

Drying Characteristics of Purslane (Portulaca oleraceae L.)

Abstract

Thin layer drying rates of purslane were determined experimentally as a function of temperature with air velocity kept constant at 1.1 m/s and relative humidity below 5%. Thin layer drying data were obtained for purslane at four drying air temperatures (35, 70, 95, and 120°C). Five thin layer-drying models (Henderson and Pabis, exponential, Page, two-term exponential, and Thompson models) were fitted to the drying data. The color of purslane was determined after drying using a spectro-colorimeter (Hunter Lab) in terms of Hunter L, a, and b values. The Page model was found to be most suitable in describing the drying characteristics of purslane. New parameters developed for the model resulted in a good fit at different temperatures. Color measurement indicated that greenness decreased with an increase in drying air temperature. Typical drying times were 88.41, 138.53, 416.38, and 1371.85 min at 120, 95, 70, and 35°C, respectively.     

From Laboratory Experiments to Design of a Conveyor-Belt Dryer via Mathematical Modeling

Abstract

A conveyor-belt dryer for picrite has been modeled mathematically in this work. The necessary parameters for the system of equations were obtained from regression analysis of thin-layer drying data. The convective drying experiments were carried out at temperatures of 40, 60, 80, and 100°C and air velocities of 0.5 and 1.5 m/sec. To analyze the drying behavior, the drying curves were fitted to different semi-theoretical drying kinetics models such as those of Lewis, Page, Henderson and Pabis, Wang and Singh, and the decay models. The decay function (for second order reactions) gives better results and describes the thin layer drying curves quite well. The effective diffusivity was also determined from the integrated Fick's second law equation and correlated with temperature using an Arrhenius-type model. External heat and mass transfer coefficients were refitted to the empirical correlation using dimensionless numbers (J _h , J _D  = m · Re ⁿ ) and their new coefficients were optimized as a function of temperature. The internal mass transfer coefficient was also correlated as a function of moisture content, air temperature, and velocity.     

Drying equations of Thai Hom Mali paddy by using hot air,carbon dioxide and nitrogen gases as drying media

The objective of this study was to develop a drying equation for predicting the thin layer drying kinetics of dried Thai Hom Mali paddy using different drying gases. Thai Hom Mali paddy cv. Khao Dok Mali 105 with initial moisture content of 32% dry basis was dried in a heat pump dryer at 0.4 m/s fixed superficial velocity, 60% fixed evaporator bypass air ratio, and varied drying temperatures of 40, 50, 60 and 70 °C using hot air, CO₂ and N₂ gases as drying media. Drying rate was not affected by drying gases but increased with drying temperatures. Moisture ratios, at any given time during the drying process, were compared among various models, namely, Newton, Page, Modified Page I, Henderson and Pabis, two-term, approximation of diffusion, and Midilli. The effect of drying air temperatures on the coefficients of the best moisture ratio model was determined by single step regression method. The R² coefficient, root mean square error (RMSE) and chi-square (χ²) were criteria for selecting the best model. The study found that the Midilli model was the best model for describing the drying behavior of Thai Hom Mali paddy in every evaluated drying gas. It should be possible to predict the moisture content of a product with a generalized model that shows the effect of drying air temperature on the model constants and coefficients.     

Modeling Drying Kinetics of Pistachio Nuts with Multilayer Feed-Forward Neural Network

Drying kinetics of pistachio nuts (Akbari v.) was simulated using a multilayer feed-forward neural network (MFNN). Experiments were performed at five drying air temperatures (ranging from 40 to 80°C) and four input air flow velocities (ranging from 0.5 to 2 m/s) with three replicates in a thin-layer dryer. Initial moisture content in all experiments was held at about 0.3 kg/kg d.b. To find the optimum model, various multilayer perceptron (MLP) topologies, having one and/or two hidden layers of neurons, were investigated and their prediction performances were evaluated. The (3-8-5-1)-MLP, namely, a network having eight neurons in the first hidden layer and five neurons in the second hidden layer resulted in the best-suited model estimating the moisture content of the pistachio nuts at all drying runs. For this topology, R² and MSE values were 0.9989 and 4.20E-06, respectively. A comparative study among MFNN and empirical models was also carried out. Among the empirical models, the logarithmic model, with MSE = 7.29E-6 and R² = 0.9982, gave better predictions than the others. However, the MFNN model performed better than the Lewis, Henderson and Pabis, two-term, and Page models and was marginally better than the logarithmic model.     

Determination of Drying Kinetics for Biomass by Thermogravimetric Analysis under Nonisothermal Condition

The nonisothermal drying kinetics of wheat straw and corn stalk has been studied by thermogravimetry. The experimental data have been obtained in order to fit to semitheoretical models widely used to describe drying behavior of agricultural products. Nonisothermal drying models—Newton, Henderson and Pabis, logarithmic, and Page—were evaluated based on the coefficient of determination (R ²), reduced chi-square (χ ²), and root means square error (RMSE). Page's model has been found to be the best for describing the nonisothermal drying characteristics of wheat straw and corn stalk. The activation energy values of wheat straw and corn stalk are determined to be 14.144 and 6.113 kJ mol^?1, respectively.     

Characterization of isotherms and thin-layer drying of red kidney beans,Part I: Choosing appropriate empirical and semitheoretical models

Desorption and adsorption isotherms and drying characteristics of red kidney beans were studied using static and dynamic methods, respectively. The desorption and adsorption isotherms were determined at 60, 50, 40, 30, 20, and 10°C with 32–91% relative humidity (RH). The constant RHs were generated using six saturated salt solutions at constant temperatures. The drying characteristics were determined using a thin-layer dryer with drying air at 50, 40, and 30°C with 35 and 50% RH. The dimensions of the kidney beans before and after drying were measured and shrinkage and sphericity of the beans were calculated. A new method to evaluate the best-fitted equation to characterize the thin-layer drying data was developed. The best-fitted equations to describe the desorption and adsorption isotherms were the modified Chung–Pfost and modified Guggenheim–Anderson–deBoer. The red kidney beans only experienced a falling rate drying period and had a largest shrinkage in the length direction during drying. The Henderson and Pabis model and the modified Page model were the best-fitted models to describe the thin-layer drying data. Using only the values of R² and mean squared error to evaluate the semitheoretical and empirical models might not be enough. The method developed in this study could help develop a semitheoretical or empirical model with a higher accuracy of drying constant, which could be used to estimate the effective water diffusivity.     

Effect of citric acid and blanching pre-treatments on drying and rehydration of Amasya red apples

Drying behaviour of red apples was experimentally examined in a laboratory dryer at drying temperatures of 55, 65 and 75 °C and a constant air velocity of 2.0 m/s. Two pre-treatments (blanching and 0.5% citric acid) were applied to prior to drying process. It was observed that both the drying temperature and pre-treatment affected the drying time. The shortest drying times were obtained from pre-treated samples with citric acid solution. Blanched samples have higher rehydration ratios than other samples. Five mathematical models namely, Newton, Henderson and Pabis, Page, Logarithmic and Parabolic models were evaluated in the kinetics research. The fit quality of the proposed models was evaluated by using the determination of coefficient (R²), reduced chi-square (χ²), root means square error (RMSE) and mean relative percent error (P). The Parabolic model provided the best representation of data. Effective moisture diffusivity (D_eff) computed on the basis of Fick's second law. D_eff value of pre-treated samples with citric acid solution was higher than the other samples.     

Drying characteristics of sweet cherry

The effects of alkali emulsion of ethyl oleate and air temperature (60, 70 and 75 °C) on the drying characteristics of sweet cherry were studied using a hot air dryer at a constant air velocity of 2.0 m/s. It was observed that both the alkali emulsion of ethyl oleate and air temperature affected the drying time. The drying times of pre-treated samples were 19.5-22.6% shorter than those of control samples. Five semi-theoretical thin-layer models, namely, Lewis, Henderson and Pabis, Logarithmic, Page, Wang and Singh models were used for the modeling of the drying kinetics. The fit quality obtained with each model was evaluated using statistical tests. After comparing experimentally obtained values with the calculated values from the models, it was concluded that Page model represents the drying characteristics better than the other models. The effective moisture diffusivity was determined by using Fick's second law and was observed to lie between 5.683 × 10⁻¹⁰ and 1.544 × 10⁻⁹ m²/s for the pre-treated and control samples. Rehydration ratio was significantly affected by pre-treatment and air temperature. It was found to increase proportionally with the increase in air drying temperature.     

STUDY OF THIN-LAYER DRYING OF GRAPE WASTES

The effect of drying temperature on grape wastes, the solid wastes of the wine and raki production processes, was investigated in a cabinet dryer. Drying experiments were performed three air temperatures of 70°, 90,° and 110°C, at constant air velocity of 1.2 m/s, and initial thickness of 1.8 cm for grape marc and 2.0 cm for grape pulp. Experimental data were fitted to Henderson and Pabis, Page, and logarithmic models, respectively. The performance of these models is evaluated by comparing coefficient of determination and reduced chi-square between the observed and predicted moisture ratios. The statistical analysis concluded that the best model was the logarithmic model. The effective moisture diffusivity varied from 8.55 × 10^?10 to 3.32 × 10^?9 m²/s over the temperature range. Temperature dependence of the diffusivity was well documented by an Arrhenius-type relationship. The activation energies for grape marc and grape pulp were calculated as 25.41 and 13.74 kJ/mol, respectively.     

Drying Characteristics of Purslane (Portulaca oleraceae L.)

Thin layer drying rates of purslane were determined experimentally as a function of temperature with air velocity kept constant at 1.1 m/s and relative humidity below 5%. Thin layer drying data were obtained for purslane at four drying air temperatures (35, 70, 95, and 120°C). Five thin layer-drying models (Henderson and Pabis, exponential, Page, two-term exponential, and Thompson models) were fitted to the drying data. The color of purslane was determined after drying using a spectro-colorimeter (Hunter Lab) in terms of Hunter L, a, and b values. The Page model was found to be most suitable in describing the drying characteristics of purslane. New parameters developed for the model resulted in a good fit at different temperatures. Color measurement indicated that greenness decreased with an increase in drying air temperature. Typical drying times were 88.41, 138.53, 416.38, and 1371.85 min at 120, 95, 70, and 35°C, respectively.     

Effect of different drying conditions on the vitamin C (ascorbic acid) content of Hayward kiwifruits (Actinidia deliciosa Planch)

In this study, drying kinetics of kiwifruit are investigated experimentally and theoretically under varying drying conditions. Experiments are conducted using air temperatures at 35, 45, 55 and 65 °C, mean velocities at 0.3, 0.6 and 0.9 m s^?1 and, relative humidity values at 40%, 55%, 70% and 85%. Initially, sorption isotherms of the dried kiwifruit slices are determined for different temperatures and equilibrium relative humidity values. The values of the moisture diffusivity, D_eff are obtained from the Fick's diffusion model. The effects of the governing drying parameters on the vitamin C content as well as on the total drying time are determined. The experimental moisture data were fitted to some models available in the literature, mainly the Henderson and Pabis model, the Lewis model and the two-term exponential model and, a good agreement was observed. In addition, it is disclosed that increasing drying air temperature causes more loss in vitamin C in the dried fruits while degradation of vitamin C is reduced with increasing relative humidity of drying air.     

Vacuum Drying of Common Date Pulp Cubes

Drying ability of date (Phoenix dactylifera L.) pulp cubes from three Algerian common varieties (Mech-Degla, Degla-Beida, and Frezza) were investigated. Drying process was carried out under partial vacuum (200 mbar) at 60, 80, and 100°C. Compared to the Newton model, the Henderson and Pabis model better described drying kinetic of Mech-Degla and Frezza pulps at 60 and 80°C with a mean relative error (MRE) not higher than 6.07%. The same model fits experimental data at 60°C for Degla-Beida (R ² = 0.988; MRE = 6.07) as well as at 100°C for only Mech-Degla (R ² > 0.98, MRE = 8.61%).     

Air drying characteristics and moisture diffusivity of carrots

The effects of air temperature on drying kinetics of carrot cubes were investigated. Convective drying characteristics of carrot cubes in a spout-fluidized bed were evaluated through the effect of air temperature on drying kinetics. Drying was carried out at 60, 70, 80 and 90 °C and the falling drying rate data were used to calculate the effective diffusion coefficients from the Fick's equation. Four mathematical models available in the literature were fitted to the experimental data. The Two-term model is given better prediction than the Henderson and Pabis, Page and Lewis model and satisfactorily described drying characteristics of carrot cubes.     

Drying of sardine muscles: Experimental and mathematical investigations

The aim of this work was to study the effect of air drying process on the dehydration kinetics of sardine muscles (Sardina pilchardus). Experimental drying kinetics were measured at five air temperatures (40, 50, 60, 70 and 80 °C), two relative humidity and at a constant air velocity of 1.5 m/s. The sardine drying kinetics were accelerated by increasing air temperature and were showed down when increasing air humidity. Moisture desorption isotherms of sardine muscles were determined at three temperatures (40, 50 and 70 °C) by using the static gravimetric method. The equilibrium moisture contents of sardine muscles were used to treat mathematically the experimental drying kinetics. Experimental drying kinetics and desorption isotherms of sardine muscles were described by using empiric models available in the literature. Eight models (GAB, BET, Henderson–Thompson, Modified Chung & Pfost, Modified Halsey, Oswin, Peleg and Adam & Shove models) were compared in order to describe the desorption isotherms. The Peleg model showed the best fitting of experimental data. For the drying kinetics, the Page model allowed a better fitting than the Newton and the Henderson and Pabis models. The Page model was thus used for simulating the drying kinetics of sardine muscles between 40 and 80 °C.     

Thin-Layer Drying of Flax Fiber: II. Modeling Drying Process Using Semi-Theoretical and Empirical Models

Thin-layer drying experiments were performed for drying flax fiber under four different drying conditions. In all drying treatments the absolute humidity of drying air was 0.0065 kg of water per kg of dry air, but the drying temperature were 30, 50, 70, and 100°C. The drying process was modeled using the drying data and five semi?theoretical and empirical models cited in different literatures. From the five tested models, the Page model gave the best fitting for experimental data with R ² equal to 0.99, for all treatments. The estimated drying constants at different drying temperatures were highly correlated with drying air temperature. The drying constants were also highly correlated with the calculated coefficient of diffusions.     

Filtration and Drying Study of Phosphatidylinositol Fraction from De-Oiled Soy Lecithin

Separation and purification of phosphatidylcholine (PC) and phosphatidylinositol (PI) fractions to their utmost purity is still a challenging task industrially due to the molecular and structural complexity of lecithin molecules. The present study deals with the filtration of the PI-rich fraction followed by drying of the cake for its further purification and value addition. Filtration of the PI-rich fraction was carried out under constant pressure conditions followed by the drying of the cake in a vacuum tray dryer. The average specific cake resistance (α_av) as a function of operating pressure was studied and it showed little variation with respect to the applied pressure differential. The initial solvent content in the cake after filtration was found to be in the vicinity of 1 kg solvent/kg dry solid, which was then subsequently reduced in the drying stage to 0.04 kg solvent/kg dry solid. The drying kinetics of the cake was studied at different drying temperatures in a vacuum tray dryer operated under varying degree of vacuum. The drying rate curve showed a prominent falling rate period with the effective solvent diffusivity in the range of 5.4 × 10^?10 m²s^?1 to 1.42 × 10^?9 m²s^?1within the temperature range of 40–60°C. Critical analysis of the dried PI fraction was carried out in terms of phosphatidylinositol content and color. The drying data were analyzed using various models and Das et al.'s model, the modified Henderson and Pabis model, and the Page model were found to provide the best fit sin terms of root mean square error (RMSE), chi square, and correlation coefficient (R ²).     

Mathematical Modeling of Mass Transfer during Convective Dehydration of Brown Algae Macrocystis Pyrifera

The aim of this research was to study and to model the drying kinetics of the brown algae Macrocystis pyrifera at 50, 60, 70, and 80°C. GAB equation showed a good fit on the sorption experimental data. Fick's diffusional model, together with Newton, Henderson-Pabis, Page, modified Page, logarithmic, and Midilli-Kukuc models were applied on the drying kinetics of the alga. The D_we increased from 5.56 to 10.22 × 10^?9 m²/s as temperature increased from 50 to 80°C. Midilli-Kukuc and logarithmic models obtained the best-fit quality for drying curves based on the statistical tests. In consequence, both models are excellent tools for estimating the drying time of this product.     

Management of Surface Drying Temperature to Increase Antioxidant Capacity of Thyme Leaf Extracts (Thymus vulgaris L.)

Thyme leaves are an important source of essential oils with antioxidant activity; these compounds are located in trichomes on the leaf surface. The drying conditions affect not only the drying time but also the antioxidant activity. In the literature, a drying temperature of 70°C appears to be the best for drying thyme leaves according to their antioxidant capacity. Considering drying periods at different temperatures also could be beneficial. With these considerations, the goal of this work was to establish a drying strategy with which to manage a drying temperature on the leaf surface that will enable the drying time to be shortened and improve the antioxidant capacity (AC) of the extract of dried thyme leaves. The drying strategy consisted of two consecutive drying periods in order to manage the drying temperature on the leaf surface. The first drying period was carried out at 80°C (T _a1) until the sample surface reached a temperature of 70°C, and the temperature was then immediately set to 70, 60, 50, and 40°C (second drying period, T _a2) at different air velocities (v; 1 and 2 m s^?1). Compared to constant drying conditions, two consecutive drying periods were found to improve the drying kinetics: the AC increased from 10.5 to 27.4% while reducing the drying time by 14.5 to 39.2%. The use of this drying strategy was found to be an interesting means of intensifying the convective drying of thyme leaves and its application should be considered when drying similar materials with bioactive compounds on the surface.     

The Effects of Predrying Treatments and Different Drying Methods on Phytochemical Compound Retention and Drying Characteristics of Moringa Leaves (Moringa oleifera Lam.)

The most appropriate maturity stage of Moringa oleifera leaves was selected for drying based on phytochemical content, including quercetin and kaempferol. Desorption isotherms were developed and were best fit by the modified Henderson model. Prior to drying, samples were left untreated, blanched in boiling water, and blanched in NaHCO₃/MgO. The leaves were dried by hot air tray drying (TD) and heat pump–dehumidified drying air (HPD) at air temperatures of 40, 50, and 60°C. Alternatively, leaves were subject to microwave drying (MWD) at 150, 450, and 900 W and to freeze drying (FD). The moisture versus time data were fitted to five drying models. In general, a three-parameter model gave the best fit. The drying constant was related to the drying temperature or microwave power using an Arrhenius model. Effective moisture diffusivity (D _eff) increased with higher drying temperature, higher microwave power, or blanching treatments. Structural changes in the leaves after drying and upon rehydration were observed by scanning electron microscopy (SEM). Leaves blanched and dried using HPD at 50°C and fresh and dried using FD showed a partial breakdown of the tissue structure upon rehydration. HPD and blanching reduced the drying time by 8.3% and increased quercetin and kaempferol levels by 42.1 and 51.4%, respectively, compared to TD at 50°C. MWD provided the quickest drying followed by HPD and TD, respectively. HPD drying of M. oleifera after blanching resulted in relatively greater quality compared to TD and MWD.