Modeling Microwave Vacuum Drying Kinetics and Moisture Diffusivity of Carrot Slices

Carrot slices of 3.5 mm thickness were dried in a laboratory microwave vacuum dryer at five different microwave power density levels of 2, 4.66, 7.33, 10, and 12.66 W/g and at three vacuum chamber pressure levels of 6.66, 19.98, and 33.3 kPa to 4–6% d.b. moisture content. Inside the dryer the sample holding plate was rotated with the speed of 4 rpm for uniform microwaves application. The drying rates were increased with the increase in microwave power density at all pressure levels and the Page model was found to be the most suitable model to predict the drying behavior of carrot slices at all process conditions. The Page model drying rate constant (k, min^?1) showed high correlation with microwave power density at constant pressure by a power law equation and showed a logarithmic relationship with the microwave power density and pressure. Similar to the drying rate constant, the average moisture diffusivity at constant pressure was found to be function of microwave power density by power law equation as well as was also dependent on the power density and pressure by a logarithmic relationship.     

Modeling Microwave Vacuum Drying Kinetics and Moisture Diffusivity of Carrot Slices

Carrot slices of 3.5 mm thickness were dried in a laboratory microwave vacuum dryer at five different microwave power density levels of 2, 4.66, 7.33, 10, and 12.66 W/g and at three vacuum chamber pressure levels of 6.66, 19.98, and 33.3 kPa to 4-6% d.b. moisture content. Inside the dryer the sample holding plate was rotated with the speed of 4 rpm for uniform microwaves application. The drying rates were increased with the increase in microwave power density at all pressure levels and the Page model was found to be the most suitable model to predict the drying behavior of carrot slices at all process conditions. The Page model drying rate constant (k, min^-1) showed high correlation with microwave power density at constant pressure by a power law equation and showed a logarithmic relationship with the microwave power density and pressure. Similar to the drying rate constant, the average moisture diffusivity at constant pressure was found to be function of microwave power density by power law equation as well as was also dependent on the power density and pressure by a logarithmic relationship.     

Constant and Intermittent Drying Characteristics of Olive Cake

The drying kinetics of olive cake, the solid by-product of the olive oil extraction process, has been experimentally investigated in a small-scale tray dryer using both constant and intermittent (on/off) heating schemes. The parameters investigated include inlet air temperature and intermittency of heat input. The drying kinetics was interpreted through two mathematical models, the Page equation and the Lewis equation. The Page equation was most appropriate in describing the drying behavior of olive cake. A diffusion model was used to describe the moisture transfer and the effective diffusion coefficient at each temperature was determined. The dependence of the effective diffusion coefficient on drying temperature can be adequately explained based on an Arrhenius-type relation. The effective diffusion coefficient varied between 7.6 × 10^-8 and 2.5 × 10^-7 m²/min with an activation energy of 38.55 kJ/mol. Comparison of time evolution of material moisture content due to intermittent and constant drying is also made.     

Constant and Intermittent Drying Characteristics of Olive Cake

The drying kinetics of olive cake, the solid by-product of the olive oil extraction process, has been experimentally investigated in a small-scale tray dryer using both constant and intermittent (on/off) heating schemes. The parameters investigated include inlet air temperature and intermittency of heat input. The drying kinetics was interpreted through two mathematical models, the Page equation and the Lewis equation. The Page equation was most appropriate in describing the drying behavior of olive cake. A diffusion model was used to describe the moisture transfer and the effective diffusion coefficient at each temperature was determined. The dependence of the effective diffusion coefficient on drying temperature can be adequately explained based on an Arrhenius-type relation. The effective diffusion coefficient varied between 7.6 × 10^?8 and 2.5 × 10^?7 m²/min with an activation energy of 38.55 kJ/mol. Comparison of time evolution of material moisture content due to intermittent and constant drying is also made.     

Drying of solids; estimation of the mathematical model parameters

In order to determine physical meaning of a thin‐layer mathematical model parameter, the Page model was modified and tested on numerous experimental data. Applicability of the model was tested on the drying kinetics data, X(t), of 11 different types of the porous materials and dried in a convective, vacuum and/or microwave dryers under the predetermined external process conditions. During the entire drying time the drying kinetics of all the investigated materials and heating methods were successfully correlated with the modified Page model. The evaluated values of a new parameter, t_k, corresponded to the time at which diffusion, as a governing mechanism of moisture movement through the material, started. The results were confirmed by the pore size distribution of some materials.     

A Quasi-stationary Approach to Drying Kinetics of Fluidized Particulate Materials

A modified quasi-stationary method has been proposed to describe drying kinetics of particulate materials dried in convective dryers with active hydrodynamic regimes. Both our own results and literature data were used. These include sliced celery, cranberry, diced carrot, wheat and polystyrene granules dried in four types of dryers: pulsed fluid bed dryer, fluid bed dryer with a mixer, spouted bed dryer with a draft tube, and vortex dryer. The method was validated by comparing experimental data with results of modeling in terms of a reduced moisture content and material temperature. A new form of the generalized drying curve has been proposed with the reduced time and the index of hydrodynamic intensity as parameters. The equations developed can be used to calculate the total drying time and determine the temporal variation of the moisture content and material temperature.     

Microwave-Assisted Thin Layer Drying of Wheat

Drying characteristics of Canada Western Red Spring (CWRS) wheat were studied using a domestic microwave convective oven. The effects of microwave power level, grain bed thickness, and initial grain moisture on the drying kinetics were investigated. Wheat samples with initial moisture levels of 0.18 to 0.29 kg water/kg of dry matter were dried for different drying periods of 180 to 360 s. The moisture loss data were recorded at regular short intervals. Then moisture loss data were fitted to various models (Page equation, modified drying equation, and Midilli equation) to study the drying kinetics of wheat. The results showed that wheat moisture loss increased with increasing microwave power level. A mathematical model was developed by coupling mass and energy balances, resulting in a system of non-linear equations. The predicted moisture loss data from the developed model were compared by fitting to experimental microwave data that were in good agreement.     

Thin-Layer Drying of Flax Fiber: III. Influence of Layer Thickness on Drying Parameters

Wet flax fiber was dried after rinsing at four layer thicknesses of 5, 10, 15, and 20 mm using four drying air temperatures of 30, 50, 70, and 100°C. The coefficients of diffusion of flax fiber at different drying conditions were estimated using a three-term series solution of Fick's second law of diffusion. The Page model was used to model the drying characteristic curves. The estimated coefficient of diffusion of the flax fiber and the drying constant of the Page model were both linearly proportional to drying air temperature and increased exponentially with the thickness of the drying layer.     

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

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 · Reⁿ) 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 behavior of prina (crude olive cake) using different types of dryers

The purpose of this research is to investigate the drying kinetics and determine the suitable drying method of prina, which is obtained after pressing of olives in olive oil factories, and which cannot be used efficiently in certain sectors. Drying experiments were performed at drying temperatures of 60°C, 70°C, and 80°C at a fixed air velocity of 2 m/s using a hot air dryer and with microwave powers of 90 W, 360 W, and 600 W using a microwave dryer. The prina layer thicknesses were selected as 7, 9, and 11 mm for both drying methods. The minimum energy consumption values were measured as 42.0 Wh for 600 W power level and 7 mm layer thickness, and 10260 Wh for 7 mm layer thickness and 80°C temperatures. It was found that energy consumption during hot air drying was more than that of microwave drying. As a result, the suitable dryer and thickness of layer were selected as microwave dryer and 7 mm, respectively. The results of statistical analyses showed that the most suitable model to define the drying behavior of prina samples were found to be the Page model for the microwave dryer and Wang &; Singh model for the hot air dryer. Also, penetration depth, the loss tangent value (tanδ), dielectric constant of material (?^?), and dielectric loss factor (?^??) of dried prina were calculated as 34.51 cm, 0.1059, 75.65, and 8.01, at 2450 MHz, respectively.     

Microwave- and ultrasound-assisted convective drying of raspberries: Drying kinetics and microstructural changes

The drying kinetics, microstructural alteration, and rehydration properties of raspberry samples were studied experimentally in this work. Five different drying programs with the application of microwaves (MW) and ultrasound (US) were used, including convective drying (CV) as a reference test. The drying experiments were performed using a hybrid chamber dryer equipped with airborne ultrasound and microwave generators. The modified Page model was successfully used to describe the drying kinetics of raspberry fruits. Next, microstructural properties (porosity and total pore volume) of the dried samples were determined from the postprocessing of the images which were acquired using a lab-scale X-ray microtomograph. The results show a significantly shorter drying time by 54–64% for CVUS, 69% for CVMW, and 79% for CVMWUS; and a lower energy consumption resulting in energy saving of 14–23% for CVUS, 54% for CVMW, and 59% for CVMWUS as compared to CV. It is also shown that the average drying rate of raspberry samples increases by maximum fourfold with the application of both ultrasound and microwave radiations in CV. In addition, a higher porosity, total pore volume, and a better rehydration property were found for the raspberry samples dried with US than with MW assistance.     

COMPARISON OF CONVECTIVE, VACUUM, AND MICROWAVE DRYING CHLORPROPAMIDE

Drying kinetics of convective, vacuum, and microwave drying of a pharmaceutical product, chlorpropamide, has been investigated on a laboratory scale, in the temperature interval from 40°C to 60°C, and the range of microwave heating power from 154 W/kg_dm to 385 W/kg_dm.

The experimental data obtained were approximated with the “thin-layer” equation and a two parameter exponential model. In order to compare convective, vacuum, and microwave drying, effective diffusion coefficients and specific heat consumption were calculated for each drying method.

Higher rates and shorter drying times were achieved at a higher temperature and microwave heating power. The highest drying rates and the lowest specific heat consumption were achieved with microwave drying. This leads to the conclusion that microwave heating is the most appropriate method for drying of chlorpropamide. The quality of product was not changed for all applied methods.     

Drying Kinetics of Tomato by Using Electric Resistance and Heat Pump Dryers

Drying kinetics of tomato was studied by using heat pump dryer (HPD) and electric resistance dryers with parallel and crossed airflow. The performance of both systems was evaluated and compared and the influence of temperature, air velocity, and tomato type on the drying kinetics was analyzed. The use of HPD showed to be adequate in the drying process of tomatoes, mainly in relation to the conversion rate of electric energy into thermal energy. The heat pump effective coefficient of performance (COP_HT,EF) was between 2.56 and 2.68, with an energy economy of about 40% when compared to the drying system with electric resistance. The Page model could be used to predict drying time of tomato and statistical analysis showed that the model parameters were mainly affected by drying temperature.     

Heat Pump Drying of Green Sweet Pepper

Thin-layer drying experiments under controlled conditions were conducted for green sweet pepper in heat pump dryer at 30, 35, and 40°C and hot air dryer at 45°C with relative humidities ranging from 19 to 55%. The moisture content of sweet pepper slices reduced exponentially with drying time. As the temperature increased, the drying curve exhibited a steeper slope, thus exhibiting an increase in drying rate. Drying of green sweet pepper took place mainly under the falling-rate period. The Page equation was found to be better than the Lewis equation to describe the thin-layer drying of green sweet pepper with higher coefficient of determination and lower root mean square error. Drying in heat pump dryer at 40°C took less time with higher drying rate and specific moisture extraction rate as compared to hot air drying at 45°C due to lower relative humidity of the drying air in a heat pump dryer though the drying air temperature was less. The retention of total chlorophyll content and ascorbic acid content was observed to be more in heat pump–dried samples with higher rehydration ratios and sensory scores. The quality parameters showed a declining trend with increase in drying air temperature from 30 to 45°C. Keeping in view the energy consumption and quality attributes of dehydrated products, it is proposed to dry green sweet pepper at 35°C in heat pump dryer.     

Drying of Guava and Papaya: Impact of Different Drying Methods

Heat pump dryers (HPD) are known as high-energy-efficiency devices with low economic cost. As it is usually a closed system, the drying media can be substituted by inert gases. In this study, the effect of nitrogen and carbon dioxide on guava and papaya were investigated. Both drying kinetics and quality of these dried fruits resulting from the two methods were compared with normal air HPD, vacuum dryer, and freeze dryer. When using CO₂, the effective diffusivity during the drying process was 44% higher in guava and 16.34% higher in papaya. There was less browning, faster rehydration, and more vitamin C retention in the final products. All these reveal the great potential of modified atmosphere heat pump dryer in the food drying industry.     

Drying Kinetics of Tomato by Using Electric Resistance and Heat Pump Dryers

Abstract

Drying kinetics of tomato was studied by using heat pump dryer (HPD) and electric resistance dryers with parallel and crossed airflow. The performance of both systems was evaluated and compared and the influence of temperature, air velocity, and tomato type on the drying kinetics was analyzed. The use of HPD showed to be adequate in the drying process of tomatoes, mainly in relation to the conversion rate of electric energy into thermal energy. The heat pump effective coefficient of performance (COP_HT,EF) was between 2.56 and 2.68, with an energy economy of about 40% when compared to the drying system with electric resistance. The Page model could be used to predict drying time of tomato and statistical analysis showed that the model parameters were mainly affected by drying temperature.     

Drying Kinetics of Sludge from a Wastewater Treatment Plant

Drying kinetics of sludge from a municipal sewage treatment plant were determined in a laboratory drying tunnel with parallel airflow at different temperatures and air velocities. The constant drying rate period was identified followed by two falling rate periods. Drying kinetics in these falling rate periods were then satisfactorily modeled using the modified quasi-stationary method and the Fick's second law. The two-period model was used, however, to describe drying kinetics over the entire drying process, and the equation for a generalized drying curve was proposed. The effective diffusivity was also determined from the integrated Fick's equation, and correlated with temperature by an Arrhenius type equation.     

DRYING CHARACTERISTICS OF THE HAZELNUT

Equilibrium moisture content isotherms for Spanish hazelnut (Corylus avellana L.) at different temperatures (30°C-80°C) were determined using static gravimetric method. Thin layer drying experiments were done with forced air circulation and were conducted with different operating conditions to determine the drying characteristics of hazelnuts. The effect of air temperature (30°C-70°C), air velocity (0.5 m/s - 2 m/s) and drying bed loading density (50 kg/m² - 150 kg/m²) on drying of unshelled and shelled hazelnuts was studied. Six mathematical models were used to fit the experimental equilibrium moisture content data, from which the G.A.B. model was found to give the best fit. Diffusion coefficients were determined by fitting experimental thin-layer drying curves to the Fick's diffusion model. Variation of the effective diffusion coefficient with temperature was of the Arrhenius type. The Page equation was found to describe adequately the thin layer drying of hazelnut. Page equation drying parameters k and n were correlated with air temperature and relative humidity.     

Effect of Processing Conditions on Drying Kinetics and Particle Microstructure of Carrot

The drying of carrot particles (6 mm × 6 mm × 12 mm) was studied in a tunnel dryer; a vacuum-freeze dryer, either with or without infrared radiation; a pulsed fluidized-bed dryer assisted by microwave radiation; and combinations of these methods. The effect of two freezing rates (quick freezing in liquid nitrogen and slow freezing in a household freezer) was also studied.

The drying kinetics for these drying methods were determined and modeled, and the dried products were subjected to texture (hardness), color, and rehydration analysis, as well as 2D and 3D image analysis of pictures from scanning electron microscope.

The combination of freeze drying with other dehydration techniques reduces the drying time by 6–70%, although, in general, the structural damage increases with respect to freeze drying alone. The hybrid drying systems did not show significant differences in drying times either for quick- or slow-frozen samples. The combination of freeze drying followed by conventional drying reduces the drying time between 23 and 40% on average.

The Page empirical model represents adequately the entire drying process for combined methods, with specific parameters for each drying zone. The values of effective diffusivity calculated with the simplified constant diffusivity model agree with those reported in the literature.