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.     

Thin-layer drying of porous materials: Selection of the appropriate mathematical model and relationships between thin-layer models parameters

Experimental investigation of the drying kinetics of various types of materials was carried out in laboratory-scale dryers under different conditions of temperature, microwave heating power and pressure. Leather samples (mechanically and vacuum-dewatered bull napa and wet blue cutting), paperboards (grafopack, testliner), wood (alder, birch, willow) and two pharmaceutical powders (chlorpropamide and hydrochlorotiazide) were dried in a microwave dryer. Thin clay slabs, Al–Ni catalyst and chlorpropamide were dried in a convection dryer, while chlorpropamide and ketoprofen were dried in a vacuum dryer. In order to compare drying kinetics, experimentally obtained data, X = f(t), were correlated with the Lewis “thin-layer” equation, the modified Page equation and Fick's second law. The drying constant, effective diffusion coefficient, mass transfer coefficient and modified Page model parameters were estimated by fitting the selected mathematical models to experimental data. High levels of correlation between measured and calculated data were obtained for all materials and dryers using modified Page model. The application of the Lewis and Fick's equation is justified only for drying of clay, catalyst and leather. Mass transfer coefficient depends linearly on the drying constant. The relation between the modified Page model parameter and the drying constant can be represented by a unique power function.     

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 Characteristics and Kinetics of Vacuum Microwave–Dried Potato Slices

Vacuum microwave dehydration characteristics and drying kinetics of potato slices were evaluated using a laboratory-scale dryer. The test materials were placed on a rotating tray to allow uniform exposure to the microwave field. The effect of drying conditions on the drying characteristics was investigated. As expected, higher drying rates were obtained with higher microwave power and lower vacuum levels. The effect of vacuum pressure on drying rate was not as significant as that of microwave power. The Henderson & Pabis model provided better simulation of the drying curves for potato slices. Empirical models are presented for the drying rate constant as a function of the microwave power and vacuum pressure for potato slices under the range of operating conditions tested.     

Vacuum dehydration kinetics of onion slices

Onion slices were dried in a single layer of thickness varying from 1 to 5 mm in the temperature range of 50-70 °C in a laboratory scale vacuum dryer. The effect of pretreatment, drying temperature and slice thickness on the drying kinetics of onion slices was studied. Four thin layer drying models namely Lewis model, logarithmic model, Page model and Fick's law model were applied on the experimental moisture loss data with respect to time to predict the drying pattern properly on the basis of coefficient of determination and standard error. The Page model showed better fit to the experimental data compared to other models. Effective moisture diffusivity of the slice was measured using Fick's second law of unsteady state diffusion. The diffusivity values were found ranging from 1.32E−10 to 1.09E−09 m²/s for untreated and 1.32E−10 to 1.09E−01 m²/s for treated onion slices. Effective moisture diffusivity showed increasing trend with increase in temperature and thickness.     

Effect of Microwave Energy on Vacuum Drying Kinetics of Alginate-Starch Gel

Microwave energy drying under vacuum was investigated for alginate-starch hydrogel. Drying was conducted using 2450 MHz microwave energy at 25 mm Hg absolute pressure and different power levels; e.g., 300, 500, 700, 900, and 1100 watts. Drying was continued until final moisture content of the sample reached less than 1% wet basis. Moisture loss during drying was measured at 3-min intervals. Drying kinetics were used to describe both macroscopic and microscopic mechanisms of heat and mass transfer. Experimental drying kinetic data were fitted to a mathematical model. Experimental drying data points were fitted to an empirical model equation.     

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.     

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.     

Physical Changes in Bamboo (Bambusa phyllostachys) Shoot During Hot Air Drying: Shrinkage, Density, and Porosity

The apparent density of bamboo (Bambusa phyllostachys) shoot was investigated at a moisture content range of 10-92% wet basis by weighing the product in air and determining the buoyancy force in toluene. An analysis of variance (ANOVA) unveiled that moisture content significantly affected apparent density at 95% confidence level. The true density of the bamboo shoot was determined by grinding the dried sample to exclude all internal pores and using density bottles. The experimental data fitted well to a general density equation for fruits and vegetables proposed by Lozano et al. (1983) and to a second order polynomial (SOP) model. The internal porosity generated during drying varied in a nonlinear (quadratic) fashion. Shrinkage at different moisture content levels was measured by evaluating the dimensional changes in bamboo shoot slabs (5.0 × 3.2 × 1.8 cm) by drying in a convection oven and a tray dryer operating at 70°C and 7.2% relative humidity. Shrinkage was affected statistically by decreasing moisture content at 95% confidence level. Shrinkage was compared with available models in literature and found to be oriented based on fiber direction and distinctly different from the isotropic volume change in fruits and vegetables.     

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.     

Kinematic Model for a Far Infrared Vacuum Dryer

Energy analyses in drying of welsh onion from one source of far infrared radiation at an absolute pressure of 2.6 and 5 kPa were carried out to determine the energy input at which the highest level of efficiency would be attained. The experimental results were used not only to formulate an advanced mathematical model for the prediction of moisture content of onion as a function of drying time but also to study the dryer efficiencies. Less than half of energy input was utilized for evaporating water from the onion. Approximately 73-99% of operating efficiency, which was dependent on the dryer configuration, was converted into radiant energy. The highest radiant efficiency was obtained at 40 W initial power supply, which was equivalent to the source temperature of about 100°C. An 80 W initial electrical power supply at a 10 cm distance of heater from the onion surface showed the highest drying efficiencies. At 80 W power, efficiency decreased with increasing distance from the heater source but at the expense of quality. For optimum drying efficiency without compromising quality, distance of heater from onion surface was proposed to be 10 cm.     

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.     

Measurement of Absorbed Power of Glass Particle Layer on Moisture Content and Drying Rate by Combined Convective and Microwave Drying

Dependency of absorbed power by microwave on the local moisture content in a glass particle layer was measured with a new method; that is, heating the wet layer. The heating experiment was performed using a laboratory-scale combined convective and microwave heater/dryer that was manufactured by modifying a domestic microwave oven at 2.45 GHz. The measured result was strongly dependent on the local moisture content and showed a maximum and a minimum within the measured range of the moisture content. This dependency can be explained by the assumption that moisture in the wet layer behaves as a mass of the free water. The combined drying rate of the wet layer measured with the heater/dryer was simulated with both the power dependency and the experimental convective-only drying rate. Power dependency on temperature is as important as the moisture content in the simulation. Simulated results agree very well with experimental ones.     

Freeze Drying of Apple Slices with and without Application of Microwaves

In this study, Fuji apple slices were dehydrated using freeze drying (FD) combined with microwave assisted with vacuum drying (VMD). The optimal parameter for the diversion point of moisture content from FD to VMD process was at the moisture level of 21%, and for VMD the optimal parameter for vacuum pressure was at 9.15 kPa and microwave power density was at a level of 3.18 w/g. The results show that the two-step technique can significantly reduce total FD time required by up to 40%, while the nutritional value of the dried apple chips remained unchanged compared to FD used alone.     

Drying Enhancement of Clay Slab by Microwave Heating

The effect of internal heating by microwave on the drying behavior of a slab was studied. A wet sample of kaolin pressed into a slab was subjected in microwave irradiation of 2.45 GHz. The absorption of microwave energy into a wet slab can be expressed by a function of the moisture content and the pathway length, which is a similar form to Lambert-Beer's law. The drying behavior was compared among three modes: microwave irradiation, hot air heating and radiation heating in an oven. Microwave heating with a constant power resulted in breaking the sample when the internal temperature achieves at 373 K. However, if the power was controlled to maintain the temperature less than the boiling point of water, the drying succeeded without any crack generation until the completion with a significantly faster drying rate than in convective heating or in the oven. It is also noted that the transient behavior of the temperature is quite different from the conventional drying.     

Heat and Moisture Transfer Model for Onion Drying

Onion slices of 3 mm thick were dried in an atmospheric batch tray dryer in order to investigate the influence of air temperature and drying time on parameters such as sample moisture content and drying rate. A model is proposed which takes into account both moisture and temperature distributions in the sample and is in a fair agreement with the experimental data. The models suggested so far by other workers take only the moisture distributions into account for onion drying.     

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.     

DRYING OF CARROTS IN A FLUIDIZED BED. I. EFFECTS OF DRYING CONDITIONS AND MODELLING

Drying curves were determined in a mechanically agitated fluidized bed dryer, at temperatures between 70°C and 160°C, air velocities between 1.1 m/s and 2.2 m/s and stirring rates between 30 rpm and 70 rpm for batch drying of 3 kg lots of carrot slices, measuring the moisture content and shrinking of the particles in time. This was complemented by a study of the rate and degree of swelling of dried carrot particles in water between 20 and 75°C. Drying kinetics were modeled by Fick's second law, for which an optimal agreement with the experimental data was obtained when the effective diffusivity (D_e) was determined by a correlation based on the air velocity (v), the air temperature (T) and the dimensional moisture content of the carrot particles (X/X_o). Loss of carotenes is minimized when dehydration is carried out at about 130°C with a drying time below 12 min.     

A Novel Design of Crop Dryer for Use in Developing Countries

The dryer is required for drying of grain as well as drying of the processed products in small catchment agro processing centers in the developing world. However, due to varied material characteristics of grain and secondary processed product, two entirely different types of dryers are required. The grain is dried in a recirculatory dryer, whereas processed product is dried in a tray dryer, where it is frequently mixed and trays are also intermittently changed. To avoid the need for two dryers, a novel design of a low-cost hot air dryer was developed where just by changing the trays the dryer can be converted from an LSU grain dryer to a tray-type product dryer. The dryer was tested for drying soybean grain as well as processed soy products like blanched soybean dal and soyflakes. The capacity of the dryer was 100 kg/batch in a tray dryer with each tray accommodating 10 kg of wet material. In case of LSU mode, the capacity of the dryer was 250 kg of grain per batch. The drying time required was 5 h for 250 kg of wet soybean from 24 to 10% moisture content, whereas in a tray dryer 100 kg blanched soybean dal was dried from 60 to 10% in 5 h and 100 kg of soyflakes from 25% moisture content to 10% moisture in 1.75 h. The cost of the dryer is estimated at US$580.00 and it can be fabricated in a moderately equipped workshop in developing countries.