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.     

Characteristics of Chard Leaves during Microwave, Convective, and Combined Microwave-Convective Drying

Chard leaves (Beta vulgaris L. var. cicla), which weighs 25 g with a moisture of 9.35 (db), were dried using three different drying methods, microwave, convective, and combined microwave-convective. Drying continued until leaf moisture fell down to 0.1 (db). Drying periods lasted 5-9.5, 22-195, and 1.5-7.5 min for microwave, convective, and combined microwave-convective drying, respectively, depending on the drying level. In this study, measured values were compared with predicted values obtained from Page's semi-empirical equation. Optimum drying period, color, and energy consumption were obtained for combined microwave and convective drying. The optimum combination level was 500 W microwave applications at 75°C.     

Effect of Pulsed Electric Field and Osmotic Dehydration Pretreatment on the Convective Drying of Carrot Tissue

The influence of pulsed electric field (PEF) and subsequent centrifugal osmotic dehydration (OD) on the convective drying behavior of carrot is investigated. The PEF was carried out at an intensity of E = 0.60 kV/cm and a treatment duration of t_PEF = 50 ms. The following centrifugal OD was performed in a sucrose solution of 65% (w/w) at 40°C for 0, 1, 2, or 4 h under 2400 × g. The drying was performed after the centrifugal OD for temperatures 40-60°C and at constant air rate (6 m³/h).

With the increase of OD duration the air drying time is reduced spectacularly. The dimensionless moisture ratio Xr = 0.1 is reached for PEF-untreated carrots after 370 min of air drying at 60°C in absence of centrifugal OD against 90 min of air drying after the 240 min of centrifugal OD. The PEF treatment reduces additionally the air drying time. The total time of dehydration operations can be shortened when OD time is optimized. For instance, the minimal time required to dehydrate untreated carrots until Xr = 0.1 is 260 min (120 min of OD at 40°C and 140 min of drying at 60°C). It is reduced to 230 min with PEF-treated carrots.

The moisture effective diffusivity D_eff is calculated for the convective air drying based on Fick's law. The centrifugal OD pretreatment increases drastically the value of D_eff. For instance, 4 h of centrifugal OD permitted increasing the value of D_eff from 0.93 · 10^-9 to 3.85 · 10^-9 m²/s for untreated carrots and from 1.17 · 10^-9 to 5.10 · 10^-9 m²/s for PEF-treated carrots.     

COMBINED MICROWAVE AND SPOUTED BED DRYING OF DICED APPLES: EFFECT OF DRYING CONDITIONS ON DRYING KINETICS AND PRODUCT TEMPERATURE

The influence of microwave power (0 to 8.0 W/g, dry basis) and hot air temperature (25°C to 95 °C) on drying rate and product temperature of diced apples (from 31 % to 5% moisture content, dry basis) in a laboratory microwave and spouted-bed combined dryer was investigated. Product temperature initially increased sharply to a plateau about 12 to 15°C above the spouted bed air temperature at a microwave input power 6.4 W/g. This temperature remained almost constant thereafter. Uniform microwave heating was achieved as evidenced by uniform product color and product temperature. Drying rates increased with increasing spouted-bed air temperature or microwave power level, But higher microwave power caused more darkening of the product. Drying of the diced apples in the microwave and spouted bed drying system exhibited two falling rates periods. The influence of air temperature on effective moisture diffusivity followed an Arrhenius type equation. The activation energies were 23.7 kJ/mol and 26.7 kJ/mol for the first and second falling rate periods, respectively.     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D_eff) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D_eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

A GRAPHICAL DESIGN METHOD FOR A PARTIAL SOLAR DRYER FOR CORN

This paper presents the application of a design method for a partial solar heating system of polyvalent modular dryers called “GJ-ABAQUE” to the drying of thick layers of grains.

This method is based on the use of charts or polynomial correlations. In the actual case where the drying air is not recycled, we only need one chart which allows one to determine the fraction of the monthly heating load supply by solar energy as a function of two dimensionless parameters. The latter implies the use of monthly average radiation data, the collector surface and estimates of drying loads.

The “GJ-ABAQUE” method was applied for drying 777 kg of corn, corresponding to 1 m³ of fresh product, in a thick layer in each modular dryer.     

Optimizing Drying Conditions for Microwave-Vacuum (MIVAC®) Drying of Russet Potatoes (Solanum tuberosum)

MIVAC® combines microwave heating with vacuum drying. Microwave power is modulated based upon product temperature and can limit overheating compared to other microwave-vacuum methods. Blanched potatoes were dried at 50, 60, and 70°C for 0 to 150 min. Potatoes dried at 70°C had a lower moisture content in less time compared to potatoes dried at 50 and 60°C, but the color of the dehydrated potatoes was affected due to overheating. Drying at 60°C for 150 min resulted in dried potatoes with acceptable color. Drying at 50°C resulted in dehydrated potatoes of acceptable color; however, it required more time.     

Characteristics of Chard Leaves during Microwave,Convective, and Combined Microwave-Convective Drying

Chard leaves (Beta vulgaris L. var. cicla), which weighs 25 g with a moisture of 9.35 (db), were dried using three different drying methods, microwave, convective, and combined microwave-convective. Drying continued until leaf moisture fell down to 0.1 (db). Drying periods lasted 5–9.5, 22–195, and 1.5–7.5 min for microwave, convective, and combined microwave-convective drying, respectively, depending on the drying level. In this study, measured values were compared with predicted values obtained from Page's semi-empirical equation. Optimum drying period, color, and energy consumption were obtained for combined microwave and convective drying. The optimum combination level was 500 W microwave applications at 75°C.     

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.     

DEHYDRATION KINETICS AND MODELLING

This paper presents a study on the kinetics of dehydration of carrot parallelepipeds which may be useful for a new method which consists in applying a freezing pretreatment. followed by a vacuum dehydration after sample defreezing.allowing instant products to be produced in terms of rehydration ( about 2 minutes rehydration). in this paperare examined effects of effects of pressure (2.6 to 75 kPa). heating conditions (single and double face heating), temperature (50 to 100°c) and sample thickness (3 to 20 mm thick) on dehydration rate.

Dehydration curves allow the identification of two main periods with variation of sample temperature during drying. The first period is a quasi-isothermal. falling-rate period characterized by a large quantity of moisture removal through diffusional transfer. Then. can be observed a second period with increase in product temperature while drying rate is governed by heat diffusion. A drying model accounting for sample shrinkage is proposed and discussed.     

MEASURED GAS VELOCITY AND MOISTURE CONTENT DISTRIBUTION IN A CONVECTIVE VACUUM KILN

Transferring the necessary heat of evaporation to the stack is the bottleneck in convective vacuum drying of wood. Higher gas velocities are applied to compensate for the lower gas density and to obtain similar heat and mass transfer characteristics as under normal pressure. Like in conventional kiln drying the region with the most unfavorable drying conditions determines drying time and product quality. To use the full potential of the meanwhile established superheated steam vacuum drying technology, it is therefore necessary to work on an improved uniformity of process conditions in the kiln.

To evaluate the fluid dynamics and its influence on the final moisture content, experimenls in a laboratory convective vacuum kiln were carried out. For different total pressures the profiles of dynamic pressure in the stack entry section were measured in a dry atmosphere. At normal pressure the profiles were determined between the board layers throughout the whole stack. For the same slack configuration vacuum drying tests were used to assess the impact of the velocity distribution in the slack on the final moisture content distribution-Regions of low gas velocities coincided well with regions of high final moisture content.     

EFFECT OF DRYING METHODS ON MOISTURE SORPTION ISOTHERMS OF FUFU AT THREE TEMPERATURES

Moisture sorption characteristics for dried fufu using three drying methods at 25°C, 32°C and 45°C were determined experimentally for water activity ranging from 0.11 to 0.96. At a given temperature and water activity, the rotary dried fufu had the highest equilibrium moisture content while the sun dried had the lowest.

Four linear and four nonlinear sorption models were used to analyze the data. The linear GAB model showed the best fit while the nonlinear Bradley model was the best over the whole range of water activity in their respective groups. Also estimates of the net isosteric heats of sorption and their dependence on moisture content were presented for each product.     

Production of Crispy Granules of Fish: A Comparative Study of Alternate Drying Techniques

Three alternate dying methods—vacuum drying (VD), vacuum microwave drying (VMD), and pulse-spouted vacuum–microwave drying (PSVMD)—were examined experimentally for their potential as an industrial scale technology to produce granules of fish. Drying kinetics as well as key quality parameters such as expansion ratio, texture, color, sensory characteristics, and microstructure of crispy granules produced by these drying techniques were examined. Results showed that the drying time is reduced with an increase in microwave power level and with reduced pressure as expected. The quality of the granules is affected by the drying method and the operating parameters employed. Granules obtained using PSVMD at a microwave power density of 6.0 W/g displayed optimal quality required for the commercial product accepted by consumers.     

Stress and Failure Prediction for the Drying, Tempering, and Cooling of Extruded Durum Semolina

This work presents a method to predict the stress and breakage that is caused by the drying of hygros-copic materials. Stresses were predicted for a viscoclasic cylinder with the properties of extruded durum semolina, or pasta noodles. The stresses were calculated as functions of the transient moisture and tem-perature gradients in the material which were predicted for the combined processes of drying, tempering,and cooling. The time and radial position of failure were predicted based on failure data for extruded semolina.

Isotherm data for extruded durum semolina were obtained for temperatures from 40 to 60°C and for relative humidities from 75 to 95%. The results were fit with a modified form of Henderson's equation.Thermal conductivities were measured for temperatures from 30 to 50°C and a moisture range of 12 to 27% (dry basis).

A drying model based on the principles of irreversible thermodynamics; (Fortes, 1978; Fortes and Okos, 1981a, 1981b) was used to successfully predict drying curves for a range of experimental conditions. Transient moisture and temperature profiles were calculated numerically, and a receding evapora-tion front was predicted to exist. Drying was predicted to be a coupled liquid, vapor, and heat transport phenomena.

The drying data were used in a stress analysis of a Maxwell viscoelastic cylinder to predict trends in stress development under various contiitions of combined drying, tempering, and cooling. High temperature-high humidity drying, HTHH, (lOO°C, 65% RH) was compared with low temperature-low humidity drying, LTLH, (53°C, 13% RH). The HTHH drying offered definite advantages in terms of reduced product breakage susceptibility. The reasons for those advantages were increased failure strength and a decreased moisture gradient at the end of drying. In a five-stage drying process, the cooling stage was shown to have a significant impact on the predicted levels of stress and on the strength of the extruded material. Analysis of the model suggested that gradual temperature and humidity transitions from stage to stage in multistage processes were important to product quality.     

HEAT AND MASS TRANSFER DURING SAPWOOD DRYING ABOVE THE FIBRE SATURATION POINT

Pine sapwood was dried in an air convection kiln at temperatures between 60-80 °C. Temperature and weight measurements were used to calculate the position of the evaporation front beneath the surface. It was assumed that the drying during a first regime is controlled by the heat transfer to the evaporation front until irreducible saturation occurs. Comparisons were made with CT-scanned density pictures of the dry shell formation during initial stages of drying of boards.

The results indicate a receding evaporation front behaviour for sapwood above approximately 40-50% MC when the moisture flux is heat transfer controlled. After that we finally reach a period where bound water diffusion is assumed to control the drying rate.

The heat transfer from the circulating air to the evaporation front controls the migration flux. In many industrial kilns the heating coils therefore have too small heat transfer rates for batches of thin boards and boards with high sapwood content.     

Osmotic Dehydration of Apple Cylinders: III. Continuous Medium Flow Microwave Heating Conditions

Continuous flow osmotic drying permits a better exchange of moisture and solids between the food particle and osmotic solution than the batch process. Osmotic drying has been well studied by several researchers mostly in the batch mode. Microwave heating has been traditionally recognized to provide rapid heating conditions. Its role in the finish drying of food products has also been recognized. In this study, the effects of process temperature, solution concentration on moisture loss (ML), solids gain (SG), and mass transport coefficients (k_m and k_s) were evaluated and compared under microwave, assisted osmotic dehydration (MWOD) versus continuous flow osmotic dehydration (CFOD). Apple cylinders (2 cm diameter, 2 cm height) were subjected to continuous flow osmotic solution at different concentrations (30, 40, 50, and 60°Brix sucrose) and temperatures (40, 50, and 60°C). Similar treatments were also given with samples subjected to microwave heating. Results obtained showed that solids gain by the samples was always lower when carried out under microwave heating, while the moisture loss was increased. The greater moisture loss strongly counteracted solids gain in MWOD and thus the overall ratio of ML/SG was higher in MWOD than in CFOD.     

Drying Sawdust in a Pulsed Fluidized Bed

The objective of this work was the experimental and theoretical study of sawdust drying, in batch and continuous experiences, using a pulsed fluidized bed dryer.

In the batch experiences, a 2³ factorial design was used to determine the kinetics of drying, the critical moisture content, and the effective coefficients of both diffusivity and heat transfer, all of them as a function of the velocity and temperature of the air, the speed of turning of the slotted plate that generates the air pulses in the dryer, using sawdust with 65% moisture in each run.

In the continuous operation, a 2³ factorial design was used to study the effect of the solid flow and the velocity and temperature of the air on both the product moisture and the distribution of residence times. In order to determine these last ones, digital image processing was used, utilizing sawdust colored by a solution of methylene blue as tracer.

The statistically significant factors were the velocity and the temperature of the heating air, for both the continuous and batch operations. Although the speed of turn of the slotted plate was not significant, it was observed that the air pulses increased the movement of particles, facilitating its fluidization, especially at the beginning of drying.

The heat transfer coefficients were adjusted according to the equation Nu = 0.0014 Re_p^1.52, whose standard deviation of fit is 0.145.

The period of decreasing rate was adjusted to several diffusivity models, giving the best fit the simplified variable diffusivity model (SVDM). The curve of distribution of residence times was adjusted using the model of tanks in series, with values between 2.6 and 5 tanks.     

DRYING OF GRANULAR PARTICLES IN A MULTISTAGE INCLINED FLUIDIZED BED WITH MECHANICAL VIBRATION

A mathematical model for the drying rate of granular particles in a multistage inclined fluidized bed(IFB) is presented from the standpoint of simultaneous heat and mass transfer, with taking the effect of mechanical vibration added vertically into consideration.

Steady-state distributions for the temperatures and concentrations of the particles and the heating gas, and for the moisture content of the particles are numerically calculated based on the present model. The calculated results show fairly good agreement with the experimental data, which were obtained from the drying experiments of brick particles in a three-stage IFB using comparatively low temperature air(40-60°C) as the heating gas.

It has been found within the range of the experimental conditions employed that, the mechanical vibration added vertically enhances the over-all drying rate of the particles and its effect can be considered equivalent to an increase in the air velocity.     

Drying Suspensions in a Pulsed Fluidized Bed of Inert Particles

The drying of carbohydrate suspensions on polypropylene particles in a pulsed fluidized bed was studied by means of a 2⁵ experimental design, to determine the effect of the air flow and temperature, suspension flow rate, and free section and rotating speed of the rotary plate on the Nusselt number, the moisture content of the product, and the percentage of solids retained inside the bed (which were minimized to 4.9 and 14.4%, respectively) with an air flow of 600 m³/h at 90°C and 720 mmHg, a suspension flow rate of 6 L/h, and a plate with 6% free section, rotating at 50 rpm.

Additionally, the effects of temperature, air flow, and suspension flow rate on the residence time distribution (RTD) were determined, using the stimulus-response methodology. The RTD was represented by 1.1 to 2 tanks in series, according to this model. The mean residence time of the dried carbohydrate particles was between 5.4 and 8.2 min.

Finally, an egg suspension could be dried at 4 L/h, with air at 90°C, with a mean residence time about 50% longer that that found for drying carbohydrate suspensions.