Mechanisms of heat and mass transfer during drying of mate (Ilex paraguariensis) twigs

Experimental results of surface temperature and moisture content of twigs of mate were obtained in a conveyor-belt dryer operated batchwise. The first response was determined with an infrared sensor, while the second was by conventional gravimetry. A set of 0.04-m-long cylindrical twigs classified manually into three different subgroups on the basis of their diameters (3.5 × 10^?3, 6.5 × 10^?3, and 10 × 10^?3 m) were used in the experiments. Drying always took place in a chamber fed with a thin single layer of material 0.5 m in length and 0.05 m wide. The fresh twigs without leaves at ambient temperature (≈27.2 ± 2.6°C) and with an initial moisture content close to 0.8 ± 0.1 were dried at three different average air temperatures (65.5, 80.2, and 83.8°C) for 7200 s. A full set of nine (3¹ × 3¹) drying experiments were performed by varying the examined factors (particle diameter and drying temperature) at three levels. The low estimated Biot numbers (<0.55) indicate that convection plays a much more important role than conduction in heat transfer. Because of this and since heating was much faster than drying, the Newton’s law of cooling alone was successfully applied to describe the increase of particle temperature with time. From a similar analysis involving a convective mass transfer coefficient calculated with the Chilton-Colburn analogy emerged high-mass-transfer Biot numbers (≈5.37 × 10³ ? 3.65 × 10⁵) that reveal drying of twigs is governed by diffusion. In fact, the equation that represents the Fick’s second law of diffusion in a long cylinder (one-dimensional transfer), solved analytically and coupled to the model of heat transfer, was able to describe the kinetics of drying of mate twigs.     

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.     

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).     

Drying Characteristics of Barley Grain Dried in a Spouted-Bed and Combined IR-Convection Dryers

A study was performed to determine the drying characteristics and quality of barley grain dried in a laboratory scale spouted-bed dryer at 30, 35, 40, and 45°C and an inlet air velocity of 23 m/s^?1, and in an IR-convection dryer under an infrared radiation intensity of 0.048, 0.061, 0.073, and 0.107 W cm^?2 at an air velocity of 0.5 m/s^?1. The results show that the first, relatively short, phase of a sharp decrease in the drying rate was followed by the phase of a slow decrease. The time of barley drying depended on temperature of inlet air in a spouted-bed dryer and on radiation intensities in an IR-convection dryer. Barley drying at 45°C in a spouted-bed dryer was accompanied by the lowest total energy consumption. The average specific energy consumption was lower and the average efficiency of drying was higher for drying in a spouted-bed dryer. The effective diffusivities were in the range 2.20–4.52 × 10^?11 m² s^?1 and 3.04–4.79 × 10^?11 m²/s^?1 for barley dried in a spouted-bed and in an IR-convection dryer, respectively. There were no significant differences in kernel germination energy and capacity between the two drying methods tested.     

Mathematical Model of Fixed-Bed Drying and Strategies for Crumb Rubber Producing STR20

The objectives of this research were to investigate empirical and diffusion models for thin-layer crumb rubber drying for producing STR20 rubber using hot air temperatures of 110–130°C and to study the effect of drying parameters such as inlet drying temperature, volumetric flow rate, and initial moisture content on the quality of dried rubber. Finally, a mathematical drying model for predicting the drying kinetics of crumb rubber was developed using inlet air flow rates of 300–600 m³/min-m³ of crumb rubber (equivalent to 1.8–5.0 m/s) with the crumb rubber thickness fixed at 0.25 m. The average initial moisture content of samples was in the ranges of 40 and 50% dry basis while the desired final moisture content was below 5% dry basis. The results showed that the drying equation of crumb rubber was highly related to the inlet air temperature, while the drying constant value was not proportional to the initial moisture content. Consequently, the experimental data were formulated using nine empirical models and the analytical solution of moisture ratio equation was developed by Fick's law of diffusion. The result showed that the simulated data best fitted the logarithmic model and was in reasonable agreement to the experimental data. The effective diffusion coefficient of crumb rubber was in the range of 1.0 × 10^?9 to 2.15 × 10^?5 m²/s corresponding to drying temperatures between 40 and 150°C, respectively. The effects of air recirculation, inlet drying temperature, initial moisture contents, air flow rate, and drying strategies on specific energy consumption and quality of samples were reported. The experiments were conducted using two different drying strategies as follows: one-stage and two-stage drying conditions. The results showed that initial moisture content and air flow rates significantly affected the specific energy consumption and quality of rubber, while the volumetric air flow rate acted as dominant effect to the specific energy consumption. The simulated results concluded that the percentage of recycled air between 90 and 95% provided the lowest specific energy consumption as compared to the others.     

Chemical Pretreatments Affecting Drying Characteristics of Chilli (cv. Huarou Yon)

One- (70°C) and two-temperature regimes (70 and 50°C) were used to dry chilli (Capsicum annuum cv. Huarou Yon) using a laboratory tray dryer compared to conventional sun drying. A pretreatment was done by soaking chilli in antibrowning solutions before drying. It was found that the drying rate of chilli soaked in chemical solutions was increased and the drying period of chilli was decreased. Page's model was found to fit well with the experiment for one- and two-temperature drying using least squares analysis. The highest value of the coefficient of determination (R² > 0.99), the lowest value of standard error of estimation (SEE < 0.00031), and the lowest value of the mean relative deviation (P < 10%) were obtained. The effective moisture diffusivities of chilli drying at 70°C and two-stage drying were between 6.01–7.22 × 10^?10 m²/s and 3.16–3.89 × 10^?10 m²/s, respectively. In contrast, the lowest value of effective moisture diffusivity of chilli was obtained by the conventional sun-drying method (0.597 × 10^?10 m²/s). The highest value of moisture diffusivity was observed for chilli soaked in sodium metabisulfite (NaMS) mixed with CaCl₂ solution for both one- and two-temperature regimes. The color of chilli was improved by using chemical pretreatments, in particular, chilli soaked in NaMS mixed with CaCl₂ solution.     

Influence of the Addition of Dietary Fiber on the Drying Curves and Microstructure of a Dry Fermented Sausage (Sobrassada)

The formulation of a dry fermented sausage has been modified by the addition of carrot dietary fiber (CDF; 3, 6, 9, and 12% [w/w]), and the influence of this change on the drying curves and food microstructure has been studied. The CDF content influenced the initial moisture content as well as the drying rate. A diffusion model taking into account the change in the product formulation has been proposed to simulate the drying curves. A constant mass transfer coefficient of 2.53 × 10^?8 m/s was obtained and the effective water diffusivity varied exponentially with the CDF content from 0.99 × 10^?11 m²/s (0% CDF) to 2.08 × 10^?11 m²/s (12% CDF). The simulation of the drying curves was satisfactory (mean relative error of 0.5 ± 0.1%). No differences in the microstructure related to the proteolytic process were found among samples with different CDF contents.     

Determination of Drying Characteristics of Timber by Using Artificial Neural Networks and Mathematical Models

In this research, poplar and pine timbers have been dried in heat pump dryer functioning on the basis of 24-h operation. The change in weight in all of the timbers was followed in the drying chamber and drying stopped when the desired weight was achieved. Initial moisture content of the poplar timbers was 1.28 kg water/kg dry matter, and the moisture content was reduced to 0.15 kg water/kg dry matter moisture content in 70 h; the moisture content of the pine timbers, which was 0.60 kg water/kg dry matter, was reduced to the same amount in 50 h. Drying air temperature, relative humidity, and stack weight were measured and collected during drying and saved on a computer and analyzed afterwards. The moisture ratios were analyzed with Statgraphic computer program by using semitheoretical models and empirical values. Correlation and standard error of estimation (SEE) and R ² values were achieved.     

Effect of Convective Air Attributes with Microwave Drying of Soybean: Model Prediction and Experimental Validation

The heat and mass transfer that occurred during drying of soybeans by a combined process using microwave (MW) and convective hot air was studied. A coupled mathematical model was developed to simulate this phenomenon. The soybean samples were re-wetted to 20% wet basis, the selected level of initial moisture content (IMC), and then dried in a domestic microwave oven under various MW power levels from 300 to 390 W, using inlet air with relative humidity of 35, 55, 75, and 95%. The simulated moisture loss profiles obtained from the coupled model compared well with those obtained in the experiments. Results showed that the drying rate decreased from 6.235 × 10^?5 to 6.192 × 10^?5 kg water/(kg wb s) as the inlet air temperature increased from 30 to 60°C. Furthermore, the drying rate was observed to increase from 6.192 × 10^?5 to 6.211 × 10^?5 kg water/(kg wb s) as the relative humidity (RH) increased from 35 to 95%.     

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%.     

Ascorbic Acid Thermal Degradation during Hot Air Drying of Camu-Camu (Myrciaria dubia [H.B.K.] McVaugh) Slices at Different Air Temperatures

Abstract

Air drying of camu-camu slices was performed in order to estimate the effect of air temperature on the kinetics of ascorbic acid thermal degradation. Moisture variation during the air drying process was monitored gravimetrically by weighing the trays at predetermined time intervals. The experimental points were adjusted by Fick's diffusion model and by the Page empirical model. The effective diffusion coefficient (D_eff) ranged from 8.48 × 10^?10 to 1.34 × 10^?9 m²/s.The ascorbic acid content was evaluated in samples taken during the drying process using Iodine titration, and the results modeled by the Weibull equation. Concerning ascorbic acid retention the best drying condition required air at 50°C. The ascorbic acid retention was 78%, when the moisture content of the product reached 10% (wet basis).     

Sugarcane Bagasse Drying in a Cyclone: Influence of Device Geometry and Operational Parameters

Sugarcane bagasse is becoming more and more commonly used in generating electrical energy, steam, and bioethanol. Drying is important in sugarcane and other types of biomass because it can be used to improve the calorific value and overall energetic use. In this work, sugarcane bagasse was treated by drying in a cyclonic dryer. The influence of the geometry of the device (the conical part of the cyclone) and process parameters (bagasse mass flow rate and temperature) were tested. The modification on the conical part was related to two different angles and with two different inferior outlets (B). Experimental design was carried out for each geometry. The independent variables were the drying agent temperature (35 to 275°C) and the bagasse mass flow rate (0.1 × 10^?2 to 2.9 × 10^?2 kg s^?1). The air flow rate was kept constant at 7.5 × 10^?2 kg s^?1. The dependent variables were moisture reduction (MR) and average particle residence time (t_res) in the cyclonic dryer. For both cyclonic geometries, it was observed that MR was directly proportional to the temperature and inversely proportional to the bagasse mass flow rate. t_res was also inversely proportional to the bagasse mass flow rate. Decreasing B tended to increase tres and MR.     

SINGLE-LAYER DRYING BEHAVIOR OF MEXICAN TEA LEAVES (CHENOPODIUM AMBROSIOIDES) IN A CONVECTIVE SOLAR DRYER AND MATHEMATICAL MODELING

Single-layer solar drying experiments were conducted for Mexican tea leaves (Chenopodium ambrosioides) grown in Marrakech. An indirect forced convection solar dryer was used in drying the Mexican tea leaves at different conditions such as ambient air temperature (21° to 35°C), drying air temperature (45° to 60°C) with relative humidity (29 to 53%), airflow rate (0.0277 to 0.0556 m ³/s), and solar radiation (150–920 W/m²). The experimental drying curves showed only a falling rate period. In order to select the suitable form of drying curves, 14 mathematical models were applied to the experimental data and compared according to their statistical parameters. The main factor in controlling the drying rate was found to be the temperature. The drying rate equation was determined empirically from the characteristic drying curve. The diffusion coefficient of the Chenopodium ambrosioides leaves was estimated and varied between 1.0209 × 10^?9 and 1.0440 × 10^?8 m ²·s^?1.The activation energy was found to be 89.1486 kJ·mol^?1.     

Sorption Isotherms and Drying Characteristics of Tomato Peel Isolated from Tomato Pomace

Tomato peel was separated from pomace by sedimentation and dried in cabinet and fluidized-bed dryer at 50–70°C using 4–12 kg/m²tray load. The drying of tomato peel took place under the falling rate period and the drying behavior was well described by Page's model with coefficient of determination greater than 0.99 and standard error of 0.003–0.016. A fluidized-bed dryer was much more efficient than a cabinet dryer to dry tomato peel. The moisture adsorption isotherms of tomato peel were obtained by equilibrating above saturated salt solutions of known a _w (0.113–0.92) at 20–60°C. The data were analyzed using fifteen sorption models based on coefficient of determination, standard error, and residual plots. Modified Henderson was the best model for tomato peel with coefficient of determination >0.99, standard error <0.210, and a scattered residual plot. The net isostearic heat of sorption, estimated using the Clausius-Clapeyron equation, was 0.74–23.23 kJ/mol at 2.0–2.5% moisture content (dry basis).     

Thin-Layer Drying of Green Peas and Selection of a Suitable Thin-Layer Drying Model

The thin-layer drying of three varieties of green peas was carried out in hot air-drying chamber using an automatic weighing system at five temperatures (55–75°C) and air velocity of 100 m/min. The green peas were blanched and sulphited before drying. The variety Pb-87 dried at 60°C was judged to be best for quality on the basis of sensory evaluation and rehydration ratio. The Thomson model was found to represent thin-layer drying kinetics within 99.9% accuracy. The effective diffusivity was determined to be 3.95 × 10^?10 to 6.23 × 10^?10 m²/s in the temperature range of 55 to 75°C. The activation energy for diffusion was calculated to be 22.48 kJ/mol. The variation in shrinkage exhibited a linear relationship with moisture content of the product during drying. The Dincer number at drying air temperature 60°C and drying air velocity 100 m/min was determined to be 2,838,087. The difference between temperatures of drying air and that of green pea kernels was found to decrease with drying time for all the drying temperatures taken for investigation.     

SPRAY DRYING DYNAMIC MODELING WITH A MECHANISTIC MODEL

ABSTRACT

In this work we suggest the dynamic modeling of a spray dryer considered as a series of well-stirred dryers. That is, a series of dryers in which the output variables are equal to the state variables. The state equations were obtained from the heat and water mass balances in product and air. Additionally, heat and water mass balances in interface jointly with water equilibrium relation between product and air were considered. A pilot spray dryer was modeled assuming one, two, five and 20 well stirred steps. Low-fat milk with 10–20% of solids was dried at different inlet air temperatures (120–160°C), air flow rate of 0.19 kg dry air s^?1 and different feed rates (1.4 ? 4.2 × 10^?4 kg dry solids s^?1). Stationary result showed that the model predicts the experimental air outlet temperature, at different inlet conditions with a maximum deviation of 6°C. The dynamic simulation reproduce the experimental one with moderate accuracy. Experimental dynamic showed that the pilot plant spray dryer has a well-stirred process behavior. The model represents a method for estimate outlet product moisture as function of the outlet air temperature. This has application for automatic control because there is not an easy way to measure on-line measure the outlet product moisture content.     

Analysis of the Shrinkage Effect on Mass Transfer During Convective Drying of Sawdust/Sludge Mixtures

Convective drying of wastewater sludges and sawdust/sludge mixtures was studied. The first part of this work was an experimental study performed in a cross-flow convective dryer using 500 g of wet material extruded through a disk with circular dies of 12 mm. The results showed that the sawdust addition has a positive impact on the drying process from a mass ratio of 2/8, on a dry basis, with observed drying rates higher than the original sludge. The second part of this work consisted of developing a drying model in order to identify the internal diffusion coefficient and convective mass transfer coefficient from the experimental data. A comparison was made between fitted drying curves, well represented by the Newton's model, and the analytical solutions of the diffusion equation applied to a finite cylinder. Variations of dimensional characteristics, such as the volume and exchange surface of the sample bed, were obtained by X-ray tomography. This technique allowed us to confirm that shrinkage, which is an important phenomenon occurring during sludge and sawdust/sludge mixture drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by mixing and sawdust addition. The internal diffusion coefficient changed from 7.77 × 10^?9 m²/s for the original sludge to 7.01 × 10^?9 m²/s for the mixed sludge and then increased to 8.35 × 10^?9 m²/s for the mixture of a mass ratio of 4/6. The convective mass transfer coefficient changed from 9.70 × 10^?8 m/s for the original sludge to 8.67 × 10^?8 m/s for the mixed sludge and then increased to 12.09 × 10^?8 m/s for the mixture of a mass ratio of 4/6. These results confirmed that sawdust addition was beneficial to the sludge drying process as the mass transfer efficiency between the air and material increased. Reinforcing the texture of sludge by adding sawdust can increase the drying rate and decrease the drying time, and then the heat energy supply will be reduced significantly. The study also showed that neglecting shrinkage phenomenon resulted in an overestimation for the internal diffusion coefficient for the convective drying of sludges and sawdust/sludge mixtures.     

A New Model and Quality of Unfrozen and Frozen Cooked Rice Dried in a Microwave Vibro-Fluidized Bed Dryer

This study aimed to develop a suitable drying model for microwave vibro-fluidized bed drying in a single-mode applicator (MVFB-SMA drying) of cooked rice with and without prefreezing treatment and to investigate the effects of prefreezing treatment and drying temperature (110–185°C) on quality of dried cooked rice. During the process of drying cooked rice from 60 to 10% (wet basis), results indicated that drying rate increased, whereas drying time decreased with prefreezing treatment and increased drying temperature. The drying rate and drying time of unfrozen and frozen cooked rice ranged from 0.196 to 0.497 g water/g dry matter/min and 0.228 to 0.554 g water/g dry matter/min; and from 7 to 2.5 min and 5.5 to 2 min, respectively. A new model was proposed in this study (MR = exp(?k t ⁿ ) + bt + c) to compare with 11 commonly used drying models. The new model describes the MVFB-SMA drying data most satisfactorily. The values of effective diffusivity were between 1.70 × 10^?7 and 5.72 × 10^?7 m²/s for the unfrozen sample and between 1.99 × 10^?7 and 5.86 × 10^?7 m²/s for the frozen sample. Their activation energy values were 23.66 and 21.19 kJ/mol, respectively. Prefreezing treatment provided a whiter product with a less uniform porous structure and higher bulk density. Slower ability to rehydrate was also observed for the frozen cooked rice dried at 160 and 185°C. An increase in drying temperature resulted in changes in whiteness, microstructure, bulk density, and rehydration capability. No prefreezing treatment and drying at 160°C seemed to be the optimal process condition for cooked rice, ensuring whiteness, a porous structure, low bulk density, and high rehydration capability.     

Microwave Drying Kinetics of a Thin-Layer Liquorice Root

Liquorice root (LR) (Glycyrrize glabra) is known as a sweetener and medicine plant. Drying kinetics of LR with initial moisture content of 49.5% (wet basis (w.b)) were experimentally investigated in a microwave drying system. The drying experiments were carried out at different drying temperatures (40, 45, 50, and 55°C) and microwave power levels (250, 500 and 750 W). Several models from literature were selected to fit the experimental data. The fit quality of models was evaluated using the coefficient of determination (R²), sum square error (SSE), and root mean square error (RMSE). A new model has been proposed for LR drying in the microwave drying. This new model best describes the experimental data for LRs. The activation energy was calculated to be 46.807 kJ/mol and effective diffusivity ranged from 2.9 × 10^?9 to 5.41 × 10^?9 m²/s, depending on drying temperatures at constant microwave power level.     

Drying with Chemical Reaction in Cocoa Beans

Desirable flavor qualities of cocoa are dependent on how the cocoa beans are fermented, dried, and roasted. During fermentation and drying, polyphenols such as leucocyanidin and apecatechin are oxidized by polyphenols oxidase to form o-quinone, which later react nonenzymatically with a hydroquinone in a condensation reaction to form browning products and moisture. The objective of this article is to model the cocoa beans drying together with the browning reaction. A Luikov drying model for the moisture and a simple Fick's law diffusion model combined with first-order reactions for both the enzymatic oxidation and nonenzymatic condensation reactions were constructed. Both models were used to identify moisture diffusivity coefficient and total polyphenols diffusivity in cocoa beans from experimental drying and polyphenols degradation data and published kinetic data of the reactions. The theoretical drying model fitted the experimental cocoa bean drying curves with low mean square of residuals. The polyphenols diffusion and reaction model also fitted the experimental polyphenols degradation curves with minimum mean residual squares. The rate of polyphenols degradation in the cocoa beans increases at higher temperature and higher relative humidity. This is because the increasing reaction rate of polyphenols oxidation reaction as well as higher moisture diffusion at higher relative humidity and temperature. The effective moisture diffusivity in cocoa beans is estimated to be between 8.194 × 10^?9 and 8.542 × 10^?9 m²·s^?1, which is of the same order of magnitude as published data. The effective total polyphenols diffusivity is estimated to be between 8.333 × 10^?12 to 1.000 × 10^?11 m²·s^?1 with minimum mean residual squares. It is three orders of magnitude less than the estimated moisture diffusivity because of the larger polyphenols molecules. The estimated polyphenols diffusivity is very close to those published in the literature for sorption and ultrafiltration processes.