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.     

Drying characteristics and modeling of yam slices under different relative humidity conditions

The drying characteristics of yam slices under different constant relative humidity (RH) and step-down RH levels were studied. A mass transfer model was developed based on Bi-Di correlations containing a drying coefficient and a lag factor to describe the drying process. It was validated using experimental data. Results showed that the drying air with constant RH levels of 20, 30, and 40%, temperature of 60°C, and air velocity of 1.5 m/s had an insignificant effect on drying time. This phenomenon was likely attributed to the fact that higher RH led to a rapid increase in sample’s temperature. The higher sample temperature could provide an additional driving force to water diffusion and thereby promote the moisture movement, which could minimize the negative effect of lower the drying rate in the initial drying stage. Applying air with 40% RH for 15 min in the initial stage achieved the desired color and reduced the drying time by 25% compared to the drying time under continuous dehumidification from an initial RH of 40%. Using the developed Bi-Di correlation, the estimated Biot number, effective moisture diffusivity, and mass transfer coefficient ranged from 0.1024 to 0.1182, 1.1133 × 10^?10 to 8.8144 × 10^?9 m²/s, and 1.8992 × 10^?9 to 1.7364 × 10^?7 m/s, respectively. A rather high correlation coefficient of determination (R² between 0.9871 and 0.9971) was determined between the experimental and predicted moisture contents. The present findings contribute to a better understanding of the effect of relative humidity on drying characteristics. The developed Bi-Di correlation provided a new method to determine the effective diffusivity of moisture in drying.     

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.     

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.     

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.     

Thin-Layer Drying of Flax Fiber: I. Analysis of Modeling Using Fick's Second Law of Diffusion

Thin-layer drying of moist flax fiber was performed at four temperatures of 30, 50, 70, and 100°C with a constant absolute humidity of 0.0065 kg water per kg dry air. The coefficients of diffusion of the fiber at different drying conditions were estimated by modeling the drying process using the one- to five-term solutions of the second Fick's law of diffusion. The models underestimated the drying process during the initial stages of drying and overestimated this process during the final stages. The estimated coefficient of diffusions ranged from 5.11 × 10^?9 to 1.92 × 10^?8 m²/s and linearly increased with the drying air temperature.     

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).     

Study on Convective Drying Characteristics of Dredged Sludge from Dian Lake

In this work, the thin layer drying behavior of dredged sludge from Dian Lake by convective drying methods was investigated. The results showed that the Modified Page-I model was more suitable for thin-layer drying of dredged sludge. The values of the diffusion coefficients at each temperature were obtained using Fick’s second law of diffusion, and it was varied from 6.472×10^?9 to 1.143×10^?8 m²/s when the temperature was changed from 100 to 160°C for the dredged sludge of 10 mm. When the thickness was changed from 5 to 20 mm, the diffusion coefficients were varied from 4.036×10^?9 to 2.648×10^?8 m²/s at 140°C. The activation energy of moisture diffusion was 13.1 kJ/mol.     

A Novel Alternative Method for Modeling the Effects of Air Temperature and Slice Thickness on Quality and Drying Kinetics of Tomato Slices: Superposition Technique

The effect of air temperature (AT) and slice thickness (ST) on the quality and drying kinetics of tomato slices were studied. The drying period of tomato slices to reach the moisture content of 15% (wb) ranged from 2.6 to 18.7 h. The water diffusivity, activation energy, and resistance to diffusion ranged from 1.4 × 10^?10 to 2.8 × 10^?9 m²/s, 21.25 to 23.4 kJ/mol, and from 939 to 4590 m² s/kg, respectively. Drying had a significant effect on ascorbic acid, soluble solid, acidity, and pH (P = 0.01). The ascorbic acid degradation was greatly influenced by ST. The results show that time-temperature superposition technique (TTST) was very efficient in the modeling of the drying process. The proposed TTST provides a novel alternative in curve-fitting exercise of drying data. Neural networks also showed favorable performance in estimating the drying functions.     

Drying Characteristics and Moisture Diffusivity of Distillers' Spent Grains Dried in Superheated Steam

Distillers' spent grain pellets were prepared from material with an initial moisture content of 25% (wb). These pellets were dried in pairs using superheated steam at 120°C in two orientations, horizontal and vertical. The drying characteristics, modeled by the Page equation, showed that there was a significant difference between orientations. The overall moisture diffusivity was calculated using a finite cylinder model based on Fick's law of diffusion accounting for a change in dimensions over the course of drying. The overall diffusivity values ranged from 4.08 × 10^?10 to 1.48 × 10^?8 m²/s.     

Osmotic Dehydration of Apple Cylinders: I. Conventional Batch Processing Conditions

Osmotic drying was carried out, with cylindrical samples of apple cut to a diameter-to-length ratio of 1:1, in a well-agitated large tank containing the osmotic solution at the desired temperature. The solution-to-fruit volume ratio was kept greater than 30. A modified central composite rotatable design (CCRD) was used with five levels of sucrose concentrations (34–63°Brix) and five temperatures (34–66°C). Kinetic parameters weight reduction (WR), moisture loss (ML), solids gain (SG) were considered. A polynomial regression model was developed to relate moisture loss and solids gain to process variables. A conventional diffusion model involving a finite cylinder was also used for moisture loss and solids gain, and the associated diffusion coefficients were computed. The calculated moisture diffusivity ranged from 8.20 × 10^?10 to 24.26 × 10^?10 m²/s and the solute diffusivity ranged from 7.82 × 10^?10 to 37.24 × 10^?10 m²/s. Suitable ranges of main parameters were identified for OD kinetics further study.     

Convective Drying of Wastewater Sludge: Introduction of Shrinkage Effect in Mathematical Modeling

Drying of two kinds of wastewater sludge was studied. The first part was an experimental work done in a discontinuous cross-flow convective dryer using 1 kg of wet material extruded in 12-mm-diameter cylinders. The results show the influence of drying air temperature for both sludges. The second part consisted of developing a drying model in order to identify the internal diffusion coefficient and the convective mass transfer coefficient from the experimental data. A comparison between fitted drying curves, well represented by Newton's model, and the analytical solutions of the equation of diffusion, applied to a finite cylinder, was made. Variations in the physical parameters, such as the mass, density, and volume of the dried product, were calculated. This allowed us to confirm that shrinkage, which is an important parameter during wastewater sludge drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by the air temperature and the origin of the sludge. The values of the diffusion coefficient changed from 42.35 × 10^?9 m² · s^?1 at 160°C to 32.49 × 10^?9 m² · s^?1 at 122°C for sludge A and from 33.40 × 10^?9 m² · s^?1 at 140°C to 28.45 × 10^?9 m² · s^?1 at 120°C for sludge B. The convective mass transfer coefficient changed from 4.52 × 10^?7 m · s^?1 at 158°C to 3.33 × 10^?7 m · s^?1 at 122°C for sludge A and from 3.44 × 10^?7 m · s^?1 at 140°C to 2.84 × 10^?7 m² · s^?1 at 120°C for sludge B. The temperature dependency of the two coefficients was expressed using an Arrhenius-type equation and related parameters were deduced. Finally, the study showed that neglecting shrinkage phenomena resulted in an overestimation that can attain and exceed 30% for the two coefficients.     

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.     

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.     

Kinetics and Mass Transfer during Atmospheric Freeze Drying of Red Pepper

Drying is applied for moisture removal to allow safe and extended storage. Red pepper (Capsicum annum) samples were heat pump dried in fluidized bed at different air temperatures. A slightly modified solution of the diffusion equation was used to describe the kinetics and drying rates of red pepper. The model well described the low- and medium-temperature drying processes. The determined effective mass diffusivities varied from 0.7831 to 4.0201 × 10^?9 m²/s and increased consistently with drying air temperature. The mass diffusivity was correlated to temperature by linear regression with coefficient of determination equal to 0.999 and negligible standard error.     

MASS TRANSFER AND DIFFUSION COEFFICIENT DETERMINATION IN THE WET AND DRY SALTING OF MEAT

ABSTRACT

Dehydrated salted meat is widely used in Brazil as a very important source of animal protein. The main objective of this kind of processing is water removal. initially by osmotic pressure changes and then by drying, resulting in a product with intermediate moisture levels.

In this work, mass transfer and salt diffusion in pieces of meat submitted to wet and dry salting were studied. Slabs of beef m. trapezius with an infinite plate geometry were salted in a NaCl saturated solution or in a dry salt bed, at two temperatures (10 and 20°C) and different time exposures (120 min and 96 hours). Equilibration studies were extended up to six days.

It was observed that water loss increased with salt uptake, for increasing periods of times. At 20°C the moisture loss was higher than it was at 10°C in both salting processes. On the other hand, the kinetics of salt uptake and moisture loss were of greater importance in the process of dry salting than in that of wet salting.

The salt diffusion coefficient for wet salting was 0.26 × 10^?10m²/s at20°C and 0.25 × 10^?10 m²/s at 10°C and for the dry salting the values were 19.37 × 10^?10 m²/s at 20°C and 17.21 × 10^?10 m²/s at 10°C.     

Microwave drying of wastewater sludge: Experimental and modeling study

This study investigates experimentally and using mathematical modeling the microwave drying of wastewater sludge with determination of moisture diffusivity at different drying conditions. The drying behavior was observed at different power levels (480, 840, and 1,080 W) and different initial masses (90, 120, and 150 g). The observed drying kinetics were divided into three parts: a short adaptation period, a long constant drying rate period, and a falling drying rate period. The maximum drying rate was observed during the constant rate period. Mainly, the results show that the drying rate decreases with the initial mass increase (from 0.45 kg·kg^?1·min^?1 for 90 g to 0.25 kg·kg^?1·min^?1 for 150 g) and increases with an increase in power level (from 0.15 kg·kg^?1·min^?1 at 480 W to 0.45 kg·kg^?1·min^?1 at 1,080 W). The measurement of the sample dimensions shows that shrinkage can occur and, depending on the drying conditions, it ranged between 0.42 and 0.37 of the sample initial volume. Presenting a more accurate solution of the diffusion model by incorporating shrinkage and finite dimensions of the sample is the novelty of this study. The drying conditions influenced the diffusion coefficient, which ranged from 1.53 × 10^?7 to 7.67 × 10^?7 m²s^?1. Similar to the drying rate, the diffusion coefficient was directly proportional to the power level and inversely proportional to the initial mass. Activation energy was determined using an Arrhenius relationship of the diffusion coefficient as a function of the ratio initial mass to the power level.     

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%.     

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.     

EFFECT OF INITIAL MOISTURE CONTENT ON THE THIN LAYER DRYING CHARACTERISTICS OF HAZELNUTS DURING ROASTING

ABSTRACT

Effect of initial moisture content on the thin layer drying characteristics of hazelnuts during roasting was described for a temperature range of 100-160°C, using several thin layer equations. The effective diffusivity varied from 2.8×10^?7 to 21.5×10^?7m²/s over the temperature and moisture range. Temperature dependence of the diffusivity coefficient was described by Arrhenius-type relationship. The activation energy for moisture diffusion was found to be 2703 kJ/kg, 2289 kJ/kg and 2030 kJ/kg for the initial moisture content of 12.3% db, 6.14% db, and 2.41% db, respectively. Two-term equation gave better predictions than Henderson and Pabis and Thompson equations, and satisfactorily described thin layer drying characteristics of hazelnut roasting. A generalised mathematical model with the linear temperature dependence for moistured, non-treated and pre-dried hazelnuts were also developed.