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%.     

The Effect of Path Diffusion on The Effective Moisture Diffuslvlty in Carrot Slabs

In order to evaluate the effect of path diffusion on the average moisture diffusivity in carrot. drying curves for different shaves (slices and cylinders) and temperatures of 50, 60 and 70°C were ohtained takine into consideration the use of an average leneth of carrot sample (slice thickness or the cylinder radio). The. results showed significant differences betuecn radial and axial average diffusivities. Significant differences were also observed between core and annular diffusivity. The experimenta1 drying curves did not show enough evidence on the effect of drying temperature on the average moisture diffusivity.     

The Effect of Path Diffusion on The Effective Moisture Diffuslvlty in Carrot Slabs

ABSTRACT

In order to evaluate the effect of path diffusion on the average moisture diffusivity in carrot. drying curves for different shaves (slices and cylinders) and temperatures of 50, 60 and 70°C were ohtained takine into consideration the use of an average leneth of carrot sample (slice thickness or the cylinder radio). The. results showed significant differences betuecn radial and axial average diffusivities. Significant differences were also observed between core and annular diffusivity. The experimenta1 drying curves did not show enough evidence on the effect of drying temperature on the average moisture diffusivity.     

Determination of appropriate effective diffusivity for different food materials

Effective diffusivity is the most important key parameter needed in the analysis, design, and optimization of heat and mass transfer during food drying process. In general, two types of effective diffusivities are used to develop the mathematical modeling of food drying, namely, moisture-dependent effective diffusivity (MDED) and temperature-dependent effective diffusivity (TDED). However, no study has extensively investigated which effective diffusivity is more accurate in predicting drying kinetics. The main goal of this study is to determine the appropriate effective diffusivity for predicting the drying kinetics. Drying models were developed for different fruits and vegetables based on moisture-dependent and temperature-dependent effective diffusivities. COMSOL Multiphysics, a finite element-based engineering simulation software is used to solve the coupled heat and mass transfer equations. 3D moisture profiles were developed to investigate the spatial moisture distribution during drying. Extensive experimental investigation on five types of fruits and vegetables was conducted and results were compared with the simulated results. The experiments were repeated thrice, and the average of the moisture content at each value was used for constructing the drying curves. Close agreement between experimental and simulated results validates the models developed. It was observed that the moisture profile and temperature profile in case of MDED were more closely fitted with the experimental results. For all fruits and vegetables, the moisture ratio with MDED was significantly lower than moisture ratio with TDED. This finding confirms that the MDED is more accurate for predicting kinetics in food drying. Moreover, the moisture ratio of apple was lowest whereas pear showed the highest moisture ratio. On the other hand, carrot showed a considerably lower moisture ratio compared to potato.     

The Moisture Migration Behavior of Plasticized Starch Biopolymer

Using plasticized starch pellets as a precursor for making thermoformed products is a commercially viable and profitable idea. However, drying of plasticized starch is quite complex in nature, partly due to the synergistic interactions between starch and plasticizers in the presence of water. The migration of water from starch pellets plasticized by two components, glycerol and xylitol, at three different temperatures was investigated in the present work. Evidence for synergistic interaction between plasticizers and water within starch is shown by the reduced effective moisture diffusivities and moisture migration fluxes at different overall plasticizer concentrations. In addition, the effective moisture diffusivities showed stronger dependence on moisture concentration and the plasticizer molecular weight even though the moisture flux was comparable. The drying process was characterized by two effective diffusion coefficients (D ₁, D ₂) and, interestingly, the coefficients were an order of significance apart. The Peleg model was investigated for predicting the drying behavior and it is shown that the Peleg constants k ₁ and k ₂ increase with temperature. k ₂, Which is related to material structure and morphology, showed comparable modification by addition of plasticizers, indicating that plasticizers were able to modify the fundamental structure, and xylitol showed greater average k ₂ values than glycerol. Further, because k ₁ is related with moisture diffusivity, the effect of temperature on diffusivity was interpreted using the Arrhenius relationship. The activation energy values confirm that plasticizers can lock in water within the new structure. Overall, the larger structure of xylitol showed better stability in controlling moisture diffusivities and migration fluxes. These findings can provide better insights in designing and controlling the vapor barrier properties of starch-based packaging materials.     

Comparative study of moisture absorption and dimensional stability of Chinese cedar wood with conventional drying and superheated steam drying

The effects of drying methods on equilibrated moisture content (MC) and swelling efficiency of Chinese cedar (Cryptomeria fortunei) wood were studied in this paper. Drying experiments were conducted with conventional (CON) drying and superheated steam (SHS) drying under atmospheric pressure. Specimens were equilibrated at two environment conditions to measure moisture and dimensional changes, and then the moisture excluding efficiency (MEE) and antiswelling efficiency (ASE) were determined. Results showed that the equilibrated MC of artificial-dried wood was lower than control samples (air drying), and the equilibrated MC of wood with SHS drying was lower than that with CON drying, which indicated that MEE was enhanced in SHS drying process. Similar results were found in swelling efficiency and ASE of artificial-dried wood and the control. The mechanism was studied by dynamic mechanical analysis (DMA) and X-ray diffraction analysis (XRD). The DMA results showed that both of relative storage modulus and relative loss modulus were the highest for SHS-dried wood and the lowest for the control samples. As for the crystalline structure assessed by changes of XRD, the results showed that the cellulose crystallinity and crystallite size of Chinese cedar wood with SHS drying were the highest, and control specimens were the lowest. All the analyses showed that Chinese cedar wood with low hygroscopic and high dimensional stability could be gotten through SHS drying process.     

Color Changes of Birch Wood During High-Temperature Drying

In low-temperature drying, a high drying rate has been found to be adequate for silver birch (Betula pendula) and European white birch (B. pubescens) timber as far as wood colour is concerned. During high-temperature drying, however, birch timber darkens significantly if steam is used as the drying medium. The objective of this research was to study the effects of drying force (wet-bulb depression), timber thickness, and initial moisture content on the color of high-temperature-dried birch wood. The reflectance spectrum of wood was measured and transformed to the CIEL?a?b? color scale.

The increase in drying force increased the lightness and decreased the redness and the yellowness of wood. At the same time, the difference in color between the surface layer and the interior of boards increased. Increase in thickness and in initial moisture content increased the difference in color between the surface and the interior of boards. Pretreatment of timber with water soaking decreased the difference in color between the surface layer and the interior of boards when low drying force was used, but this difference was increased when high drying force was used.     

Some Considerations In Simulation Of Superheated Steam Drying Of Softwood Lumber

ABSTRACT

A mathematical model for high-temperature drying of softwood lumber with moist air has been modified and extended to simulate wood drying with superheated steam. In the simulation, differences between the two types of drying are considered, these include: external heat and mass transfer processes and calculation of equilibrium moisture content. The external mass transfer coefficient in the perheated steam drying was found to be much higher than that in the moist air drying, however, the heat ransfer coefficients for these two cases were of the same order. The predicted drying curves and wood temperatures from the superheated steam drying model were compared with experimental data and there was close agreement. Further studies will apply the model to development of commercial drying schedules for wood drying with superheated steam.     

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.     

Effective Diffusivity and Evaporative Cooling in Convective Drying of Food Material

This article presents mathematical models to simulate coupled heat and mass transfer during convective drying of food materials using three different effective diffusivities: shrinkage dependent, temperature dependent, and the average of those two. Engineering simulation software COMSOL Multiphysics was utilized to simulate the model in 2D and 3D. The simulation results were compared with experimental data. It is found that the temperature-dependent effective diffusivity model predicts the moisture content more accurately at the initial stage of the drying, whereas the shrinkage-dependent effective diffusivity model is better for the final stage of the drying. The model with shrinkage-dependent effective diffusivity shows evaporative cooling phenomena at the initial stage of drying. This phenomenon was investigated and explained. Three-dimensional temperature and moisture profiles show that even when the surface is dry, the inside of the sample may still contain a large amount of moisture. Therefore, the drying process should be dealt with carefully; otherwise, microbial spoilage may start from the center of the dried food. A parametric investigation was conducted after validation of the model.     

Simulation of Convective Drying of Wet Porous Materials

Abstract

A simulation model for convective drying of wet porous materials was developed. For the simulation, we measured the moisture diffusivities within them and applied a modified Dubinin-Astakhov equation to the moisture sorption data for a membrane filter. The simulation results not accounting for internal mass transfer resistance were quite different from the experimental ones. The drying characteristics calculated by a shrinking core model with effective moisture diffusivity represented a much lower drying rate and much higher temperatures, respectively, than the experimental ones. This meant that we must consider the plural moisture transport mechanisms within the samples. Therefore, we calculated the drying rate and temperatures with an apparent overall mass transfer coefficient damping with a decrease in the moisture content. The results accounting for the hygroscopic effects broadly agreed with the experimental ones by the evaluation.     

DETERMINATION OF MOISTURE DIFFUSIVITY OF RED DELICIOUS APPLE TISSUES BY THERMOGRAVIMETRIC ANALYSIS

ABSTRACT

Moisture diffusivity is an important parameter needed in the analysis, design and optimization of drying processes for food and other materials. Published data on moisture diffusivities of food materials are scarce and, sometimes, inconsistent due to a lack of a precise and repeatable experimental technique. Most experimental data are limited to low and moderate drying temperature (<70°C), whereas in the food industry hot air of up to 100°C is usually used in the falling rate period to speed up the drying processes. In this study, the effective moisture diffusivities of Red Delicious apple tissues were determined from drying curves produced with a Perkin Elmer thermogravimetric analyzer, using the slope method. The experiments were conducted at lour temperatures 60, 80, 100 and 120°C. Two well defined falling rate periods were observed. The effective moisture diffusivity, for the four temperature levels ranged from 3.2 × 10^?7 to 7.9 × 10^?8 m²/s for the first falling rate period and 3.8 × 10^?8 to 4.7 × 10^?8 m²/s for the second falling rate period. The temperature dependence of the effective diffusivity can be described with an Arrhenius-type equation.     

MODELLING OF STRESS DEVELOPMENT DURING DRYING AND RELIEF DURING STEAMING IN PINUS RADIATA LUMBER

ABSTRACT

A one-dimensional stress model was proposed for drying of radiata pine lumber, which has considered wood moisture shrinkage, instantaneous stress-strain relationships, mechano-sorptive creep, time-induced creep and temperature effects. In addition, wood hardening behaviour in the plastic region and differences between stress increase and decrease have been taken into account. The proposed Stress model can predict stress development and relief in a drying cycle once the required wood mechanical and Theological properties have been quantified.

Drying experiments were performed to dry Pinus radiata sap wood boards of 100×40×590 mm in a tunnel dryer. In the experiment, wood temperature, moisture content gradient and residual stress through board thickness were measured. The drying cycle included HT drying, cooling and final steam conditioning. The measured stress patterns were in agreement with the model predictions. However, more accurate calculations will be made once the detailed experimental data for radiata pine wood mechanical and rheological properties are available.     

Finite element simulation for coffee (Coffea arabica) drying

This paper describes moisture diffusivity, shrinkage, equilibrium moisture content and finite element simulated drying of coffee. The moisture diffusivities in different components of parchment coffee were determined by minimizing the sum of square of deviations between the predicted and the experimental values of moisture contents during thin layer drying under controlled conditions of drying air temperature and relative humidity. The drying of coffee bean and parchment was conducted in thin layers at a temperature of 40, 50 and 60 °C with relative humidity in the range of 14–25%. The mean diffusivity values of coffee bean and parchment are related to the temperatures and are expressed by Arrhenius-type equations. The moisture diffusivities of parchment are lower than those of the coffee bean. The shrinkage of coffee bean derived from experiments is expressed as a function of moisture reduction. GAB model is sufficient for the prediction for sorption isotherm of parchment coffee and the parameters of the GAB model are a function of temperature and it is expressed by Arrhenius-type equations. Sensory evaluation of the coffee dried at 40, 50 and 60 °C shows that the overall acceptance by coffee cupping test and the concentration of caffeine is within the acceptable limit. A two-dimensional finite element model was developed for simulate moisture diffusion during drying process of parchment coffee. The finite element model was programmed in Compaq Visual FORTRAN version 6.5. The model simulates the moisture contents in different components of parchment coffee well and it provides a better understanding of the transport processes in the different components of the parchment coffee.     

Superheated Steam Drying of Single Wood Particles: Modeling and Comparative Study with Hot Air Drying

A deterministic model is developed to describe the superheated steam drying process of single wood particles. A comparison between calculated data and experimental observations infers that the moisture‐dependent effective diffusivity is suitable to be used for beechwood material drying. To reduce the computational cost of the deterministic drying model, a semi‐empirical model is proposed within the framework of a reaction engineering approach (REA). The validity of the proposed model is checked by comparing against experimental data from literature. The experimental drying behavior may fairly be reflected by the reduced model. Due to the simplicity and predictive ability of the REA model, this semi‐empirical model can be implemented to describe heat and mass transfer between a population of single particles and a drying agent in dryer models.     

A SHORT-CUT METHOD FOR DETERMINING CONCENTRATION DEPENDENT DIFFUSIVITY IN LIQUID FOODS AND POLYMER SOLUTIONS FROM REGULAR REGIME DRYING CURVES

A simple method for determining concentration (water or solvent content) dependent diffusivity in liquid foods and polymer solutions from the regular regime drying curve was developed on the basis of the power-law diffusion model. The method was first tested to the drying data generated from numerical solutions of the diffusion equation with various types of concentration dependent diffusivities. The present method was found to be very simple yet accurate compared with the previous methods. Then, the drying rates of various sugar solutions experimentally obtained were analyzed on the basis of the present method to determine the moisture content dependent diffusivities.     

A SHORT-CUT METHOD FOR DETERMINING CONCENTRATION DEPENDENT DIFFUSIVITY IN LIQUID FOODS AND POLYMER SOLUTIONS FROM REGULAR REGIME DRYING CURVES

A simple method for determining concentration (water or solvent content) dependent diffusivity in liquid foods and polymer solutions from the regular regime drying curve was developed on the basis of the power-law diffusion model. The method was first tested to the drying data generated from numerical solutions of the diffusion equation with various types of concentration dependent diffusivities. The present method was found to be very simple yet accurate compared with the previous methods. Then, the drying rates of various sugar solutions experimentally obtained were analyzed on the basis of the present method to determine the moisture content dependent diffusivities.     

太阳能-除湿-常规分段组合木材干燥工艺优化

为降低木材干燥能耗,通过对杨木进行太阳能-除湿-常规分段组合干燥,即含水率40%以上采用太阳能进行预干,25%—40%采用除湿干燥,25%以下采用常规干燥,并与常规干燥进行干燥能耗和木材质量的对比。结果表明,分段组合干燥比常规干燥节能19%左右,而且干燥质量和常规干燥基本一致。分段组合干燥充分利用了三者各自的优势,从而达到节能的目的。     

THE INFLUENCE OF COMPRESSION WOOD ON THE DRYING CURVES OF PINUS RADIATA DRIED IN DEHUMIDIFIER CONDITIONS

ABSTRACT

Measurements of drying rate of Pinus radiata at 55°C and 30% RH are presented. The data, which has been used to establish empirical models for P. radiata under dehumidifier drying conditions, was obtained in four drying runs in a drying tunnel, each yielding detailed drying curves for twelve sample sapwood boards of size 350 × 100 × 50 mm. Compression wood was found to have a significant effect on the drying rate curve, giving lower drying rates at 40–100% MC. This effect is interpreted through the use of a numerical multiple-mechanism two-zone model and quantified by using best-fit diffusion parameters from an isothermal diffusion model. A positive correlation was discovered between the moisture diffusion coefficient and initial moisture content, a strong indicator for the presence of compression wood. In the two-zone model, the compression wood effect was replicated by using a tenfold decrease in permeability to liquid flow. Attributes of compression wood that could cause reduced permeability include an increased proportion of latewood, narrower lumen, and a scarcity of bordered pits on the radial walls of longitudinal tracheids.     

Simulation of Convective Drying of Wet Porous Materials

A simulation model for convective drying of wet porous materials was developed. For the simulation, we measured the moisture diffusivities within them and applied a modified Dubinin-Astakhov equation to the moisture sorption data for a membrane filter. The simulation results not accounting for internal mass transfer resistance were quite different from the experimental ones. The drying characteristics calculated by a shrinking core model with effective moisture diffusivity represented a much lower drying rate and much higher temperatures, respectively, than the experimental ones. This meant that we must consider the plural moisture transport mechanisms within the samples. Therefore, we calculated the drying rate and temperatures with an apparent overall mass transfer coefficient damping with a decrease in the moisture content. The results accounting for the hygroscopic effects broadly agreed with the experimental ones by the evaluation.