Mass Transfer in the Celery Slice: Effects of Temperature,Moisture Content,and Density on Water Diffusivity

Abstract

Statistical tests were applied to determine the effects of temperature, moisture content, density, and porosity of material on the effective moisture diffusion coefficient during convective drying of root celery. In biological materials with colloidal capillary-porous structure (like root celery), which shrink considerably during drying and show high heterogeneity, the effective water diffusion coefficient depends not only on material temperature and moisture content, but also on its density. It was found that statistical tests can be applied to predict which independent variables should describe the water diffusivity in colloidal capillary-porous materials. A mathematical model of the effective water diffusion coefficient in root celery was formulated as Arhenius-type equation with moisture content of the raw material, its temperature and density as independent variables.     

The Comparison of Two Models of Convective Drying of Shrinking Materials Using Apple Tissue as an Example

Modeling of drying of capillary-porous materials is a mathematically complex problem. It takes into consideration simultaneous heat and mass transfer inside the material with physicochemical properties changing during the drying process. Modeling of the process mentioned above consists of describing the heat and mass transfer balances by means of differential equations. Moisture diffusion coefficient as a function of moisture content and temperature of the material is a crucial parameter that controls the process. An additional problem occurs when moving boundary of the shrinking material is taken into account. In the present work, the identification of diffusion coefficient as a function of moisture content and temperature on the basis of two different models is shown. The two models include the Pakowski model (defined in the stationary coordinates) and the Kechaou model (defined in moving coordinates). Experimental data necessary to verify the models were obtained on the basis of series of tests for different boundary conditions performed on an apple tissue. During the drying process, samples of apple undergo significant volumetric shrinkage. In this article, the comparison of the two models describing the convective drying process of shrinking material is presented together with the comparison of the identified moisture diffusion coefficient.     

The Comparison of Two Models of Convective Drying of Shrinking Materials Using Apple Tissue as an Example

Modeling of drying of capillary-porous materials is a mathematically complex problem. It takes into consideration simultaneous heat and mass transfer inside the material with physicochemical properties changing during the drying process. Modeling of the process mentioned above consists of describing the heat and mass transfer balances by means of differential equations. Moisture diffusion coefficient as a function of moisture content and temperature of the material is a crucial parameter that controls the process. An additional problem occurs when moving boundary of the shrinking material is taken into account. In the present work, the identification of diffusion coefficient as a function of moisture content and temperature on the basis of two different models is shown. The two models include the Pakowski model (defined in the stationary coordinates) and the Kechaou model (defined in moving coordinates). Experimental data necessary to verify the models were obtained on the basis of series of tests for different boundary conditions performed on an apple tissue. During the drying process, samples of apple undergo significant volumetric shrinkage. In this article, the comparison of the two models describing the convective drying process of shrinking material is presented together with the comparison of the identified moisture diffusion coefficient.     

INFLUENCE OF THE DRYING MEDIUM PARAMETERS ON DRYING INDUCED STRESSES

A thermomechanical model of drying of capillary-porous materials whose material constants depend on moisture content and temperature is presented in the paper. The finite element method is used for the solution of two-dimensional problem of convective drying of a prismatic bar. The moisture distributions, temperature distributions, drying induced strains and stresses for various drying medium parameters are determined. The effect of these parameters on moisture distribution and in particular on drying induced stresses is discussed.     

Estimation of the Effect of Shape and Temperature on Drying Kinetics Using MLP

The kinetics of drying is described in the article using artificial neural networks (multilayer perceptron MLP). Drying curves for vegetables are possible to obtain theoretically on the basis of the equations of mass transfer in a porous material. A key role in these equations is played by the effective coefficient of water diffusion in the form of liquid, vapor or jointly as liquid and vapor. The diffusion coefficient which depends both on moisture content in the material and temperature should be determined experimentally. The drying kinetic curve in this article is treated as a time series dependent on the state of material prior to drying and on the constant K characterizing process parameters such as drying temperature and describing the material, e.g., its shape and moisture content. Constant K characterizes the analyzed material from the drying point of view because it contains a diffusion coefficient and depends on the shape of material. The following materials were analyzed: beetroot and potato dried in the form of cubes, slices, chips, and strips. Experiments were carried out in a laboratory oven dryer at process temperature 50, 60, 70, 90, and 106°C.     

OPTIMIZATION OF THE VACUUM DEHYDRATION OF CELERY (APIUM GRAVEOLENS) USING THE RESPONSE SURFACE METHODOLOGY

The response surface methodology (RSM) was used to optimize the vacuum dehydration conditions of celery. The independent variables were drying temperature (65 to 75°C), vacuum pressure (16 to 20 in Hg) and slice thickness (1 to 3 mm). The responses were rehydration ratio, bulk density, final moisture content and over-all acceptability rating. Statistical analysis revealed that temperature, vacuum pressure and slice thickness significantly affected (90% confidence interval) bulk density and final moisture content. Rehydration ratio on the other hand, was affected only by temperature and slice thickness while over-all acceptability rating was not significantly affected by any of the three variables. Contour plots for each of the responses were used to generate an optimum area through superimposition. Model validation was conducted using separate experiments at optimum conditions. Resulting drying curves at optimum conditions showed that vacuum drying of celery occurred in the falling rate period.     

INFLUENCE OF THE DRYING MEDIUM PARAMETERS ON DRYING INDUCED STRESSES

ABSTRACT

A thermomechanical model of drying of capillary-porous materials whose material constants depend on moisture content and temperature is presented in the paper. The finite element method is used for the solution of two-dimensional problem of convective drying of a prismatic bar. The moisture distributions, temperature distributions, drying induced strains and stresses for various drying medium parameters are determined. The effect of these parameters on moisture distribution and in particular on drying induced stresses is discussed.     

OPTIMIZATION OF THE VACUUM DEHYDRATION OF CELERY (APIUM GRAVEOLENS) USING THE RESPONSE SURFACE METHODOLOGY

The response surface methodology (RSM) was used to optimize the vacuum dehydration conditions of celery. The independent variables were drying temperature (65 to 75°C), vacuum pressure (16 to 20 in Hg) and slice thickness (1 to 3 mm). The responses were rehydration ratio, bulk density, final moisture content and over-all acceptability rating. Statistical analysis revealed that temperature, vacuum pressure and slice thickness significantly affected (90% confidence interval) bulk density and final moisture content. Rehydration ratio on the other hand, was affected only by temperature and slice thickness while over-all acceptability rating was not significantly affected by any of the three variables. Contour plots for each of the responses were used to generate an optimum area through superimposition. Model validation was conducted using separate experiments at optimum conditions. Resulting drying curves at optimum conditions showed that vacuum drying of celery occurred in the falling rate period.     

Numerical Simulation of Vacuum Drying by Luikov's Equations

A two-dimensional mathematical model was developed to simulate coupled heat and mass transfer in apple under vacuum drying. Luikov's equations are the governing equations in analyzing heat and mass diffusion problems for capillary-porous bodies. The model considers temperature- and moisture-dependent material properties. The aim of this study is to analyze the influence of some of the most important operating variables, in particular, pressure and temperature of drying air, on the drying of apple. The resulting system of unsteady-state partial differential equations has been solved by a commercial finite element method (FEM) package called FEMLAB (COMSOL AB, Stockholm, Sweden). Simulations, carried out in different drying conditions, showed that temperature is more effective than air pressure in determining the drying rate. A parametric study was also carried out to determine the effects of heat and mass transfer coefficients on temperature and moisture content distributions inside apple during vacuum drying. A comparison between the theoretical predictions and a set of experimental results reported in the literature showed very good agreement, especially during the first 4,200 s, when experimental data and theoretical predictions overlapped and relative errors never exceeded 2%.     

The System of Correlations Between Moisture,Shrinkage, Density,and Porosity

The system of four correlations, establishing relationship between moisture, shrinkage, density, and porosity in three-phase capillary-porous materials was introduced. It is based on the fundamental relationship between these variables and useful for real-time estimation of density and porosity from measurable moisture content and shrinkage.     

A New Correlation for the Estimation of Moisture Diffusivity in Corn Kernels from Drying Kinetics

ABSTRACT

The modelisation of cereal drying kinetics is more, and more often performed by the diffusion equation (Fick's law) Eor homogeneous materials rather than lumped or semi-empirical equations. The heterogeneity of the material is accounted for by the use of an effective diffusivity the prediction of which is essential for the determination of the functional relationship between diffusion coefficient and arain moisture content and temperature. For this dependence, the method of resolution may be analytical or numerical. In this study, the estimation of diffusion coefficient is based on drying curves obtained with arains in the ranae of initial moisture content of 18-509 and a temperature of 50:120??. The important result corresponds to the finding that the moisture diffusivity is a function not only of variabies of the state i.e. moisture content and temperature, but also of the initial moisture content as in the following : 'D = P4g X, exp(8 X ). AD and B are both dependent on temperature     

茭白片热风对流干燥模型与传质性能

为了探讨茭白干燥的传递特性,在对流热风干燥实验装置中进行了茭白片薄层干燥实验,研究了干燥温度、片的厚度对干燥过程的影响,将试验的水分比与数学模型进行了拟合,计算了不同温度下的水分扩散系数,并关联了其与干燥温度的关系.结果表明:干燥温度对干燥过程影响显著,薄片有利于水分扩散:用Page模型来描述茭白片热风干燥动力学令人满意;茭白片厚度为0.003m时,随风温升高,水分扩散系数从3.440×10-9 m2·s-1增大到6.357×10-9m2·s-1,并符合阿累尼乌斯方程,活化能为27.86 kj·mol-1.相同温度下,物料中水分的扩散系数基本不受厚度影响.     

Stresses Generated During Convective and Microwave Drying

An outline of the mechanistic model of convective and microwave drying of saturated capillary-porous materials is presented. The model was derived in the framework of irreversible thermodynamics. Particular attention is devoted to construction of the term describing the power of microwave radiation absorbed per unit volume, which is converted into internal heat source. The qualitative difference in distribution of temperature, moisture content, and the drying-induced stresses in materials under convective and microwave drying is illustrated in the examples of cylindrical kaolin samples. The diagrams of acoustic emission are taken off on-line from these samples in order to illustrate the development of material destruction caused by the stresses induced during both convective and microwave drying.     

DENSITIES, SHRINKAGE AND POROSITY OF SOME VEGETABLES DURING AIR DRYING

Bulk density, particle density, shrinkage and porosity were experimentally determined at various moisture content during air drying for apple, carrot and potato cubes. A simple mathematical model was used to predict the above properties versus material moisture content. Four parameters were incorporated in the model: enclosed water density, dry solids' density, bulk density of dry solids, and volume-shrinkage coefficient. The model was fitted to experimental data satisfactorily, and the parameters were estimated. The influence of varying drying conditions was also investigated.     

Moisture Diffusivity in Food and Biological Materials

The spatial distributions of water content and temperature inside moist food or biological materials (native or manufactured) during drying are important in interpretation and prediction of quality changes. The dynamics of drying in modern devices is not simple—for instance, the process of intermittent drying—thus, a liquid diffusion model is expected to be the simplest and hopefully the very effective. In this article, some controversial aspects of the concept of the effective Fickian liquid moisture diffusivity are described and discussed. These discussions are intended to stimulate more interest in working toward a better rationalization of the liquid diffusion concept. It is suggested that such a parameter may even be called a “liquid depletion coefficient” instead to avoid confusion at the fundamental level. An improved alternative model from the effective liquid diffusion model is possible and some new ideas have been explored.     

Stresses Generated During Convective and Microwave Drying

Abstract

An outline of the mechanistic model of convective and microwave drying of saturated capillary-porous materials is presented. The model was derived in the framework of irreversible thermodynamics. Particular attention is devoted to construction of the term describing the power of microwave radiation absorbed per unit volume, which is converted into internal heat source. The qualitative difference in distribution of temperature, moisture content, and the drying-induced stresses in materials under convective and microwave drying is illustrated in the examples of cylindrical kaolin samples. The diagrams of acoustic emission are taken off on-line from these samples in order to illustrate the development of material destruction caused by the stresses induced during both convective and microwave drying.     

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.     

Variability in Transport Properties Regarding Drying Behavior for Blackbutt Timber in New South Wales

Variability is a key issue in the processing of many biological materials, in this case the drying of hardwood timber. This article reports the measurements of variability of the diffusion coefficient (a transport property), the initial moisture content, and the basic density that are relevant to the drying of blackbutt, Eucalyptus pilularis Sm, from northern New South Wales in Australia. The diffusion coefficient was quantified using a mathematical model solving Fick's second law of diffusion for mass transfer, and Fourier's law for heat transfer. The initial moisture content and the basic density were measured using experimental procedures. Specifically, within-tree and between-tree variations are reported. The coefficients of variation of the initial moisture contents and final moisture contents are 0.24 and 0.19, respectively, for within-tree variability. A similar result was found for the amount of between-tree variability. Compensating differences in the diffusion coefficients of the timber boards were a significant reason for the small dispersion of final moisture contents, despite the large variation in initial moisture contents.

An analysis of variance showed that some timber properties were affected by the board positions within trees and between trees. Circumferential and radial effects were significant for the within-tree variability of most transport properties. Moreover, principal components analysis suggested that timber boards with low densities have high initial moisture contents and high diffusion coefficients. A potential reason is that if there is less wood material per unit volume (lower density), then there is more space to be occupied by water (higher initial moisture content), and there is also less resistance to the diffusive transport of moisture (higher diffusion coefficients).     

Diffusive Model with Variable Effective Diffusivity Considering Shrinkage for Hot-Air Drying of Lightly Salted Grass Carp Fillets

A diffusion model has been developed for predicting the change of moisture content in lightly salted grass carp fillets under the consideration of shrinkage and variable volumetric effective diffusivity. The established relationship between moisture content, temperature, and effective diffusivity validated the effectiveness of considering the variable volumetric effective diffusivity. The appearance of shrinkage during drying and the shrinkage coefficient have been determined for better predicting the variation of moisture content during drying to provide a thorough theoretical basis for industrial processes.     

DENSITIES,SHRINKAGE AND POROSITY OF SOME VEGETABLES DURING AIR DRYING

Abstract

Bulk density, particle density, shrinkage and porosity were experimentally determined at various moisture content during air drying for apple, carrot and potato cubes. A simple mathematical model was used to predict the above properties versus material moisture content. Four parameters were incorporated in the model: enclosed water density, dry solids' density, bulk density of dry solids, and volume-shrinkage coefficient. The model was fitted to experimental data satisfactorily, and the parameters were estimated. The influence of varying drying conditions was also investigated.