Principle and Applications of Drying Characteristic Functions

This article focuses on the concept of a 'drying characteristic function,' which is an effective way to correlate drying rate curves for convective drying of homogeneous nonporous, hygroscopic porous and non-hygroscopic porous materials. The characteristic function, obtained bv a certain transformation of a drying rate curve, is independent of drying conditions and hence characterizes the transport kinetics in the material. The principle and some applications of the functions are reviewed. The first application is estimation of dryinge rate curves. Because any drying rate curve can be transformed into the characteristic function and vice versa, the drying rate can be estimated for various drying conditions from a single drying experiment. Another aoolication is determination of the moisture diffusivity. Using the 'flux ratio method' an analytical expression of the characteristic function can be obtained for any aiven moisture diffusivity. The exprcssion enables one to determine the moisture diffusivity for a wide range of moisture content from a single drying experiment.     

A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

ABSTRACT

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

ABSTRACT

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

Characteristic Drying Curves of Cocoa Beans

ABSTRACT

The characteristic drying curves of cocoa beans are determined by using a tunnel drier where conditioned air passes a single cocoa berm suspended from an electronic balance in the test section. Weight loss, and temperatures of air, testa and nib of the cocoa bean is monitored on personal computers. The nornmalised drying rate versus the normalised moisture content is regressed by least square method to fit a new polynomial model for the penetration falling rate period and a linear model for the regular regime falling rate period. It can be concluded that there are three drying periods for cocoa beans namely the constant drying rate period, the penetration falling rate period and the regular regime falling rate period. The polynomial model estimates the penetration period quite well whereas the linear model estimates the regular regime quite well as well. There is no observable influence of relative humidity and air temperature on the characteristic drying curve of cocoa beans. However, the air velocity seems to have some influence on the curve.     

DRYING OF PARTICULATE SOLIDS: DETERMINATION OF THE CHARACTERISTIC CURVE OF BROWN COAL.

ABSTRACT

Variation on the rate of drying of brown coal powder as a function of environmental and intrinsic properties has been studied in a gravimetric laboratory-scale drier.

Raw data have been treated to correlate the constant rate of drying and the equilibrium moisture content as a function of flow rate and temperature of the gas phase, particle size and surface additives. The characteristic drying curve occurs when the reduced rate of drying is plotted as a function of a dimensionless moisture potetial.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

DETERMINATION METHOD OF VARIABLE DIFFUSION COEFFICIENTS OF HYGROSCOPIC MATERIAL FROM DRYING RATE CURVES OF THE SINGLE PARTICLE

ABSTRACT

The concentration dependency of diffusion coefficients of hygroscopic materials can usually only be calculated by cumbersome experimental techniques.

Taking the diffusion rate in the fictious steady state with the same mean moisture concentration as in the regular regime of the drying process of a spherical hygroscopic particle (which means the drying period not influenced by initial moisture distributions) into account, a simple method is proposed to estimate the dependency of diffusion coefficients on the moisture concentration for hygroscopic materials from drying rate curves of the single particle.     

A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

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.     

Highfrequency Drying of Porous Material

ABSTRACT

Highfrequency drying of a porous ceramic has been studied experimentally. The influence of electrode voltage, electrode distance, electric conductivity of the moisture and geometry of the product on the drying rate was investigated. There exists an optimal conductivity for maximum power dissipation and the geometry of the product has a focusing effect on the electric field. A theoretical discussion concludes, that the eddy current free quasi-stationary field is the type of field commonly present in highfrequency drying. With this type of field and the fact, that the complex permittivity of the product changes during drying, the experimental observations can be understood. From theory and experiment, conclusions are drawn in respect to a typical drying curve at highfrequency drying.     

Air Drying Kinetics of Potato Cylinders

ABSTRACT

An experimental air tunnel dryer was used to investigate the kinetics of moisture transport in potato cylinders (Solanum tuberasum). Acoordingly, the experimental results, represnting only falling-rate drying behaviour and hence. dehydration completely controlled by internal mass transfer, were interpreted on the basis of Fick's diffusional model for non-stedy state radial diffusion. The effects of air velocity and temperature on the drying rate were studied. with he temperature being the principal controlling factor. Analysis of the drying curves by the method of slopes resulted in a variable effective moisture diffusivity. Shrinkage as a function of moisture content under various drying conditions was investigated. The volumetric shrinkage of the samples was affected mainly by air velocity. whilst air temperature had a negligible effect. Good agreement was obtained between the experimental apparent density data and the predicted correlation.     

Drying Kinetics of Pinus Rqdiata Boards at Elevated Temperatures

ABSTRACT

From the numerical results of a rigorous, mathematical model, the rate–o–drying curves for high–temperature seasoning of Pinus radiata board show that the drying process can be divided into three periods. Based on the mechanistic picture of moisture movement and differences in the movement in each period, this paper simplifies the model by using the concept of the haracteristic drying curve.

In heartwood drying, the first period is very short (5–15 minutes), hence it can be neglected, whereas for sapwood, the first period is substantial with the drying rate being taken as constant in the analysis. Since the physical characteristics of the second and third drying periods are different, separate characteristic drying curves have been developed for each period. It has been found that common normalised drying curves are able to describe the results generated from the earlier model for normal range of kiln conditions over the examined ranges in dry–bulb temperatures of 1 10–140°C, wet–bulb temperatures of 70–90°C and air velocity of 3–7 m s^-1. Therefore. the derived simplified model can directly be used to calculate kiln–wide variations in moisture content and drying rate.     

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     

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.     

Characteristic Drying Curves of Cocoa Beans

The characteristic drying curves of cocoa beans are determined by using a tunnel drier where conditioned air passes a single cocoa berm suspended from an electronic balance in the test section. Weight loss, and temperatures of air, testa and nib of the cocoa bean is monitored on personal computers. The nornmalised drying rate versus the normalised moisture content is regressed by least square method to fit a new polynomial model for the penetration falling rate period and a linear model for the regular regime falling rate period. It can be concluded that there are three drying periods for cocoa beans namely the constant drying rate period, the penetration falling rate period and the regular regime falling rate period. The polynomial model estimates the penetration period quite well whereas the linear model estimates the regular regime quite well as well. There is no observable influence of relative humidity and air temperature on the characteristic drying curve of cocoa beans. However, the air velocity seems to have some influence on the curve.     

Drying and Heat Transfer Characteristics for a Novel Fluidized Bed Dryer

Abstract

The use of a fluidized bed dryer with a lateral air flow and mechanical agitation to the drying of sludge from a wastewater treatment plant was investigated. Experimental curves of moisture content vs. drying time, as well as heat transfer coefficients and the size characteristics of the products, were determined at temperatures between 80°C and 110°C, a stirring rate of 55 rpm and air velocity of 0.9 m/s for 3 kg sludge batches with initial moisture contents of 0.55 and 0.65 (d.b.). Experimental drying kinetics were compared with values derived from three models based on Fick's second law, namely: the constant diffusivity model, the simplified variable diffusivity model, and the modified quasi-stationary model.     

Effect of Particle Structure on Quality Retention of Bio-Products During Thermal Drying

ABSTRACT

To study the influence of particle structure on quality retention of hioproducts during thermal drying, the porous particles formed of albumin and solid carriers were dried in a vibm-fluidized bed dryn at different inlet air temperatures and different initial bulk porosities. Equations to predict temperature and moishrre content of panicles as well as the kinetics of biomass degradation were developed. The particle bulk porosity was incorporated into concentration-dependent moisture diffusivity model to estimate the erect of particle structure on product quality. The analysis of both calculated and experimental results indicates that the more porous structure promotes moisture diffusion, increases drying rate and finally improves the quality retention of bio-products. An extensive literature survey on quality retention issues during thermal drylng has been done.     

An Artificial Neural Network Model for Prediction of Drying Rates

Abstract

Drying rate data were generated for training of an ANN model using a liquid diffusion model for potato slices of different thicknesses using air at different velocities, humidities and temperatures. Moisture content and temperature dependence of the liquid diffusivity as well as the heat of wetting for bound moisture were included in the diffusion model making it a highly nonlinear system. An ANN model was developed for rapid prediction of the drying rates using the Page equation fitted to the drying rate curves. The ANN model is verified to provide accurate interpolation of the drying rates and times within the ranges of parameters investigated.     

A Method of Determination of Concentration Dependent Effective Moisture Diffusivity

ABSTRACT

A method based on Fourier series solution to Fick's diffusion equation has been proposed to evaluate effective diffusivity (D) as a function of moisture content in agricultural materials undergoing shrinkage during drying process. The shrinkage kinetics of the particulate was used to correlate its instantaneous size (spherical equivalent diameter) as a function of material moisture content A computer program was used to evaluate D based on shrinkage kinetics and experimental drying data and relate it to moisture content. The method was used to obtain moisture diffusivity data for thin layer drying of grape and corn.