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.     

MOISTURE DIFFUSION IN GELATIN SLABS BY MODELING DRYING KINETICS

ABSTRACT

The aim of this work is to improve the knowledge concerning moisture mobility in gelatin slabs, through the evaluation of moisture diffusivity (function of temperature and moisture content) by modeling of drying kinetics

The first part of this work is devoted to the determination of the gel characteristics needed for a good modeling. Drying experiments were then carried out on a pilot drier according to a central composite design with 3 factors (temperature, moisture content and pH).

Moisture diffusivity was finally calculated by fitting a model to the drying experiments. The chosea model (a conventional diffusive model with variable diffusion coefficient, solved by finite difference calculations in a solid-related frame of coordinates) did not perfectly fit the experimental results. It especially under-estimates moisture gradients at the surface of the gel     

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 Moisture Diffusivity by Thermo-Gravimetric Analysis under Non-Isothermal Condition

In drying of solids, the diffusion model based on Fick's second law is usually applied to interpret the moisture migration within the solid. Then the temperature dependence of the moisture diffusivity, generally described by an Arrhenius-type equation, is obtained through the drying kinetics. In this article, a nonisothermal (linearly increasing temperature) procedure was used to determine the moisture diffusivity as a function of temperature with the complex optimization method, and the result was accessed by comparison with a classical isothermal procedure. All the experiments were conducted in a thermogravimetric analyzer (TGA) for accurately recording the mass loss from the sample and easily programming the heating profile.     

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     

A Simulation Study on Convection and Microwave Drying of Different Food Products

Abstract

It is now well recognized that matching the external drying condition with the drying kinetics of a material can lead to substantial savings of energy and in the case of heat-sensitive products, even to higher quality product. In this work, the effect of convection and microwave heat input and other product parameters on the batch drying characteristics of model materials, potato and carrot slabs, whose thermo-physical data are readily available in the literature, was modeled using a one dimensional liquid diffusion model. The influence of various thermo-physical properties of the product in drying of heat-sensitive materials was quantitatively assessed. Heat of wetting, temperature and moisture dependent effective diffusivity and thermal conductivity are considered in this model. The effect of moisture diffusivity on drying using convection and a microwave field is simulated in view of the interest in predicting the drying performance by simplified method. Conditions under which the drying rate is controlled by the external drying conditions and the internal thermo-physical properties of the product are computed and discussed.     

Effective Moisture Diffusivity Estimation from Drying Data. A Comparison Between Various Methods of Analysis

ABSTRACT

Moisture diffusivity is the most crucial property in drying calculations. Literature data are scarce due to the variation of both experimental measurement techniques and methods of analysis. The effect of using different methods of analysis on the same experimental drying data is examined in this work. Detailed and simplified mathematical models, incorporating moisture diffusivity as model parameter, are applied. It is proved, that significant differences in the calculated values of moisture diffusivity result when different models are used, and probably these differences explain the variation in literature data. Thus, the adoption of a standardised methodology will be of great importance in moisture diffusivity evaluation.

The above findings resulted from the application of four alternative models on the drying data of three common food materials, potato, carrot and apple. A typical pilot plant scale dryer with controlled drying air conditions was used for the experiments. The moisture content dependence of the diffusion coefficient was proved significant at the last drying stage, while the temperature dependence followed the well known Arrhenius relation. The effects of considering external mass transfer and volume shrinkage during drying, were also investigated.     

WATER ADSORPTION AND DRYING CHARACTERISTICS OF OKRA Hibiscus Esculentus L

ABSTRACT

Moisture adsorption characteristics of okra were evaluated at 10, 20, 30° C. Isotherms were found to be of type III. Monolayer moisture contents were evaluated with GAB model. Drying was carried out at 60, 70, 80° C and drying data were analysed to obtain diffusivity values from the period of first felling drying rate. Effective diffusivity increased with increasing temperature. Calculated values of the effective diffusivity showed an Arrhenius type temperature dependence.     

DETERMINATION OF MOISTURE DIFFUSIVITY AND BEHAVIOR OF TOMATO CONCENTRATE DROPLETS DURING DRYING IN AIR

ABSTRACT

The drying mechanism and diffusion coefficient of water in spherical droplets (1.73 – 2.08 mm diameter) of tomato concentrates were successfully interpreted and modelled by using Fick's law. Solids content of the initial concentrate (5–15% w/w), and drying temperature (60^° – 100^° C) were varied but the drying air was kept at constant velocity and humidity.

The effective moisture diffusivity was estimated from the drying rate curves and expressed by an Arrhenius relation. Further, it was observed that case hardening has a large effect on the diffusion process causing the effective diffusional distance and the rate of moisture accumulation in the hardened crust to vary with the moisture content, according to a sorption controlled mechanism.     

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.     

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.     

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.     

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.     

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.     

A Vacuum Drying Model for Mango Pulp

Abstract

Vacuum drying of mango pulp at varying conditions of pulp thickness (2, 3, and 4 mm) and vacuum chamber plate temperature (65, 70, and 75°C) was carried out under 30–50 mm of mercury absolute pressure. A model based on moisture diffusivity was found to give close prediction to moisture content of the pulp at different times of drying with correlation coefficient varying between 0.98–0.99 for pure mango pulp and pulp with ingredients. Color change of reconstituted pulp made from mango powder was found to depend more on pulp thickness than plate temperature. For getting low color change vacuum drying should be carried at maximum pulp thickness of 2.6 mm and vacuum chamber plate temperature of 72.3°C.     

CONTRIBUTIONS OF T. K. SHERWOOD AND ASSOCIATES TO THE FIELD OF DRYING (Part 3, Final)

ABSTRACT

Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information.

Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.     

MODELING OF ROUGH RICE DRYING IN THIN VERTICAL COLUMNS

ABSTRACT

The solution of classical diffusion equation based on the assumption of average moisture diffusion coefficient did not adequately represent natural convection drying of rough rice in thin vertical columns exposed on both sides to hot air. Instantaneous moisture diffusivity coefficients determined from experimental drying curves decreased continuously with an increase in exposure duration and were linearly related to moisture ratio. The proponionality constant which was called apparent moisture diffusion coefficient was distinctly related to air temperature, relative humidity, and initial moisture content of rough rice. The modified moisture diffusion model using the instantaneous moisture diffusion coefficient was found to best represent the moisture removal from bulk rough rice.     

DETERMINATION OF MASS DIFFUSIVITY COEFFICIENT OF SWEET POTATO

Abstract

Using Luikov's heat and mass transfer equations and a finite element formulation, the drying process of an anisotropic biological product (sweet potato) was investigated. The model was used to determine the coefficients of heat and mass transfer, the mass diffusivity normal and parallel to the fibers of sweet potato samples. These parameters were estimated by minimizing the deviation of experimental data and numerical predictions.

Laboratory experiments with three different configurations were conducted to measure the temperature and moisture content of sweet potato samples during drying. Numerical simulation showed good agreement with the measured values.     

Principle and Applications of Drying Characteristic Functions

ABSTRACT

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.