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.     

MODELISATION PRINCIPLES FOR DRYING OF GELS

ABSTRACT

When one wants to understand and model the drying of high water content gels, one needs to gather all thermal physical parameters and to derive a physical model based on independently measured parameters. We chose to work experimentally and theoretically on water diffusion and drying of spheres of polyacrylamide gel.

We have demonstrated the strong influence of vitreous transition on the relationship of water diffusivity with moisture content. Values of the diffusion coefficient and temperature shift factor for diffusion have been proposed.

Convective and micro-wave drying kinetics show the presence of a drying phase purely specific to radiation absorption. Finally, we have proposed a mathematical model containing independent physical parameters, which' not only predicts mass fluxes but also analyses critical physical phenomena.     

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

Abstract:

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 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.     

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.     

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.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

Experimental benchmarking of diffusion and reduced models for convective drying of single rice grains

Abstract

In this work, the drying behavior of single rice grains at moderate and elevated air temperatures (i.e. 60?°C, 120?°C, and 140?°C) is experimentally investigated by using a magnetic suspension balance system. To describe the experimental drying behavior, a diffusion model is developed. The reference moisture diffusivity of the rice grains is determined by using an inverse method, whereas other thermo-physical properties are measured. Next, the diffusion model is reduced to a semi-empirical model within the frame of reaction engineering approach (REA). Both models are successfully benchmarked against the experimental observations. The results indicate that the moisture diffusivity of rice grains can be represented as a linear function of the moisture content and the drying process at high temperatures is controlled by both intra- and extra-particle mass transfer resistances. In addition to these results, this study favors a practical application of the REA in drying calculations to derive a simple, robust, and extrapolative semi-empirical model since the parameter of this model seems to be insensitive to variations of drying conditions.     

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.     

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     

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.     

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.     

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.     

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.     

DRYING OF BIOLOGICAL PRODUCTS WITH SIGNIFICANT VOLUME VARIATION. EXPERIMENTAL AND MODELING RESULTS FOR POTATO DRYING.

ABSTRACT

This work is devoted to the experimental investigation and theoretical modeling of biological products with high initial moisture content which implies significant volume contraction. Firstly, experimental equipment which was designed to continuously determine variations in the global moisture content and in the temperature of the sample is introduced. Furthermore, the equipment is controlled by a PC which records experimental information in real time. In particular, measurement of the radial and temporal distributions of moisture content and temperature during the drying process of the homogeneous porous media potato are given. The mean moisture content and temperature curves are also given.     

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.     

Kinetic and Quality Study of Mushroom Drying under Microwave and Vacuum

Abstract

The aim of this work is to model the drying kinetics of mushrooms under several operational conditions, to evaluate the effective diffusivity coefficient of moisture removing by a drying model and inverse calculus method in finite differences and to study the effect on the final quality of dehydrated mushrooms. Different ways of microwave vacuum drying were compared to freeze-drying. Results show that a decrement of the applied pressure produces a certain increase in the drying rate together with a lower moisture in the dehydrated product at the end. Temperature control inside the sample helps to ensure a better quality in the dehydrated product, than when controlled at the surface. Diffusivity coefficients show a correspondence with product temperature during drying. The microwave dried samples obtained with moderate power and temperature control of product shown an important degree of quality similar to that obtained by freeze-drying.     

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.     

Moisture Diffusivity Data Compilation in Foodstuffs

ABSTRACT

A review of the recently reported moisture diffusivity experimental data in food materials is presented in this work. Values are classified and analysed statistically to reveal the influences of temperature and moisture content. Empirical models relating moisture diffusivity with the above variables, along with relevant graphs for various materials, are included. Other factors affecting moisture diffusivity prediction are also discussed.     

THIN-LAYER DRYING CHARACTERISTICS OF ROUGH RICE AT LOW AND HIGH TEMPERATURES

Abstract

Thin-layer drying characteristics of rough rice were determined at temperature ranging from 11.8 to 51 °C and for relative humidities ranging from 37.1% to 91.3%, with initial moisture contents in the range of 24.7 to 41.6% dry basis. An oven, a self contain air conditioning unit, recently developed in Japan, was used for this experiments. With this apparatus, very smooth drying curves were obtained. The data of sample weight, and dry and wet bulb temperatures of the drying air were recorded continuously throughout the drying period for each test. The drying process was terminated when the moisture content change in 24 h was less than 0.2 % d.b. (weight change was less than 0.05 g). The final points were recorded as the dynamic equilibrium moisture contents.

The drying data were than fitted to the Page model. The model gave a very good fit for the moisture content with an average standard error of 0.294 % d.b? Both the drying parameters, K and N, are function of drying air temperature and relative humidity. The effect of variable initial moisture content was also described effectively by the empirical Page model. The drying time employed had a large effect on the K and N values. The results presented here, over typically 5 day drying, will be useful in the long term moisture transfer process occurring during ventilated storage.