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 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.     

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     

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.     

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.     

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.     

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 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.     

DRYING OF POROUS MATERIALS AT LOW MOISTURE CONTENT

ABSTRACT

Drying experiments were conducted using packed beds of glass beads with initial moisture content near or slightly above the irreducible moisture content. The objective was to validate the vapor phase diffusion coefficient determined in earlier experiments and to quantify the effect of temperature gradient on vapor phase diffusion in the presence of irreducible saturation. The resulls indicate that for isothermal drying the enhancement factor, β, which is the ratio of the diffusion coefficient in the packed bed to that in free space, is slightly less than unity. This is consistent with previous results. However, the results for non-isothermal drying show little effect of temperature gradient for temperature gradients either assisting the concentration gradient or opposing the concentration gradient. This is contrary to the traditional thinking about enhanced vapor diffusion originally proposed by Philip and deVries (1957).     

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

ABSTRACT

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).     

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.     

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.     

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.     

PARAMETERS INFLUENCING DRYING BEHAVIOR OF RUBBER WOOD (HEVEA BRAZILLIENSIS) AS DETERMINED FROM DESORPTION EXPERIMENT

ABSTRACT

In this study, the drying properties of rubber wood, which are the basic parameters for kiln scheduling design, were determined from desorption experiment. Equilibrium moisture content expression was developed. The diffusion coefficients at different drying environments were evaluated. It is more appropriate to determine the diffusion coefficients by the optimum scheme in comparison to other schemes; the logarithmic, square-root and half-fraction of evaporable moisture schemes. Finally, the diffusion coefficient of rubber wood was described by, instead of wood moisture content, the drying temperature and relative humidity, which are the parameters controlling the drying kiln operation.     

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.     

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.     

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

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.     

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.