PROCESSES RELATED TO DRYING: PART I,THEORETICAL MODEL

The aim of this paper is to summarize ten years of work in order to model the drying of solids. Nowadays there is a general agreement amongst the various researchers worldwide. If the porous medium is viewed at the so-called “macroscopic” scale (that is to say when it is viewed as a continuous and homogeneous equivalent medium) a set of three partial derivative equations is derived, three state variables being necessary to thermodynamically describe the medium (temperature, moisture content and total pressure in the gaseous phase for example).

After a short historical survey of the modeling of drying, we want to obtain this set of equations drawing the readers attention to three particular points : the importance of the air mass balance, the right way to write the energy equation (and the associated boundary conditions) and the taking into account of the adsorbed water.

A second part of this article [I] will be devoted to the numerical solution of this problem and will illustrate these points.     

PROCESSES RELATED TO DRYING: PART II USE OF THE SAME MODEL TO SOLVE TRANSFERS BOTH IN SATURATED AND UNSATURATED POROUS MEDIA

From the mathematical formulation presented in part I, a numerical code is developed to simulate heat and: mass transfers in porous media. The aim of this· tool is to understand and to improve each process related to drying. The association of a comprehensive set of equations with a efficient 2-D computer code allows us to predict the comportment of several porous media even if submitted to severe drying conditions. A few runs have been selected with special attention paid to the effect of internal gaseous pressure:

Convective drying of softwood at high temperature illustrate the typical two-dimensional transfers that occur in an anisotropic medium.

Microwave drying of light concrete pinpoints liquid expulsion of water which is driven by the pressure due to internal heating.

Finally, appropriate physical behaviours of a bed of glass spheres allows one to deal with simple processes for which full saturation occurs.     

PROCESSES RELATED TO DRYING: PART II USE OF THE SAME MODEL TO SOLVE TRANSFERS BOTH IN SATURATED AND UNSATURATED POROUS MEDIA

From the mathematical formulation presented in part I, a numerical code is developed to simulate heat and: mass transfers in porous media. The aim of this· tool is to understand and to improve each process related to drying. The association of a comprehensive set of equations with a efficient 2-D computer code allows us to predict the comportment of several porous media even if submitted to severe drying conditions. A few runs have been selected with special attention paid to the effect of internal gaseous pressure:

Convective drying of softwood at high temperature illustrate the typical two-dimensional transfers that occur in an anisotropic medium.

Microwave drying of light concrete pinpoints liquid expulsion of water which is driven by the pressure due to internal heating.

Finally, appropriate physical behaviours of a bed of glass spheres allows one to deal with simple processes for which full saturation occurs.     

SOVIET BOOKS ON DRYING AND RELATED PROCESSES

A method to minimize twist has been investigated; i.e., drying the boards in a pre-twisted position. It has been found that Norway spruce boards can be deformed toward straightness by this method. The force exerted by a board on its holders during drying in a pre-twisted position has been measured. When the variation in torsional stiffness as a function of temperature and moisture content is accounted for, it is found that a creep deformation of the board occurs both during the drying phase and the cooling phase. In addition to mechano-sorptive creep, a deformation released by a change in temperature also seems to occur.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING, PART I: MODEL DEVELOPMENT AND PREDICTIONS

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART I: MODEL DEVELOPMENT AND PREDICTIONS

ABSTRACT

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

CURING STUDY AND OPTIMIZATION OF A POLYURETHANE-BASED MODEL PAINT COATED ON SHEET MOLDING COMPOUND PART II: DRYING DEFECTS RELATED TO CURING CONDITIONS

ABSTRACT

This study deals with the bubbling phenomenon which appears in some drying conditions on paint films applied as thin layers on SMC substrates. The bubbles and craters origin can be due either to reactions which may occur at the interface paint / SMC either to inadequate drying conditions which affect the polymerization reaction (gelation, viscosity) and the solvent vaporization.

Firstly, we reported data describing the solvent interaction with the SMC substrate - namely the contact angle, the interfacial tension, the absorption kinetics and the sorption isotherms - and the relationship between the bubbling defects and the numerous process variable (operating conditions, paint formulation and support properties).

Then, we gathered experimental data concerning the influence of different parameters (state and type of substrate, temperature, heating mode, film thickness. paint formulation, etc.) on the bubbling phenomenon and we tried to establish some quantitative interpretation. It proved that this defect was mainly due to the SMC heterogeneity expressed by the porosity of this composite material.     

CURING STUDY AND OPTIMIZATION OF A POLYURETHANE-BASED MODEL PAINT COATED ON SHEET MOLDING COMPOUND PART II: DRYING DEFECTS RELATED TO CURING CONDITIONS

This study deals with the bubbling phenomenon which appears in some drying conditions on paint films applied as thin layers on SMC substrates. The bubbles and craters origin can be due either to reactions which may occur at the interface paint / SMC either to inadequate drying conditions which affect the polymerization reaction (gelation, viscosity) and the solvent vaporization.

Firstly, we reported data describing the solvent interaction with the SMC substrate - namely the contact angle, the interfacial tension, the absorption kinetics and the sorption isotherms - and the relationship between the bubbling defects and the numerous process variable (operating conditions, paint formulation and support properties).

Then, we gathered experimental data concerning the influence of different parameters (state and type of substrate, temperature, heating mode, film thickness. paint formulation, etc.) on the bubbling phenomenon and we tried to establish some quantitative interpretation. It proved that this defect was mainly due to the SMC heterogeneity expressed by the porosity of this composite material.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS. PART I: THEORETICAL CONSIDERATIONS

Abstract

This is the first of two papers concerning conjugate transport in convective drying of multiparticle systems. In this study, a methodology for the solution of conjugate transport problems is proposed. The theoretical aspects and relevant assumptions are briefly discussed and the results for convective heat and mass transfer in assemblages of spheres are presented. It is shown that both heat and mass transfer rates for an assemblage of two spheres in tandem arragement are significantly different from those of a single sphere case, and that care should be taken when modeling multiparticle systems by means of single-particle analysis.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS. PART I: THEORETICAL CONSIDERATIONS

This is the first of two papers concerning conjugate transport in convective drying of multiparticle systems. In this study, a methodology for the solution of conjugate transport problems is proposed. The theoretical aspects and relevant assumptions are briefly discussed and the results for convective heat and mass transfer in assemblages of spheres are presented. It is shown that both heat and mass transfer rates for an assemblage of two spheres in tandem arragement are significantly different from those of a single sphere case, and that care should be taken when modeling multiparticle systems by means of single-particle analysis.     

DRYING WOOD: A REVIEW - PART I

This paper reviews the technology of wood drying and recent developments in the field. The importance of drying is reviewed first. Then the fundamentals of wood properties as they relate to drying are discussed, including how water is held in wood, how it moves through wood, and how drying stresses that lead to drying defects develop. Traditional drying technology for lumber, veneer, and heavy timbers is then presented. With this background, the discussion moves to recent developments in drying technology that have been implemented commercially, such as high-temperature drying, low-temperature drying, continuously rising temperature drying, vacuum drying, and advances in process control. Finally, a discussion is presented on drying technology of the future. This topic describes processes that offer potential improvements in drying technology, but are still in the research and development stage.     

DRYING WOOD: A REVIEW - PART I

ABSTRACT

This paper reviews the technology of wood drying and recent developments in the field. The importance of drying is reviewed first. Then the fundamentals of wood properties as they relate to drying are discussed, including how water is held in wood, how it moves through wood, and how drying stresses that lead to drying defects develop. Traditional drying technology for lumber, veneer, and heavy timbers is then presented. With this background, the discussion moves to recent developments in drying technology that have been implemented commercially, such as high-temperature drying, low-temperature drying, continuously rising temperature drying, vacuum drying, and advances in process control. Finally, a discussion is presented on drying technology of the future. This topic describes processes that offer potential improvements in drying technology, but are still in the research and development stage.     

TOWARDS A COMPREHENSIVE MODEL BASED CONTROL OF MILK DRYING PROCESSES

Milk powder manufacture is carried out on large scale and to exacting standards. To date, process control has been largely empirical. Recent advances in the understanding of process mechanisms and product properties is allowing model-based process control strategies to be developed. This review briefly describes the manufacture of milk powder and discusses in detail milk concentrate viscosity and atomization, particle size distribution, the drying mechanism and protein denaturation, in relation to the development of such strategies.     

TOWARDS A COMPREHENSIVE MODEL BASED CONTROL OF MILK DRYING PROCESSES

ABSTRACT

Milk powder manufacture is carried out on large scale and to exacting standards. To date, process control has been largely empirical. Recent advances in the understanding of process mechanisms and product properties is allowing model-based process control strategies to be developed. This review briefly describes the manufacture of milk powder and discusses in detail milk concentrate viscosity and atomization, particle size distribution, the drying mechanism and protein denaturation, in relation to the development of such strategies.     

PHYSICAL PROPERTIES OF RICE RELATED TO DRYING THE GRAIN

Stresses in the rice grain can be produced by mechanical equipment such as the combine, elevator, auger and the rice mill. There are, however, other and more insidious means of producing severe stresses in the grain with moisture and thermal gradients. Moisture gradients can be found 1) in the field on a humid night before harvest, 2) in a hopper of freshly harvested rice containing high-, low- and intermediate-moisture grains, and 3) in certain types of dryers ahead of the drying front. A single high humidity exposure of rough rice at storage moisture can be very detrimental to the quality of the grain. Other steep moisture gradients can be produced by rapidly drying high-moisture rice, With time, after drying, the gradients cause moisture to diffuse from the center to the surface thus causing 1) the moisture gradient to decrease, 2) the grain surface to gain moisture and expand, 3) the grain interior to lose moisture and contract, and 4) the grain to fissure several hours after it has been dried. Fissured rice will usually break when it is milled.     

A CONTINUUM MODEL OF DRYING PROCESSES INVOLVING A JUMP THROUGH HYSTERESIS

A continuum model of equilibrium drying processes developed by Ilic and Turner [6], [19] is reformulated in such a way that the source terms are absent. The model is also extended by including a jump through the hysteresis formed by the wetting and drying curves. The jump is expressed in terms of Heaviside unit function. When the unit function is approximated by a sequence of functions, a single system of three coupled nonlinear partial differential equations results. The system is solved numerically using finite difference