Thermomechanics of Drying Processes

Dried materials constitute colloidal or capillary-porous bodies. The space occupied by the solid particles is termed the skeleton of the body. The liquid-gas mixture filling the pore space will be called the moisture.

Drying is one of the fundamental manufacture stages of many products. Almost every industry has wet products that have to be dried as, for example, powders, food products, polymers, wood, ceramics, etc. One estimates that the annual costs of drying constitute a dozen or so percent of total manufacturing costs.

Dried materials have been called wet porous bodies under drying conditions. All dried materials (bodies) may be considered as almost fully saturated during the constant drying rate period. When the drying process reaches the critical point, that is, since the beginning of the falling rate period, the body will be considered as partly saturated.

The thermodynamics of irreversible processes deals with systems that are in a thermodynamic non-equilibrium. We have accepted tacitly in our previous considerations that the thermodynamic parameters of state, and thus also the thermodynamic functions, are defined in some way during drying processes. However, the issue of determination of these parameters is not quite clear, since the systems are heterogeneous and the parameters undergo continuous changes in time as in space during irreversible processes in general, and in particular in drying processes. At least some thermodynamic parameters are not constant but are functions of drying time and position in the dried body. Therefore, an issue arises of how to determine the magnitude of these parameters varying continuously in time and space.

This Chapter presents the theoretical basis to be applied in the analysis of the creep and relaxation effects occurring during drying of wet materials. Drying is a combined process of heat and mass transfer resulting in moisture and temperature gradients, which are the main causes of generation of internal stresses. It is usually a prolonged technological process under raised temperature. This promotes viscoelastic behavior of dried materials, which creates conditions conductive to creep and relaxation.

Dried materials can be considered as solids that are weakened by numerous cracks or voids. The fracture of such materials has frequently been observed to be a result of the growth and coalescence of microscopic voids due to drying induced stresses. In some cases a complete spallation may occur.

In this Chapter we shall analyze two approaches to the problem of fracture during drying: a microscopic approach that explains fracture as a result of the interaction of body particles and growth of individual cracks; and a macroscopic approach that attributes fracture to stresses generated during drying. Experimental observations and numerical simulations show that nucleation, growth and coalescence of microvoids and microcracks play the most important role in the process of ductile and brittle failure. These physical mechanisms of fracture (ductile, brittle and mixed, brittle-ductile) are sensitive to the history of acting stresses. In the case of dried materials the history of stresses is rather not involved. Fracture is involved in the actual state of stress and is influenced by the microstructure, the level of moisture content and temperature. Any suitable fracture theory for dried materials should account for the common observation that fracture is more likely if the dried body is thick or the drying rate is high. Both these items are conductive to generation of the internal shrinkage stresses.

Three types of strains of moist materials under drying may be mentioned: shrinkage strains due to alteration of moisture content, being the largest ones, thermal strains due to alteration of temperature, and finally mechanical strains caused by stresses generated during drying, when the distributions of moisture content and temperature are non-uniform. Mechanical strains are the most undesirable as they can be permanent (viscoelastic, plastic, or even in the form of cracks). Permanent strains may lower the quality of dried products because they deform their shape, which involves warping and cracking. Therefore, it is important to analyze the conditions at which the stress may be generated in wet materials during drying.

The fundamental constitutive equations of drying theory have been presented in the previous Chapters. The balance equations and the physical relations between the thermodynamic parameters of state allow us to formulate the governing set of differential equations, which describe mathematically drying processes, and in particular, the spatial distribution and time evolution of such quantities as: moisture content, temperature, strains and stresses in a dried body.

We known from experiments that deformation of a body under drying is associated with a change of moisture content and temperature of the body. The motion of a saturated porous solid under drying, described by velocity v^s (see Section 3.1). is characterized by mutual interaction between deformation, moisture content and temperature fields. The domain of science dealing with the mutual interaction between these fields can be termed as thermoporoelasticity or thermoporoplasticity, depending on whether the strains due to thermal and/or moisture expansion of the material remain purely elastic and are of reversible nature or become permanent in the body or a part there of. The notion “thermoconsolidation of dried materials” also seems to be a proper term for this domain, as the wet material under drying consolidates itself due to shrinkage.

In this Chapter we are going to illustrate the problem of stress reverse in dried products, which may occur during intensive drying. The reason for stress reverse can be explained as follows: when the sample dries, its surface attempts to shrink but is restrained by the wet core. The surface is stressed in tension and the core in compression. When the stresses are large enough, inelastic strains may occur both on the surface and in the core. During further drying, the core dries and attempts to shrink but the shrinkage is restrained again, this time by the surface, which has not been sufficiently shrunk and tensioned permanently at the initial stage of drying. Therefore, tensional stresses arise in the core.

The main aim of this Section is to examine the influence of the shape of dried materials on the deformations and stresses generated in them by drying. We elucidate this problem by considering the convective drying of two bars of different crosssections, namely, rectangular and square, see Fig. 12.1.

Some materials subjected to drying are characterized with anisotropic structure. Mathematical description of mechanical behavior, and in particular deformation, of anisotropic materials subjected to drying is more complex than that of isotropic ones. Therefore, we concentrate our attention on a special case of anisotropy, namely, on orthotropy. The reason for this choice is that wood, a very important and common material in drying industry, belongs to materials, which have orthotropic structure.

The development of an analytical description of drying processes is based upon the expression of physical laws in a mathematical form suitable for drying processes. The fundamental physical laws, i.e. conservation of mass, momentum, moment of momentum, energy, and the law of increase of entropy, with the exception of relativistic and nuclear phenomena, apply to each and every process independently of the nature of the matter under consideration.