Solidification by Convective Drying of Particle Layer Wetted with Dilute Agar Gel

Abstract:

Solidified porous slab is formed through convective drying of glass particle layer wetted with aqueous dilute agar gel. Measured critical mean moisture content increases with increasing initial moisture or agar content. The agar gel moves in viscous flow caused by capillary pressure during drying. A new drying model based on the receding evaporation plane model is proposed. Drying period is divided into surface and internal evaporation periods. Wet slab consists of dried and wet zones during the internal evaporation period, while the wet slab consists of wet zone only during the surface evaporation period. In the new model, the evaporation rate from the wet zone in the internal drying period is estimated with the linear driving force (LDF) approximation in the field of adsorption engineering. Critical moisture content, that is, mean moisture content between the surface and internal periods, is estimated with a mass balance on the surface. Simulated results by the new drying model with reasonable fitting parameters agree very well with measured drying data.     

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.     

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.     

HIGH-INTENSITY DRYING OF PAPER

High-intensity contact drying denotes drying under suf- ficiently intensive heating conditions that, following a brief warmup period, the mist paper web operates at internal tem- peratures in excess of the ambient boiling point. A simplified, two-zone analytical model is first presented. The paper is depicted as having a dry layer, of ever-increasing thickness, adjacent to the hot surface. Heat conduction through this layer (the rate-limiting step) causes evaporation at the interface with the “wet zone.” The vapor is then considered to flow through the wet zone into the ambient. Results of bench-scale experiments are discussed. Drying rates as much as twenty times conventional rates are indicated. The drying rate increases with hot surface/boiling point tem- perature difference and applied mechanical pressure. The instsn- taneous drying rate decreases continuously after a brief warmup period. The vapor pressure at the hot surfacelpaper interface rises quickly to a peak value, followed by a continuously- diminishing level. The heat flux shows a rapid rise to boiling- like conditions, followed by a drop to a range compatible with measured drying rates. The temperature of the open side of the sheet is constant during drying, after its initial rise to the boiling point. The experimental results are compatible with pre- dictions of the model.     

HIGH-INTENSITY DRYING OF PAPER

High-intensity contact drying denotes drying under suf- ficiently intensive heating conditions that, following a brief warmup period, the mist paper web operates at internal tem- peratures in excess of the ambient boiling point. A simplified, two-zone analytical model is first presented. The paper is depicted as having a dry layer, of ever-increasing thickness, adjacent to the hot surface. Heat conduction through this layer (the rate-limiting step) causes evaporation at the interface with the “wet zone.” The vapor is then considered to flow through the wet zone into the ambient. Results of bench-scale experiments are discussed. Drying rates as much as twenty times conventional rates are indicated. The drying rate increases with hot surface/boiling point tem- perature difference and applied mechanical pressure. The instsn- taneous drying rate decreases continuously after a brief warmup period. The vapor pressure at the hot surfacelpaper interface rises quickly to a peak value, followed by a continuously- diminishing level. The heat flux shows a rapid rise to boiling- like conditions, followed by a drop to a range compatible with measured drying rates. The temperature of the open side of the sheet is constant during drying, after its initial rise to the boiling point. The experimental results are compatible with pre- dictions of the model.     

QUANTIFICATION OF THROUGH DRYING RATE DATA

ABSTRACT

For through drying there are three distinct drying rate periods, increasing rate, constant rate and falling rate. The increasing rate period is so important that nearly half of the drying is completed in this period only. A drying rate - moisture content relationship for this period was obtained based on theoretical analysis. It was verified with experimental data. A quantitative representation of the complete drying rate curve was established using this relationship and a modified power law equation for the falling rate period drying rate - moisture content relation. It needs five parameters to quantify the through drying from wet to dry: moisture content at the end of the increasing rate period; exponent for the drying rate - moisture relationship during the increasing rate period; constant drying rate; critical moisture content and the power-law exponent for the falling rate period.     

Mathematical modeling of combustion and gasification of a wet coal slab—I: Model development and verification

A one-dimensional model has been developed for the simultaneous drying and combustion of a semi-infinite wet coal slab. The model takes into account the vaporization of coal moisture and the existence of a moving evaporation front, pyrolysis and char/gas reactions occurring in the dry coal zone, Darcy flow of vapor and gases through the coal, variation in porosity and permeability of the coal, temperature dependence of the physical properties of the coal, transpiration cooling effect of the water vapor and pyrolysis gases, multi-component diffusion in the ash and gas film, and oxidation reactions in the ash. The model is capable of predicting the flame position, the combustion rate, the flame temperature, and the temperature on the coal surface.The performance of the model is compared with experimental data. Agreement between the computed results and the observed data is good.     

Drying Enhancement of Clay Slab by Microwave Heating

The effect of internal heating by microwave on the drying behavior of a slab was studied. A wet sample of kaolin pressed into a slab was subjected in microwave irradiation of 2.45 GHz. The absorption of microwave energy into a wet slab can be expressed by a function of the moisture content and the pathway length, which is a similar form to Lambert-Beer's law. The drying behavior was compared among three modes: microwave irradiation, hot air heating and radiation heating in an oven. Microwave heating with a constant power resulted in breaking the sample when the internal temperature achieves at 373 K. However, if the power was controlled to maintain the temperature less than the boiling point of water, the drying succeeded without any crack generation until the completion with a significantly faster drying rate than in convective heating or in the oven. It is also noted that the transient behavior of the temperature is quite different from the conventional drying.     

升华干燥过程的(火用)损失分析

通过对物料在升华干燥过程中的Yong损失分析，建立了升华干燥过程的Yong损失分析模型。结合升华干燥动力学模型和Yong损失分析模型，以牛肉为冷冻干燥过程的模型物料，计算了物料表面加热温度、干燥室压力和物料厚度等操作条件的变化对升华干燥过程Yong损失的影响。计算结果表明：随着干燥室压力的增大，物料的Yong损失减小;随着物料表面加热温度的降低，Yong损失减小：随着物料厚度的减小，Yong损失逐渐减小；在冷冻干燥过程中，Yong损失主要集中在升华干燥阶段，在解析干燥阶段，物料表面加热温度的升高不会引起Yong损失的大幅度增加。     

A Numerical Study of Transient Deformation and Stress Behavior of a Clay Slab During Drying

A transient three-dimensional analysis was carried out on internal strain-stress as well as heat and the moisture transfer in a ceramic slab during drying. A model was developed to analyze viscoelastic behavior, heat conduction and moisture diffusion. The basic equations were solved by the finite element method. The effects of several dimensionless parameters are discussed to find an optimum drying process and a precise design of molds in ceramic production. The stress and the gradient of moisture content were influenced significantly by the Biot or Lewis number. When the moisture diffusion is enhanced or the drying is controlled well so as to form only gentle gradients of moisture content in the slab, the maximum tensile stress can be reduced. Nonuniform drying results in the develoment of warp and increase in the maximum tensile stress. The drying characteristics were not appreciably influenced by shrinkage.     

A New Variable Diffusion Drying Model for the Second Falling Rate Period of Paddy Dried in a Rapid Bin Dryer

The objectives of this article is to propose a new drying model for the second falling rate period known as the variable diffusion controlled period that follows after the first falling rate period and to propose a new method to determine the second critical moisture content that separates these two periods. Experimental work on paddy drying at minimum fluidization velocity was carried out in a rapid bin dryer. The effects of operating temperatures (60-120°C) and bed depths (2-6 cm) on the paddy drying characteristics were investigated. It was found that the normalized drying rate of paddy was proportional to the normalized moisture content in the first falling rate period but in the second falling rate period, the normalized drying rate of the material varies exponentially with the normalized moisture content. The different relationship between the normalized drying rate and the normalized moisture content in the first and second falling rate periods indicate that two different mechanism of moisture transport are at work. The new exponential model of the second falling rate period and the linear model of the first falling rate period were found to fit the experimental data very well. Derivation from variable diffusion equation shows that the linear model is the result of constant diffusion coefficient whereas the new exponential model is the result of linear diffusion coefficient. This also implies that the first falling rate period is a constant diffusion controlled period and the second falling rate period is a variable diffusion controlled period. In addition, drying kinetics data of a drying process that fits the exponential model over a very slow drying period will show that the drying process is under the effect of a linear diffusion coefficient. It was also found that the proposed new method to determine the second critical moisture content that distinguishes between the first and second falling rate periods by using a sudden change in the value of the drying rate gradient to a much lower value at that point is more rigorous and yet simpler than the method of determining the specific location of the receding drying boundary since it is based on the behavior of the actual drying kinetic data.     

X-ray absorption study of drying cement paste and mortar

X-ray absorption was used to observe water evaporation with hydration time in paste and mortar specimens, with the aim of studying the influence of water/cement (w/c) ratio, presence of aggregates, curing conditions on drying during early hydration. For the samples subjected to surface drying immediately after mixing, there exists a moisture gradient within the internal part of the specimen. However, obvious top-down drying only occurs within a small zone near the surface for early age cement pastes and mortars. The evaporation rate of water is very high in the first day after casting and is drastically reduced afterwards due to the formation of a microstructure that greatly improves specimens resistance to moisture loss. Mortars reveal a slightly lower evaporation rate since the aggregate increases the length of the transport route because of a larger tortuosity. However, the effect of sealed curing is much more important than the tortuosity effect of the aggregates.     

COMBINED CONVECTIVE-MICROWAVE DRYING OF AGAR GELS: INFLUENCE OF MICROWAVE POWER ON DRYING KINETICS

The use of microwave energy in the drying of deformable material such as gel considerably reduces drying time and enables the control of retraction in the sample. A further advantage is that no hot spots are produced, allowing a dry product of superior quality to be obtained.The aim of this work has been to determine the kinetics of the convective-microwave drying process of agar gel plates. For this purpose, we developed a pilot closed loop, computer-controlled apparatus of convective-microwave drying, that enables the drying air conditions to be changed and the microwave power to be supplied over a wide value range. The equipment also records the sample surface temperature by means of an infrared thermometer. The drying curves obtained for plane geometry present four different drying phases: an initial phase where a rapid increase in the drying rate and in the surface temperature can be observed, as well as a constant rate phase that ends in the so-called convective critical moisture content, a first falling rate phase that concludes in the microwave critical moisture point, and finally a second falling rate phase. Combined convective-microwave drying enables a considerable reduction in drying time compared to convective drying, the time required being inversely proportional to the microwave power supplied. The empirical equation that best represents the kinetics is of the Page type. The absorbed volumetric power in terms of the moisture content was experimentally estimated, with the experimental data fitting an empirical equation.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

Computer model of drying behaviour of ceramic green bodies with particular reference to moisture content dependent properties

A numerical model was developed to predict the drying behavior of ceramic green bodies. Resolution of the simultaneous heat and mass transfer equations involved finite elements and the Backward Euler method. Based on experimental data, the model uses equivalent moisture diffusivity, water activity, thermal conductivity and heat capacity as input parameters which depend on moisture content. In particular, the equivalent moisture diffusivity is a key parameter controlling water transport from the body interior to the surface. A simple method was used to estimate the effect of shrinkage on drying rate during the initial drying stage. Predictions of the internal moisture distribution, drying rate and surface temperature as a function of time gave good agreement to experiment for green bodies of alumina paste. External conditions of convection coefficient and relative humidity are shown to sensitively control drying rate and surface temperature evolution during the constant rate period.     

Drying of Porous Material During the Constant and the Falling Rate Period: A Critical Review of Existing Hypotheses

Abstract

During drying of porous material a so-called “falling rate” period is observed, where the drying rate decreases as the moisture content decreases. This behavior is usually described by the well known “shrinking core model.” This model, however, contradicts experimental findings and violates basic laws of multiphase mass transfer in porous media as well. A new model, named “wet surface model,” is suggested which eliminates those discrepancies.     

Three-Layer Model for Drying of Coating Applied on Silicone-Coated Paper

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate.     

COMBINED CONVECTIVE-MICROWAVE DRYING OF AGAR GELS: INFLUENCE OF MICROWAVE POWER ON DRYING KINETICS

ABSTRACT

The use of microwave energy in the drying of deformable material such as gel considerably reduces drying time and enables the control of retraction in the sample. A further advantage is that no hot spots are produced, allowing a dry product of superior quality to be obtained.The aim of this work has been to determine the kinetics of the convective-microwave drying process of agar gel plates. For this purpose, we developed a pilot closed loop, computer-controlled apparatus of convective-microwave drying, that enables the drying air conditions to be changed and the microwave power to be supplied over a wide value range. The equipment also records the sample surface temperature by means of an infrared thermometer. The drying curves obtained for plane geometry present four different drying phases: an initial phase where a rapid increase in the drying rate and in the surface temperature can be observed, as well as a constant rate phase that ends in the so-called convective critical moisture content, a first falling rate phase that concludes in the microwave critical moisture point, and finally a second falling rate phase. Combined convective-microwave drying enables a considerable reduction in drying time compared to convective drying, the time required being inversely proportional to the microwave power supplied. The empirical equation that best represents the kinetics is of the Page type. The absorbed volumetric power in terms of the moisture content was experimentally estimated, with the experimental data fitting an empirical equation.     

TWO-FLUID MODEL FOR PNEUMATIC DRYING OF PARTICULATE MATERIALS

The Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a one-dimensional steady-state condition and was applied to the drying process of wet PVC particles in a large-scale pneumatic dryer and to the drying process of wet sand in a laboratory-scale pneumatic dryer. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The drying process is assumed to stop when the moisture content of a particle falls to a predefined value or when the particle riches the exit of the pneumatic dryer. Our developed model was solved numerically and two operating conditions, adiabatic and given pneumatic dryer wall temperature, were simulated. Comparison between the prediction of the numerical models of Rocha and DryPak, (Pakowski, 1996), which were presented by Silva and Correa (1998), with the prediction of our numerical simulation reviled better agreements with DryPak then with the models of Rocha. The results of the developed model were also compared with experimental results of Baeyens et al. (1995) and Rocha.