Characterization of the First Falling Rate Period During Drying of a Porous Material

Abstract

This study deals with the evolution of the surface state and its influence on the drying of porous media. Surface temperature and saturation values are obtained using optical metrology. Analysis of the experimental results allows discussion of the apparition of constant drying rate period and to characterize the transition to the falling rate period. A mathematical model is developed to account for these observations and experimental results for some physical properties of a model material. It allows determination of the internal profile of moisture and the penetration of the drying front during the falling rate period.     

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.     

碱式碳酸镁纳米花的干燥动力学研究

以六水氯化镁和尿素为原料,采用均匀沉淀法制备出碱式碳酸镁纳米花。通过干燥动力学实验得到碱式碳酸镁纳米花的干燥曲线和干燥速率曲线。研究结果表明：在一定温度下碱式碳酸镁纳米花干燥速率曲线呈现明显的升速、恒速和降速三个干燥阶段;随着干燥介质温度的升高,干燥速率增大．干燥时间缩短。通过比较得出的干燥方程符合Page模型。     

HYBRID DRYING OF GRANULAR MATERIALS BY COMBINED RADIATIVE AND CONVECTIVE HEATING

As one of the basic steps of the R&D on hybrid drying by combined radiative and convective heating, drying experiments of a stagnant horizontal wet granular layer heated simultaneously by infrared lamps and hot air were conducted throughout a whole period of the drying. An opaque model, in which the incident radiation is assumed to be absorbed only on the surface of the layer, was introduced to explain experimental trends. Then, the effects of combined heating on drying characteristics of three kinds of samples, a silica sand, a brick and a brown coal were discussed by comparing the experimental data with the calculated results.

The calculated results were found to be in a close agreement with the experimental data obtained on the time behaviors of the drying rate and the temperature distribution in the- layer during not only the preheating and the constant rate periods but also the falling rate period. In the case of the coal layer, however, the falling drying rate different from that in ordinary convective drying had to be considered since it appeared that the radiative heating had an effect to enhance the falling drying rate of the coal owing to some interactions of the coal and water.     

探讨物料工业干燥动态特性的新方法

针对小质量物料干燥动态过程恒速率干燥阶段和降速率干燥阶段，提出了用偏差活化能的方法来避免寻找该两个干燥阶段临界湿分点的困难，并从物理化学的概念推导出了理论动态数学模型，建立了物料干燥动态特性实验台，以实验数据验证模拟结果，效果较好。研究结果表明，利用物料干燥过程偏差活化能的变化特性来研究物料的工业干燥动态特性和干燥机理是可行的。     

HYBRID DRYING OF GRANULAR MATERIALS BY COMBINED RADIATIVE AND CONVECTIVE HEATING

ABSTRACT

As one of the basic steps of the R&D on hybrid drying by combined radiative and convective heating, drying experiments of a stagnant horizontal wet granular layer heated simultaneously by infrared lamps and hot air were conducted throughout a whole period of the drying. An opaque model, in which the incident radiation is assumed to be absorbed only on the surface of the layer, was introduced to explain experimental trends. Then, the effects of combined heating on drying characteristics of three kinds of samples, a silica sand, a brick and a brown coal were discussed by comparing the experimental data with the calculated results.

The calculated results were found to be in a close agreement with the experimental data obtained on the time behaviors of the drying rate and the temperature distribution in the- layer during not only the preheating and the constant rate periods but also the falling rate period. In the case of the coal layer, however, the falling drying rate different from that in ordinary convective drying had to be considered since it appeared that the radiative heating had an effect to enhance the falling drying rate of the coal owing to some interactions of the coal and water.     

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.     

Evaporation Kinetics of Single Droplets Containing Dissolved Bioaiass

Luikov approach was applied to predict drying time and temperature of a droplet containing liquid substrate of entobacterin in the falling drying rate period. Analytical expressions describing both average and local temperatures of the particle in the drying process were derived and solved. Constants necessary to solve the equations, describing certain material properties and material moisture bonding were found in simple experiments. An experimental relationship of Rebinder number and moisture content of the material enabled to calculate changes of average droplet temperature in the falling drying rate period. Analytical solutions of heat transfer equations for shrinkage core model both for a linear and exponential change of moisture content of the droplet in the drying process were delivered. Employing experimental heat transfer coefficient, drying time and droplct temperature field were determined. Comparison of experimental and predicted drying times as well as droplet temperatures shows small discrepancy. Results obtained can be used to predict quality of labile products in the course of drying.     

Characteristic Drying Curves of Cocoa Beans

The characteristic drying curves of cocoa beans are determined by using a tunnel drier where conditioned air passes a single cocoa berm suspended from an electronic balance in the test section. Weight loss, and temperatures of air, testa and nib of the cocoa bean is monitored on personal computers. The nornmalised drying rate versus the normalised moisture content is regressed by least square method to fit a new polynomial model for the penetration falling rate period and a linear model for the regular regime falling rate period. It can be concluded that there are three drying periods for cocoa beans namely the constant drying rate period, the penetration falling rate period and the regular regime falling rate period. The polynomial model estimates the penetration period quite well whereas the linear model estimates the regular regime quite well as well. There is no observable influence of relative humidity and air temperature on the characteristic drying curve of cocoa beans. However, the air velocity seems to have some influence on the curve.     

Mechanism of the First Falling Rate Period: An Alternative Approach by Image Analysis

An alternative experimental approach using the image luminosity of a drying surface photographed by a bore scope was conducted in order to elucidate the drying mechanism for the first falling rate period including the critical moisture content. The observed luminosity was in fair agreement with the luminosity predicted from the model of the configuration of water, indicating that the configuration of water plays a critical role for the drying mechanism, especially for the first falling rate period and the critical moisture content. The parameters of the configuration of water estimated in this work could be effective for prediction of drying rates along with other transport properties.     

Drying of Porous Medium Containing Concentration Sodium Chloride Solution

This work experimentally determined drying rates for beds of glass beads containing a concentrated sodium chloride solution and noted the existence of a constant rate period following a falling rate period. A one-dimensional model was developed to interpret the experimental findings. The salt movement carried by up-flow of solution reduced the chemical potential of the solution near the top surface, hence limiting the drying rate. The model suggested that once the salt concentration at the top reached saturation, the process entered the constant rate drying stage. The proposed model reproduced the drying characteristics for the studied medium with a concentrated NaCl system.     

Characteristic Drying Curves of Cocoa Beans

ABSTRACT

The characteristic drying curves of cocoa beans are determined by using a tunnel drier where conditioned air passes a single cocoa berm suspended from an electronic balance in the test section. Weight loss, and temperatures of air, testa and nib of the cocoa bean is monitored on personal computers. The nornmalised drying rate versus the normalised moisture content is regressed by least square method to fit a new polynomial model for the penetration falling rate period and a linear model for the regular regime falling rate period. It can be concluded that there are three drying periods for cocoa beans namely the constant drying rate period, the penetration falling rate period and the regular regime falling rate period. The polynomial model estimates the penetration period quite well whereas the linear model estimates the regular regime quite well as well. There is no observable influence of relative humidity and air temperature on the characteristic drying curve of cocoa beans. However, the air velocity seems to have some influence on the curve.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Evaporation Kinetics of Single Droplets Containing Dissolved Bioaiass

ABSTRACT

Luikov approach was applied to predict drying time and temperature of a droplet containing liquid substrate of entobacterin in the falling drying rate period. Analytical expressions describing both average and local temperatures of the particle in the drying process were derived and solved. Constants necessary to solve the equations, describing certain material properties and material moisture bonding were found in simple experiments. An experimental relationship of Rebinder number and moisture content of the material enabled to calculate changes of average droplet temperature in the falling drying rate period. Analytical solutions of heat transfer equations for shrinkage core model both for a linear and exponential change of moisture content of the droplet in the drying process were delivered. Employing experimental heat transfer coefficient, drying time and droplct temperature field were determined. Comparison of experimental and predicted drying times as well as droplet temperatures shows small discrepancy. Results obtained can be used to predict quality of labile products in the course of drying.     

AIR DRYING OF ONION: SOME THEORETICAL CONSIDERATIONS

Abstract

The equation for the air drying of solids during a constant drying-rate period was modified to formulate a new model for describing the initial phase of onion drying, with volume shrinkage of dried particle taken into account. The model was fitted to experimental data satisfactory, and the parameters were estimated. It was shown that drying shrinkage of the onion particle, caused that initial phase of the falling drying-rate period is controlled by the external water transfer resistance. It was recommended that the Neuman-type, rather than Dirichlet-type, boundary conditions should be used for calculation of the effective diffusivity during the first phase of the falling rate period of drying of the onion.     

Effect of Segment Scale in a Pore Network of Porous Materials on Drying Periods

Drying periods of porous glass disks of nonhygroscopic MPG glass and hygroscopic Vycor glass were investigated. A simple model of dimensionless segment sizes is proposed where a dimensionless segment size is equal to the value of the tortuosity factor of gas diffusion. This model was applied to the estimation of the segment size and the drying periods of a porous Vycor glass disk. The drying rate curve of the Vycor glass disk showed that the first falling rate period appeared to be included in the constant rate period and that the second falling rate period started right after the constant rate period ended, whereas the drying rate curve of the MPG glass disk estimated from previous models showed that the first falling rate period and the second falling rate period were clearly distinguished. The difference in drying periods between two porous glass disks was caused by a large difference in the respective segment sizes.     

Microwave-Vacuum Drying of Wood: Model Formulation and Verification

Based on the mechanism of moisture and heat transfer in wood during microwave-vacuum drying (MVD), a one-dimensional mathematical model to describe the process of wood MVD was established and verified by experiments in this research. The results showed that the process of MVD of wood experienced three distinct periods: (1) accelerating rate with rapid warming-up drying period, (2) a constant temperature and constant rate drying period, and (3) a heating-up with falling rate drying period. Compared with conventional hot air drying, the total drying process is almost governed by a constant rate period in vacuum-microwave drying of wood. The predicted temperature and moisture content in wood match well with the experimental data, the square of the relevant coefficient of the values of simulation and test is above 0.9, and the simulation precision of the change rule of the moisture is higher than that of the temperature.