Mathematical modeling and influence of ultrasonic pretreatment on microwave vacuum drying kinetics of lotus (Nelumbo nucifera Gaertn.) seeds

The people of Southeast Asia often use lotus as a highly sought-after food source. Here, the effects of ultrasonic pretreatment on the drying kinetics of lotus (Nelumbo nucifera Gaertn.) seeds under microwave vacuum drying were investigated. The best fit model to predict the drying kinetics was also proposed. Lotus seeds were subjected to ultrasonic pretreatment at frequencies of 20, 35, and 80?kHz and power intensity of 0.75 and 1.50?W/g for 10?min using an ultrasonic bath and then to microwave vacuum drying. Five different mathematical models were fitted to the experimental data and a newly proposed model was selected based on model with highest regression coefficient (R²), lowest root mean square error (RMSE), sum square error (SSE), and chi-square (χ²), respectively. Time-domain nuclear magnetic resonance and field scanning electron microscope were used to describe the water state of ultrasonic samples and examine microstructure, respectively. The results showed that ultrasonic pretreatment performed at a relatively low frequency and relatively high power intensity had a positive effect on reducing the drying time (6.25–31.25%) during microwave vacuum drying because of the redistribution of water and the formation of microchannels. In parallel studies, the new model showed the best fit to the drying curve.     

SHRINKAGE OF APPLE DISKS DURING DRYING BY WARM AIR CONVECTION AND FREEZE DRYING

Volumetric and thickness shrinkage evaluated by direct measurement and n-heptane displacement were determined during convective and freeze drying of Golden delicious apples. For convective drying, the influence of blanching and diameter/thickness ratio of the apple disks used were analysed at different levels of moisture content under constant conditions. It was found that shrinkage of dried samples, both by convection and by freeze-drying, is anisotropic to a level which depends on sample geometry (ratio diameter/thickness) used. Blanching did not affect shrinkage results.

Based on results obtained a new model to predict bulk density of materials during drying is proposed, showing a better fit to experimental data than previous models reported in the literature. This model was further used to predict changes in apple porosity during drying.     

SHRINKAGE OF APPLE DISKS DURING DRYING BY WARM AIR CONVECTION AND FREEZE DRYING

ABSTRACT

Volumetric and thickness shrinkage evaluated by direct measurement and n-heptane displacement were determined during convective and freeze drying of Golden delicious apples. For convective drying, the influence of blanching and diameter/thickness ratio of the apple disks used were analysed at different levels of moisture content under constant conditions. It was found that shrinkage of dried samples, both by convection and by freeze-drying, is anisotropic to a level which depends on sample geometry (ratio diameter/thickness) used. Blanching did not affect shrinkage results.

Based on results obtained a new model to predict bulk density of materials during drying is proposed, showing a better fit to experimental data than previous models reported in the literature. This model was further used to predict changes in apple porosity during drying.     

Drying characteristics of Orthosiphon stamineus Benth by solar-assisted heat pump drying

Processing methods of Misai Kucing still remain crude and lack technological advancements. In terms of drying, very few studies have attempted to apply advanced drying technology to improve Misai Kucing quality and drying time. This paper presents first attempt to improve Misai Kucing drying kinetics and product quality through solar-assisted heat pump drying and comparison was made against solar drying. Experimental results showed that solar-dried samples had the greatest total color change and loss of two bioactive ingredients as compared to solar-assisted heat pump-dried samples due to its longer time process, higher drying temperature, and chlorophyll degradation. By comparing the statistical values, it showed that the Page model had the best goodness of fit at all tested dried samples by both drying methods.     

Modeling of Drying of Food Materials with Thickness of Several Centimeters by the Reaction Engineering Approach (REA)

Food materials are highly perishable. Drying is necessary to restrict biological and chemical activity to extend shelf life. A good drying model is useful for design of a better dryer, evaluation of dryer performance, prediction of product quality, and optimization. The reaction engineering approach (REA) is a simple-lumped parameter model revealed to be accurate and robust to model drying of various thin layers or small objects. Modeling drying behavior of different sizes is essential for a good drying model, yet it is still very challenging, even for a traditional diffusion-based model, which requires several sets of experiments to generate the diffusivity function. The REA is implemented in this study, for the first time, to model drying of rather thick samples of food materials. An approximate spatial distribution of sample temperature is introduced and combined with the REA to model drying kinetics. Results have indicated that the REA can model both moisture content and temperature profiles. The accuracy and effectiveness of the REA to model drying of thick samples of food materials are revealed in this study. This has extended the application of REA substantially. The application of the REA is currently not restricted for thin layesr or small objects but also for thick samples.     

生物质型煤热风干燥特性及模型研究

为降低生物质型煤干燥成本,提高干燥效率,研究热风干燥风速和温度对热风干燥特性的影响,拟合了生物质型煤在不同热风干燥条件下水分随时间变化的模拟曲线。结果表明:生物质型煤与多数多孔介质类似,干燥过程可分为加速干燥、恒速干燥、降速干燥3个阶段,其中恒速干燥阶段的干燥时间约25 min;热风温度越高,风速越大,生物质型煤的干燥速率越大,干燥时间越短,干燥时的裂纹率也越高。当干燥温度180℃,风速1.2 m/s时,生物质型煤热风干燥效果较好,干燥热效率最高为48.34%。通过对不同温度、风速条件下的生物质型煤干燥试验数据与常用干燥模型进行拟合分析,发现Sabbet干燥模型拟合度最好,当干燥温度180℃,风速1.2 m/s时相关性系数为0.997,二者相关性显著,因此Sabbet干燥模型可较好地反映生物质型煤在不同温度、风速下的干燥特性。     

A Model for Through Drying of Tissue Paper at Constant Pressure Drop and High Drying Intensity

A mathematical model for through drying of paper at constant pressure drop was developed. The model is based on physical properties; hence, basis weight, pressure drop, drying air temperature, pore size distribution, initial gas fraction, and tortuosity are important input parameters to the model. The model was solved for different combinations of the variables basis weight, drying air temperature, and pressure drop corresponding to industrial conditions and the results were compared with data from bench-scale experiments. The simulations show that the drying rate curve is very sensitive to the air flow rate and that correctly modeling the correlation between pressure drop and air flow rate is the most important factor for a successful model for through drying. The model was tuned by adjusting the parameters initial gas fraction and tortuosity in order to give the best possible fit to experimental data. For a given basis weight and pressure drop, different drying air temperatures resulted in relatively constant values of the fitted parameters. This means that the model can well predict the effects of changes in drying air temperature based on a tuning of the model performed at the same basis weight and pressure drop. However, for a given basis weight, an increase in pressure drop yielded fitted parameters that were somewhat different; i.e., a lower initial gas fraction and a higher tortuosity, a change that increases the resistance to air flow. This implies that the correlation between pressure drop and air flow rate in the model does not quite capture the nonlinear relationship shown by the experiments.     

A Model for Through Drying of Tissue Paper at Constant Pressure Drop and High Drying Intensity

A mathematical model for through drying of paper at constant pressure drop was developed. The model is based on physical properties; hence, basis weight, pressure drop, drying air temperature, pore size distribution, initial gas fraction, and tortuosity are important input parameters to the model. The model was solved for different combinations of the variables basis weight, drying air temperature, and pressure drop corresponding to industrial conditions and the results were compared with data from bench-scale experiments. The simulations show that the drying rate curve is very sensitive to the air flow rate and that correctly modeling the correlation between pressure drop and air flow rate is the most important factor for a successful model for through drying. The model was tuned by adjusting the parameters initial gas fraction and tortuosity in order to give the best possible fit to experimental data. For a given basis weight and pressure drop, different drying air temperatures resulted in relatively constant values of the fitted parameters. This means that the model can well predict the effects of changes in drying air temperature based on a tuning of the model performed at the same basis weight and pressure drop. However, for a given basis weight, an increase in pressure drop yielded fitted parameters that were somewhat different; i.e., a lower initial gas fraction and a higher tortuosity, a change that increases the resistance to air flow. This implies that the correlation between pressure drop and air flow rate in the model does not quite capture the nonlinear relationship shown by the experiments.     

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.     

Dry colour prediction of leather from its wet state

The present investigation describes the development of a regression model for dry colour prediction based on the colour of wet leather. Such a prediction will be useful in the colour matching of leather – the time delay in drying of wet leather and determination of the final colour can be avoided. The use of computer technology interfaced with a reflectance spectrophotometer provides a novel approach to the prediction of dry colour from wet colour. In this study, five different regression models, i.e. linear fit, log fit, quadratic fit, log quadratic fit and cubic fit, were developed, with the dry reflectance of the leather sample as a dependent variable and the wet reflectance of the leather as an independent variable. The relationship between moisture content and surface leather colour, a prerequisite for enabling prediction, was studied. The obtained log quadratic model can be used for accurate prediction of dry colour from wet colour.     

On the investigation into the kinetics of the ultrasound-assisted atmospheric freeze drying of eggplant

Atmospheric freeze drying is a highly attractive process for the dehydration of thermosensitive products, like food, due to the fact that water is removed at low temperature by sublimation. Unfortunately, drying times can be very long because of the internal resistance of the product to vapor diffusion: power ultrasound can be an effective means of accelerating the process, thus reducing the operating cost. The aim of this study was to assess the effect of air temperature and velocity, ultrasound power and sample size on the drying kinetics of eggplant (Solanum melongena L.) samples and, afterward, to analyze in silico an industrial process. Experiments were performed under various conditions regarding air temperature (?5, ?7.5, ?10°C), velocity (2 and 5?m?s^?1), power ultrasound (0, 10.3, 20.5?kW?m^?3, 21.9?kHz), and sample size. Drying rate was measured experimentally. The air velocity showed no relevant effects on the drying kinetics, and the effect of air temperature was slight when compared to the marked reduction in the drying time obtained when ultrasound was applied. The uniformly retreating interface model was modified to account for the cubic shape of the samples and used to establish the kinetic parameters, in particular to evaluate water diffusivity in the dried product, searching for the best fit between measured and calculated moisture content. The model was finally used to optimize the process in silico, considering an industrial unit as test case. In this case, it appeared that power ultrasound can increase the productivity of a tunnel dryer up to four or five times, and it allows the operational and fixed costs of the plant to be reduced significantly.     

A method based on isothermal calorimetry to quantify the influence of moisture on the hydration rate of young cement pastes

Cement hydration needs water to proceed and if water is lost by drying, the hydration rate will decrease. This can be of importance in cases when concrete surfaces are exposed to drying so that their strength development will be retarded. We describe a method based on isothermal calorimetry to assess how the rate of cement hydration is influenced by removal of water (drying) at different times up to three days after mixing. Thin samples of cement pastes are hydrated in a calorimeter and at different times exposed to one hour drying periods. The resulting decrease in thermal power following the removal of water is quantified as a measure of the reduction in hydration rate. The mass loss is found by weighing the samples before and after a measurement, and the change in water activity of a sample during drying can be found from the slope of the thermal power during the drying period.     

Modeling of Drying Curves for Some Foodstuffs Using a Kinetic Equation of High Order

Non-linear regression was used to fit a high order kinetic model to drying curves for mango and cassava. For comparison purposes, the same experimental data were also adjusted by non-lines regression to a model based on exponential series, and to another exponential model by simple linear regression. The high order model fit the experimental data with higher precision (r2 Al.98) than the other exponential series models. The proposed higher order model is mathematically simple as compared to the exponential series, and could be used for simulation of drying processes.     

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.     

Control of drying shrinkage in magnesium silicate hydrate (m-s-h) gel mortars

Magnesium silicate hydrate (M-S-H) gel can be formed by the reaction of MgO with amorphous silica in the presence of sodium hexametaphosphate (Na-HMP). Typical pastes contain 40% MgO and 60% SF and have a w/c ratio of 0.5, but these exhibit shrinkage cracking on drying. The shrinkage characteristics of M-S-H mortar samples containing different additions of sand have been studied using dilatometry. The drying shrinkage was found to decrease with increasing sand addition and to increase with increased water content. Mortars with 60 wt.% sand addition and a w/c ratio of 0.5 had a drying shrinkage of 0.16% and did not show shrinkage cracking. A simple geometrical model based on particle packing is presented that explains the observed changes in drying shrinkage. Based on the geometrical model, the shrinkage of M-S-H mortar system can be reduced to zero when the volume fraction of sand in the mortar is about 0.77.     

Microwave Drying Kinetics of Okra

In this work, the effects of power level and sample mass on moisture content, moisture ratio, drying rate, and drying time of Turkey okra (Hibiscus esculenta L.) were investigated using microwave drying technique. Various microwave power levels ranging from to 180 to 900 W were used for drying of 100 g of okra. To investigate the effect of sample mass on drying, the samples in the range of 25 to 100 g were dried at microwave power level of 360 W. To determine the kinetic parameters, the drying data were fitted to various models based on the ratios of the differences between the initial and final moisture contents and equilibrium moisture content. Among of the models proposed, Page's model gave a better fit for all drying conditions used. The activation energy for microwave drying of okra was calculated using an exponential expression based on Arrhenius equation and was found to be 5.54 W/g.     

超细矿物掺合料对高强混凝土干燥收缩影响

开展了微珠、超细矿粉及硅灰三种超细矿物掺合料对高强混凝土干燥收缩变化规律的研究,采用干燥收缩模型对试验结果进行拟合,并预测其收缩终值.结果表明:微珠和超细矿粉均能减小高强混凝土干燥收缩,且随掺量增加干燥收缩减小越明显;而硅灰的加入会增大高强混凝土的干燥收缩,其掺量越高,混凝土干燥收缩程度越大.采用指数方程得到的预测曲线随着龄期的发展与实测收缩值接近,拟合优度均达到99％以上.     

Intermittent drying of initially saturated porous materials

The aim of this paper is to examine the advantages of convective non-stationary (intermittent) drying and the possibility of its application to materials susceptible to crack formation (wood and ceramics). The notion “non-stationary” means here drying with periodically changeable parameters (air temperature and humidity). The drying time, energy consumption, and quality of dried samples are examined at different schedules of intermittent drying. The acoustic emission (AE) method is applied to monitor on line the material behavior and to detect the commencement of material cracking, and thus to find the moment at which the changes in drying conditions should be initiated. The mathematical model is developed to describe and imitate the intermittent drying kinetics determined experimentally. This model is used next for numerical calculation of the net energy used for drying, and to compare it with the measured total electric energy consumption. The tests were carried out on cylindrically shaped samples of wood and kaolin-clay. The benefits of non-stationary drying with respect to that performed in constant conditions were assessed. Such a formulated subject is a novelty in drying area.     

Comparative study of droplet drying models for CFD modelling

CFD simulation is used to study wall deposition and agglomeration phenomena commonly encountered in industrial spray dryers. This paper initially provides a comparison of two drying kinetics models: Characteristic Drying Curve (CDC) and Reaction Engineering Approach (REA). Comparisons are made with experimental data with application to carbohydrate droplet drying obtained from past workers. These models were then extrapolated to actual drying conditions to assess their performance. The REA model predicts the progressive reduction in drying rate better than the CDC model for the carbohydrate droplets. A modified CDC model incorporating a convex falling rate produced better agreement than the conventional linear falling rate model. Further analysis showed that the REA model can be extended to simulate the particle surface moisture which may affect the agglomeration process. The proposed concept was compared with reported simulation results from a diffusion model which showed reasonable fit with data.     

Modeling of Drying Curves for Some Foodstuffs Using a Kinetic Equation of High Order

ABSTRACT

Non-linear regression was used to fit a high order kinetic model to drying curves for mango and cassava. For comparison purposes, the same experimental data were also adjusted by non-lines regression to a model based on exponential series, and to another exponential model by simple linear regression. The high order model fit the experimental data with higher precision (r2 Al.98) than the other exponential series models. The proposed higher order model is mathematically simple as compared to the exponential series, and could be used for simulation of drying processes.