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.     

Quality Evaluation of Microwave-Dried Packham's Triumph Pear

Abstract

The objectives of this work were to carry out the microwave and microwave-convective drying of pear, in order to preserve the quality by reducing the drying time of the fruit; to compare the kinetic with convective drying mode data and to fit the comparative data to models from literature. The effect of osmotic dehydration and the variation in the microwave power were analyzed at constant values of air temperature and velocity. The experimental data fit well the proposed kinetic model. The processed pear was evaluated with respect to water content, quantity of calcium, phosphorus and potassium, water activity and apparent density. The best results were found for the samples osmotically dehydrated and dried in the microwave-convective dryer. The osmotic dehydration and the short drying times were important to maintain sample characteristics.     

DRYING KINETICS FOR SOME FRUITS: PREDICTING OF POROSITY AND COLOR DURING DEHYDRATION.

ABSTRACT

Drying kinetics of four fruits (prune, quince, fig and strawberry) were studied by using a simple mass transfer mathematical model involving a characteristic parameter (K) as a function of process variables. The model was tested with data produced in a laboratory air dryer, using non-linear regression analysis. The investigation involved three values of sample thickness (5, 10, 15mm) and three different air temperatures (50, 60, 70?°C).

The parameters of the model were found to be greatly affected by sample thickness and air temperature. The effect of moisture content on the porosity of three fruits (namely avocado, prune and strawberry) was also investigated. A simple mathematical model was used to correlate porosity with moisture content. It was found that porosity increased with decreasing moisture content.

Samples of three fruits (avocado, prune and strawberry) were investigated to estimate color changes during conventional drying at 70?°C. A first order kinetic model was fitted to experimental data with great success. It is found that the color of avocado and strawberry change while the color of prune remains the same.

Furthermore, the water sorption isotherms of three fruits (avocado, prune and strawberry) at 25° temperature were determined experimentally and the parameters at the GAB equation were evaluated by means of non-linear regression analysis. The use of the above equation produced a very good fit.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

ABSTRACT

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

Drying Characteristics of Purslane (Portulaca oleraceae L.)

Abstract

Thin layer drying rates of purslane were determined experimentally as a function of temperature with air velocity kept constant at 1.1 m/s and relative humidity below 5%. Thin layer drying data were obtained for purslane at four drying air temperatures (35, 70, 95, and 120°C). Five thin layer-drying models (Henderson and Pabis, exponential, Page, two-term exponential, and Thompson models) were fitted to the drying data. The color of purslane was determined after drying using a spectro-colorimeter (Hunter Lab) in terms of Hunter L, a, and b values. The Page model was found to be most suitable in describing the drying characteristics of purslane. New parameters developed for the model resulted in a good fit at different temperatures. Color measurement indicated that greenness decreased with an increase in drying air temperature. Typical drying times were 88.41, 138.53, 416.38, and 1371.85 min at 120, 95, 70, and 35°C, respectively.     

Determination of Drying Kinetics for Biomass by Thermogravimetric Analysis under Nonisothermal Condition

The nonisothermal drying kinetics of wheat straw and corn stalk has been studied by thermogravimetry. The experimental data have been obtained in order to fit to semitheoretical models widely used to describe drying behavior of agricultural products. Nonisothermal drying models—Newton, Henderson and Pabis, logarithmic, and Page—were evaluated based on the coefficient of determination (R ²), reduced chi-square (χ ²), and root means square error (RMSE). Page's model has been found to be the best for describing the nonisothermal drying characteristics of wheat straw and corn stalk. The activation energy values of wheat straw and corn stalk are determined to be 14.144 and 6.113 kJ mol^?1, respectively.     

A STUDY OF TEMPERATURE AND SAMPLE DIMENSION IN THE DRYING OF POTATOES

Abstract

It is common knowledge that sample size and drying temperature are two of the most important factors affecting the drying rate and quality of food. However, what is less commonly known are how these two factors interact relative to each other and their effects on the drying behaviour of potato. These effects were evaluated under controlled drying conditions using a thermogravimetric analyser. The least-squares method was used to fit a model to the experimental data and the response variables (slope of the first drying stage, transition moisture content and slope of the second drying stage) were determined systematically. Central composite design was applied for response surface modelling of the factors and regression methodology was used to analyse the results. The results showed that both temperature and sample dimension have significant (P=0.01) effect on drying behaviour of potato. Sample dimension significantly affected the transition moisture content, whilst both temperature and sample dimension significantly affected the slopes of the first and second stage of drying.     

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.     

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.     

A Model of Drying Kinetics of Acacia mangium Wood at Different Temperatures

The objective of this study was to determine the isothermal drying kinetics of Acacia mangium wood blocks by employing a relative humidity-controlled drying chamber. A model was developed based on solution of Fick's second law and evaluated through the coefficient of determination (R ² ), sum of square error (SSE), root mean square error (RMSE), and reduced chi-square (χ ² ). This model was compared to semi-theoretical models which are commonly used to describe the drying behavior of biomass in previous studies. The porosity and shrinkage characteristics of dried specimens were also evaluated. Based on the findings in this work, it was determined that the proposed model resulted in an excellent fit with experimental data for all four drying temperature levels of 30, 35, 40, and 45 ^° C to describe the isothermal drying kinetics of Acacia mangium . It appears that volumetric shrinkage of the samples decreased quadratically with decreasing moisture ratio. The activation energy of the drying process was determined to be 41.07 kJ/mol.     

DRYING CHARACTERISTICS OF THE HAZELNUT

Abstract

Equilibrium moisture content isotherms for Spanish hazelnut (Corylus avellana L.) at different temperatures (30°C-80°C) were determined using static gravimetric method. Thin layer drying experiments were done with forced air circulation and were conducted with different operating conditions to determine the drying characteristics of hazelnuts. The effect of air temperature (30°C-70°C), air velocity (0.5 m/s - 2 m/s) and drying bed loading density (50 kg/m² - 150 kg/m²) on drying of unshelled and shelled hazelnuts was studied. Six mathematical models were used to fit the experimental equilibrium moisture content data, from which the G.A.B. model was found to give the best fit. Diffusion coefficients were determined by fitting experimental thin-layer drying curves to the Fick's diffusion model. Variation of the effective diffusion coefficient with temperature was of the Arrhenius type. The Page equation was found to describe adequately the thin layer drying of hazelnut. Page equation drying parameters k and n were correlated with air temperature and relative humidity.     

THIN-LAYER DRYING CHARACTERISTICS FOR GREEN CHILLI

ABSTRACT

Thin-layer drying experiments under overflow–underflow and through flow conditions of green chilli were conducted with air temperature ranging from 40 to 65°C, relative humidity ranging from 10 to 60% and air velocity ranging from 0.10 to 1.0 m/s. The single exponential equation and the Page equation were used to determine the thin-layer drying characteristics for green chilli. Both the equations fitted well to the experimental data. The Page equation was found to describe the thin-layer drying of chilli better than the single exponential equation. The parameters of the Page equation and the single exponential equation were expressed as a function of drying air temperature, relative humidity and air velocity.     

Effect of two stage, tray and heat pump assisted-dehumidified drying on drying characteristics and qualities of dried ginger

Desorption isotherms for sliced gingers have been measured. A non-linear regression programme was used to fit four moisture sorption isotherm models to the experimental data. The Modified Halsey and Modified Oswin models gave the best fit for X_e = f(RH_e, T) and RH_e = f(X_e, T), respectively. Tray and heat pump dehumidified drying incorporated by single and two stage drying were conducted. It was found that the modified Page model was the most effective. The drying constant was fitted to drying air temperature using the Arrhenius model. Effective moisture diffusivities were determined using the drying data. The heat pump dehumidified drying incorporated by the two stage drying could reduce the drying time at 40 °C by 59.32% and increase 6-gingerol content by 6%. Quality evaluation by 6-gingerol content, rehydration ratio and ΔE* showed the best quality for dried sliced gingers in the heat pump dehumidified drying incorporated by the two stage drying at 40 °C.     

THIN-LAYER DRYING BEHAVIOUR OF VEGETABLE WASTES FROM WHOLESALE MARKET

ABSTRACT

The thin-layer drying behaviour of vegetable wastes (as a mix of lettuce and cauliflower leaves) from wholesale market for a temperature range of 50-150^°C was determined. Drying of this material was found to take part only in the falling-rate period. The experimental data were fitted to the simple exponential model and the Page model. Both models have good prediction capability, Effective diffusion coefficient varied from 6.03*10^-9to 3.15*10^-8m3/s with an activation energy of diffusion of 19.82 kJ/mol. The temperature dependence of the effective diffusion coefficient was expressed by an Arrhenius-type relationship.     

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.     

Analysis of the Drying Kinetics of Brachiaria brizantha (Hochst. Stapf) Grass Seeds at Different Drying Modes

Forage grass seeds have a high economical importance in the Brazilian bovine cattle breeding and seed drying is a fundamental stage of processing to guarantee their stability and allow their storage for long periods. In this context, the objective of this work was to develop a pilot-scale belt dryer, which operates also as a fixed and fluidized bed. Brachiaria brizantha seeds dehydration was analyzed under different air velocities and temperatures. Experimental data of moisture content variation along the drying time was successfully fit to a one-term exponential model. The experimental drying rate points were calculated by approximating the derivatives to finite differences. Its behavior was accomplished fitting curves of the drying rate versus water content and time. Finally, fissure, germination, and vigor rates were analyzed as a function of the drying conditions so that the experimental conditions combine the best process efficiency with the best physiological quality maintenance.     

Experimental determination and mathematical modeling of the drying kinetics of a single droplet of colloidal silica

ABSTRACT

Colloidal silica has been used frequently as a model material of drying in the past two decades. Several models of single droplet drying have been validated against the sole experimental evidence by Ne?i? and Vodnik (Kinetics of droplet evaporation. Chemical Engineering Science 1991, 46(2), 527–537), in which relatively scattered experimental data on drying of single droplet of colloidal silica were provided. Due to the importance of this sort of data, the drying of single droplet of colloidal silica was determined more accurately under more extensive conditions in this work. The effect of air temperature on the drying of single droplet of colloidal silica was probed as well as the evolution of particle morphology. The droplet of colloidal silica was found to shrink irregularly during drying due to uneven exposure of droplet surface to air stream. The moisture within the droplet appears to transfer freely to the surface, keeping the surface highly moist. For a large part of drying process, drying of single droplet of colloidal silica is similar to the evaporation of water droplet, which can be predicted well using a simple mathematical model.     

Kinetic studies on radio-selenium uptake by ion exchange resin

Kinetic studies on the sorption of radioactive Se (IV) ion on Amberlite MB9L have been carried out under a wide range of temperature, pH, initial concentration, and resin weight. Analyses of the experimental data by two theoretical models commonly used to explain the ion exchange kinetics and shrinking core model (SCM), and homogeneous diffusion model (HDM) against exponential diffusion decay model (EDM) show a greater preference of EDM over HDM and SCM at all reaction conditions. The obtained regression coefficient values in case of HDM and SCM are in general not high enough to give a satisfactory fit for the experimental data. The estimated values for EDM parameters provides a good satisfactory fit for the yielded adsorption results as the corresponding linear regression values are high. The sorption process is found to be accompanied with fast film diffusion and slow diffusion between the reacted layer and the shrinking un-reacted core within the ion exchange resin. It also shows that ion exchange as the controlling step offers the lowest probability due to the highest obtained diffusion parameters over the normal tested reaction conditions.     

Some Considerations In Simulation Of Superheated Steam Drying Of Softwood Lumber

ABSTRACT

A mathematical model for high-temperature drying of softwood lumber with moist air has been modified and extended to simulate wood drying with superheated steam. In the simulation, differences between the two types of drying are considered, these include: external heat and mass transfer processes and calculation of equilibrium moisture content. The external mass transfer coefficient in the perheated steam drying was found to be much higher than that in the moist air drying, however, the heat ransfer coefficients for these two cases were of the same order. The predicted drying curves and wood temperatures from the superheated steam drying model were compared with experimental data and there was close agreement. Further studies will apply the model to development of commercial drying schedules for wood drying with superheated steam.     

COMBINED CONVECTIVE AND INFRARED DRYING OF A CAPILLARP POROUS BODY

Abstract

This work investigates the effect of spray drying conditions on some properties of tomato powder prepared by spray drying of tomato pulp. A pilot scale spray dryer (Buchi, B-191) with cocurrent regime and a two-fluid nozzle atomizer was employed. Sixty-four different experiments were conducted keeping constant the feed rate, the feed temperature, and the atomizer pressure, and varying the compressed air flow rate, the flow rate of drying air, and the air inlet temperature. Tomato powders were analyzed for moisture, solubility, density (bulk and packed), and hygroscopicity. Analysis of experimental data yielded correlations between powder properties and the above-mentioned variable operating conditions. Regression analysis was used to fit a full second order polynomial, reduced second order polynomials and linear models to the data of each of the properties evaluated. F values for all reduced and linear models with an R ² ≥ 0.70 were calculated to determine if the models could be used in place of full second order polynomials.