Apple osmotic dehydration described by three-dimensional numerical solution of the diffusion equation

ABSTRACT

In the present study, experimental data of osmotic dehydration kinetics of apple, cut into slices with parallelepiped shape, were simulated using two types of diffusion models. Model 1 considers the constant values of mass diffusivities and volume of the slices. Model 2, on the other hand, considers variable mass diffusivities and also the shrinkage of the product. The numerical solution of the three-dimensional diffusion equation in Cartesian coordinates was obtained through the finite volume method, with a fully implicit formulation and boundary condition of the first kind. Process parameters were determined by optimization using the experimental data sets, through the minimization of an objective function, called χ². The results of the osmotic dehydration kinetics were compatible with those of other studies found in the literature. Process temperature and osmotic solution concentration had influence on the phenomenon, but temperature was preponderant. A study was conducted on water and sucrose distribution during the osmotic dehydration. The results obtained through the mathematical model that considered the variable diffusivity and shrinkage showed greater adequacy to the experimental data.     

An Experimental Study on Drying of Green Apples

Drying behavior of green apples in a laboratory dryer was examined. Prior to drying, the apples were cut in 8 mm thick slices, which were then treated with citric acid solution and blanched hot water at 80°C. Next, they were dried at 65°C with an air velocity of 2.0 m/s. The shortest drying time (270 min) was obtained with apples pretreated with citric acid solution. The drying data were fitted with 11 mathematical models available in the literature. Selection of the best model was investigated by comparing the determination of coefficient (R ²), reduced chi-square (χ²), root means square error ( RMSE ), and mean relative percentage error (P) between the experimental and predicted values. The results showed that the Wang and Singh, logarithmic, and Verma et al. models gave the best results in describing thin-layer drying of apple slices. The effective moisture diffusivity of pretreated samples with citric acid solution was higher than the other samples.     

Enthalpy-Entropy Compensation for Water Loss of Vegetable Tissues during Air Drying

Transition state theory was used to study enthalpy-entropy compensation for water loss during air drying of potato and apple slices. Slices of either potato or apple of 4-mm thickness, 40 mm diameter and air drying temperatures of 323, 333, 343, and 353 K were employed in the experiments. Moisture content and internal potato and apple slice temperatures were recorded during the drying runs. Water loss during drying was described by the unsteady-state Fick's equation and moisture diffusivity evolution was established by applying the method of the slopes. Thus, the experimental drying curve was compared to the theoretical diffusion curve, and the slope of the two curves were estimated at the same moisture content to in order give the corresponding value of diffusivity. During drying, the moisture diffusivity reached a maximum value as the water content of potato and apple slice was around 1 kg water/kg dry solid, regardless of the air temperature. The isokinetic temperature was found to be 320.2 and 312.8 K for potato and apple tissues, respectively. These values were greater than the experimental harmonic mean temperature, which was found to be 307.4 and 308.3 K for potato and apple tissues, respectively. Thus, it was concluded that the water loss process is enthalpy controlled.     

DRYING OF ONION: EFFECTS OF PRETREATMENT ON MOISTURE TRANSPORT

ABSTRACT

This study investigated the drying of osmosed and fresh onions. Onion slices (0.8 × 0.8 × 0.15 cm) soaked in sodium chloride solutions (10 and 15% w/w) for 60 min at 22°C were submitted to air drying. The experimental kinetics data obtained were employed to determine effective diffusivity, using a mass transfer model based on Fick's law of diffusion applied to thin slabs. The results show those samples soaked in the 10% NaCl solution had faster drying rates and larger moisture diffusion coefficients. The drying time of onions can be reduced to less than half by introducing an hour of osmotic dehydration in a salt solution. The dried previously osmosed samples presented a more natural coloration than the untreated ones did.     

Effective Moisture Diffusivity Estimation from Drying Data. A Comparison Between Various Methods of Analysis

ABSTRACT

Moisture diffusivity is the most crucial property in drying calculations. Literature data are scarce due to the variation of both experimental measurement techniques and methods of analysis. The effect of using different methods of analysis on the same experimental drying data is examined in this work. Detailed and simplified mathematical models, incorporating moisture diffusivity as model parameter, are applied. It is proved, that significant differences in the calculated values of moisture diffusivity result when different models are used, and probably these differences explain the variation in literature data. Thus, the adoption of a standardised methodology will be of great importance in moisture diffusivity evaluation.

The above findings resulted from the application of four alternative models on the drying data of three common food materials, potato, carrot and apple. A typical pilot plant scale dryer with controlled drying air conditions was used for the experiments. The moisture content dependence of the diffusion coefficient was proved significant at the last drying stage, while the temperature dependence followed the well known Arrhenius relation. The effects of considering external mass transfer and volume shrinkage during drying, were also investigated.     

MODELING SIMULTANEOUS HEAT AND MASS TRANSFER FOR MICROWAVE DRYING ON APPLE

Abstract

The effects of heat on moisture diffusion, inner evaporation and internal-heat generation were considered by numerically simultaneous models of heat and mass transfer for microwave drying on apple, assuming that the heat-transfer and mass-transfer coefficients are variable. Application was made to drying by finite difference calculus and predicted results agree with the experimental data.     

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

This article aims to study the mass transient diffusion in solids with a cylindrical shape. To this end, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation. The solution can be used to simulate diffusive processes and to determine thermophysical parameters via optimization techniques. The computational package developed was applied to study the thin-layer drying of peeled bananas. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant; (2) variable V and constant D; (3) V and D are considered variable. For all models, the convective mass transfer coefficient h is considered constant. The statistical indicators show that for the two cases analyzed (low and high temperature), model 3 describes the drying process better than the other models.     

Analysis of the Drying Processes of Osmotically Dehydrated Apple Using the Characteristic Curve Model

ABSTRACT

Round slices (2 mm thick) of fresh apple and of apple subjected to osmo-dehydration processes in sucrose syrups until reaching a_w values of 0.979, 0.968. and 0.958. were air-dried at 50. 60. and 70°C. Analysis of the drying curves showed that the products do not present a constant rate period (except for fresh apple) but showed two falling rate periods. Initial a_w greatly affects the fraction of water lost during the drying processes. The use of the Fick's Second Law was not adequate to describe the experimental drying curves. However, apple drying processes can be modeled by the Characteristic Drying Curve model, using several equations (polynomial and logarithmic) with a high confidence level. The parameters of each equation showed a great dependence on product's a_w These models can be used to predict drying curves within the studied limits in each case, presenting great advantages when compared to classical models based on effective diffusion coefficients.     

DIFFUSION MODELS OF PAPAYA AND MANGO GLACe’ DRYING

ABSTRACT

The objective of this research was to develop diffusion models for papaya and mango glace’ drying. Effective diffusion coefficients of papaya and mango glace’ were evaluated by regression analysis of the experimental data to drying kinetic equation. Models 1 and 2 were developed by assuming that effective diffusion coefficients were constant and varied proportionally with the moisture ratio. Model 3, which the Arrhenius factor was a second-degree polynomial function of moisture content, was developed by assuming that the value of effective diffusion coefficient was constant over a short time interval. Model 4, which was similar to Model 3, was developed by considering the effect of volume shrinkage during drying. Four diffusion models were compared and it was found that the predicted values of moisture contents calculated by using Models 1 and 2 were close to experimental values during the early period of drying. Models 3 and 4 were able to have better predictions particularly towards the final period of drying. However, Model 4 was complicated. Therefore, Model 3 was recommended for calculating drying curves of papaya and mango glace’ drying.     

A Method of Determination of Concentration Dependent Effective Moisture Diffusivity

ABSTRACT

A method based on Fourier series solution to Fick's diffusion equation has been proposed to evaluate effective diffusivity (D) as a function of moisture content in agricultural materials undergoing shrinkage during drying process. The shrinkage kinetics of the particulate was used to correlate its instantaneous size (spherical equivalent diameter) as a function of material moisture content A computer program was used to evaluate D based on shrinkage kinetics and experimental drying data and relate it to moisture content. The method was used to obtain moisture diffusivity data for thin layer drying of grape and corn.     

Kinetics of ultrasound pretreated apple cubes dried in fluidized bed dryer

Abstract

This work evaluated the effect of ultrasonic pretreatment on the production of dehydrated apples (Malus domestica L. var Granny Smith) in a fluidized bed dryer. Cube-shaped apple samples were subjected to ultrasound in an ultrasonic bath and dried in a fluidized bed drier. The experimental design evaluated the effect of ultrasound pretreatment time (0 to 30?min) on the soluble solids loss during pretreatment and on the drying time. The ultrasonic pretreatment was carried out in a bath ultrasound operating at 25?kHz and outputting 55?W/m³ of power density. Distilled water was applied in the pretreatment to produce low-calorie apple cubes. Fluidized bed drying was carried out at 30, 40, and 50?°C. Fick’s law was used to model the drying process and to determine the apparent water diffusivity. The soluble solid loss ranged between 8.7 and 21.2% during the pretreatment, and the apparent water diffusivity during air drying ranged from 1.09?×?10^?6 to 2.81?×?10^?6 m²/min. Ultrasound pretreatment increased the apparent water diffusivity up to 58%. Apple cubes subjected to 20?min of ultrasound pretreatment and dried at 50?°C presented the highest apparent water diffusivity and dried to achieve a water activity of 0.4 in 100?min.     

Air-Drying Kinetics of Osmotically Dehydrated Fruits

ABSTRACT

The air drying kinetics of fresh and osmotically dehydrated fruits (apples) was determined. Two sugars, glucose and sucrose, were used as osmotic dehydration agents. Three levels of sugar concentration (15%, 30% and 45%) and several times of immersion into the sugar solution were used. Following the osmotic preconcentration, the fruit samples were dried at 55°C and the weight of material was recorded. The effective water diffusivity of samples treated under various osmotic conditions was estimated and the results were related to the sugar content and the bulk porosity of the samples. The effective water diffusivity, resulting from the application of the diffusion equation to the drying kinetics of the apples was found to decrease significantly for the samples pretreated by a concentrated sugar solution (e.g. 45%), evidently due to the lower porosity and other physicochemical factors. The low diffusivity may be beneficial in the storage stability and utilization of dehydrated fruits.     

Air Drying Kinetics of Potato Cylinders

ABSTRACT

An experimental air tunnel dryer was used to investigate the kinetics of moisture transport in potato cylinders (Solanum tuberasum). Acoordingly, the experimental results, represnting only falling-rate drying behaviour and hence. dehydration completely controlled by internal mass transfer, were interpreted on the basis of Fick's diffusional model for non-stedy state radial diffusion. The effects of air velocity and temperature on the drying rate were studied. with he temperature being the principal controlling factor. Analysis of the drying curves by the method of slopes resulted in a variable effective moisture diffusivity. Shrinkage as a function of moisture content under various drying conditions was investigated. The volumetric shrinkage of the samples was affected mainly by air velocity. whilst air temperature had a negligible effect. Good agreement was obtained between the experimental apparent density data and the predicted correlation.     

PNEUMATIC DRYING OF MEALS: APPLICATION OF THE VARIABLE DIFFUSIV1TY MODEL

ABSTRACT

The superficial and bound moisture removal from soya meal was studied in a pneumatic dryer. The effect of external condition over the effective diffusivity in drying kinetics prediction has been demonstrated and a model that considers time variable diffusion coefficient was developed and correlated with gas temperature and velocities. A simple experimental technique using a pulse injection of humected solid was utilized to determine real drying kinetics under steady state operation with solids recycling. The model fitted the experimental data well over a gas temperature range between 100° C and 300° C and gas velocities of 3.5 m/ s and 20 m/ s.     

Comparison of four pretreatments on the drying behavior and quality of taro (Colocasia esculenta L. Schott) slices during intermittent microwave vacuum-assisted drying

ABSTRACT

Effect of different pretreatments on drying behavior and quality of taro slices during intermittent microwave vacuum-assisted drying were investigated. Taro slices were subjected to the following pretreatments: blanching (B), blanching and freezing (B?+?F), blanching and immersion in maltodextrin solution (B?+?M), and blanching and immersion in maltodextrin solution and freezing (B?+?M?+?F). The reduction in amylose content, the increase in amylose to amylopectin ratio, the change of mechanical properties, the increase in sample bulk density and reduction in sample porosity and structure collapse during pretreatment processes facilitated heat and moisture transfer and quality changes during drying of taro slices. During drying process, all the pretreatment reduced the drying time of samples. The drying rate included a warming-up period and a falling rate period. The values of effective moisture diffusivity increased gradually as the moisture content decreased. The B?+?M?+?F pretreatment had the shortest drying time, the highest drying rate and the biggest effective moisture diffusivity. Moreover, for B?+?M?+?F pretreatment, the parameters including hardness, crispness, color, and microstructure had remarkable changes as compared with the other pretreatments.     

EVALUATION AND MODELING OF TWO-STAGE OSMO-CONVECTIVE DRYING OF APPLE SLICES

ABSTRACT

Two-stage drying kinetics of cylindrical pieces of apples were evaluated by subjecting test samples first to various osmotic treatments and then to convective air drying to complete the drying process. Osmotic drying was carried out with cut apple cylinders of three different sizes (12, 17 and 20 mm diameter), all with a length to diameter ratio of 1 : 1, in a well agitated large tank containing the osmotic solution at the desired temperature. Solution to fruit volume ratio was kept greater than 60. After the osmotic treatment, apple slices were further dried in a cabinet drier at an average temperature 58°C. A central composite rotatable design (CCRD) with five levels of sucrose concentrations (34–63°Brix) and five temperatures (34–66°C) was used for osmotic treatment. Half-drying time and solids gain time were used as measures of rate of drying and associated diffusion coefficients for moisture loss and solids gain were evaluated. Half-drying time decreased with an increase in temperature or concentration, or a decrease in sample size. Diffusion coefficients were lower for smaller samples, and were higher for migration of moisture as compared to solids. For a given level of moisture removal, air drying times were shorter than osmotic drying times. Composite models were developed to describe the effect of process variables and particle size on the drying behavior of apple slices.     

Effect of sucrose concentration of osmotic dehydration pretreatment on drying characteristics and texture of peach chips dried by infrared drying coupled with explosion puffing drying

Effects of osmotic dehydration (OD) pretreatment on the texture characteristics of peach chips after combination drying were investigated. Peach slices were immersed into 100, 300, and 500?g/L sucrose solution for 4?h, respectively, at room temperature and then predried to a critical moisture content of 0.5?kg water/kg dry matter that was determined by the effective moisture diffusivity (D_eff) curves under infrared drying at 80°C. The peach chips were then dried using explosion puffing drying (EPD). The sucrose solution with lower concentration (100?g/L) would improve the drying rate (DR) of peach slices during infrared drying. However, sucrose solution with higher concentration (500?g/L) might affect water diffusion, resulting in lower drying rate. The changes of texture characteristics of dehydrated peach were ascribed to sucrose uptake during the impregnation step. The content and constitutes of soluble sugars in peach tissue, which was significantly affected by OD treatment, were also detected in the research. The results indicated that the combined infrared and EPD drying, in which OD with appropriate concentration (300?g/L) was applied as pretreatment, could improve the drying characteristics and texture of peach chips.     

The Effect of Path Diffusion on The Effective Moisture Diffuslvlty in Carrot Slabs

ABSTRACT

In order to evaluate the effect of path diffusion on the average moisture diffusivity in carrot. drying curves for different shaves (slices and cylinders) and temperatures of 50, 60 and 70°C were ohtained takine into consideration the use of an average leneth of carrot sample (slice thickness or the cylinder radio). The. results showed significant differences betuecn radial and axial average diffusivities. Significant differences were also observed between core and annular diffusivity. The experimenta1 drying curves did not show enough evidence on the effect of drying temperature on the average moisture diffusivity.     

Mass Transfer in the Celery Slice: Effects of Temperature,Moisture Content,and Density on Water Diffusivity

Abstract

Statistical tests were applied to determine the effects of temperature, moisture content, density, and porosity of material on the effective moisture diffusion coefficient during convective drying of root celery. In biological materials with colloidal capillary-porous structure (like root celery), which shrink considerably during drying and show high heterogeneity, the effective water diffusion coefficient depends not only on material temperature and moisture content, but also on its density. It was found that statistical tests can be applied to predict which independent variables should describe the water diffusivity in colloidal capillary-porous materials. A mathematical model of the effective water diffusion coefficient in root celery was formulated as Arhenius-type equation with moisture content of the raw material, its temperature and density as independent variables.     

Influence of Process Conditions on the Mass Transfer Kinetics of Pulsed Vacuum Osmotically Dehydrated Mango Slices

The pulsed vacuum osmotic dehydration of mango slices was studied using a 2^5–1 fractional factorial design. The process responses were water loss, solids gain, water activity, and the effective diffusivities of the water or solids. Statistical analyses revealed that temperature and solution concentration were significant for all the responses studied. Vacuum time was significant for solids gain and the effective diffusivity of water. Diffusion coefficients were determined using an analytical solution of Fick's unidirectional diffusion equation for flat plates, showing a good fit to the experimental data. Osmotic recirculation and vacuum pressure had no effect on any of the responses studied.