Drying description of cylindrical pieces of bananas in different temperatures using diffusion models

Three diffusion models were used to describe drying of bananas cut into cylindrical pieces. Analytical solutions of the diffusion equation with boundary conditions of the first and third kind were used to describe the process. In the drying experiments using hot air, the cylindrical pieces had the following dimensions: length of about 21 mm and radius of 15 mm, on average. The drying air temperatures were 40, 50, 60 and 70 °C. To determine the process parameters, an optimizer was coupled to the analytical solutions. For the best model, the effective mass diffusivities were 2.53 × 10⁻⁸; 3.12 × 10⁻⁸; 6.19 × 10⁻⁸ and 7.32 × 10⁻⁸ m² min⁻¹, while the convective mass transfer coefficients were 1.93 × 10⁻⁵; 3.04 × 10⁻⁵; 3.18 × 10⁻⁵ and 4.97 × 10⁻⁵ m min⁻¹. The determination coefficients were greater than 0.9990 and the chi-squares were less than 5.3 × 10⁻³ for all simulations of the experiments.     

A new solution approach for simultaneous heat and mass transfer during convective drying of mango

The present investigation is contemplated to fill a gap in analytical modelling of coupled heat and mass transfer during convective drying process. A transport model to describe the temperature and moisture evolutions of mango slab is established. The main innovation introduced in this study is represented with the procedure of temperature and moisture predictions. Mango fruit dehydration can be easily simulated with implementation of the present advanced analytical technique at different operating conditions. Moreover, the temperature and moisture history of mango slice are presented for varying values of the drying air factors counting temperature, velocity, relative humidity and initial food temperature. This work confirms that notable time can be saved without sacrificing accuracy by applying proposed model. This method is expected to be useful for fast and accurate drying simulation. The agreement between published experimental results and model predictions is remarkable and an accurate simulation of experimental drying curves is obtained.     

Osmotic dehydration kinetics of banana slices considering variable diffusivities and shrinkage

This article studied the use of diffusion models to describe variation of water quantity and sucrose quantity during osmotic dehydration of bananas cut into cylindrical slices. Bananas with radius of 1.7 cm and 18 °Brix (on average) were cut into 1.0 cm of thickness. A solution was proposed for the diffusion equation in cylindrical coordinates using the finite volume method, with fully implicit formulation. The diffusion equation was discretized assuming diffusivities and dimensions with variable values for the banana slices. Boundary conditions of the third kind have also been considered. The osmotic dehydration experiments were conducted in binary solutions (water and sucrose) under conditions of 40 and 60 °Brix and temperatures of 40 and 70°C. Mathematical modeling was proposed to describe the processes presented good results for water quantity and sucrose quantity, with good statistical indicators for all fits.     

Evaluation of water, sucrose and NaCl effective diffusivities during osmotic dehydration of banana (Musa sapientum, shum.)

Osmotic dehydration of banana (Musa sapientum, shum.) was optimized with respect to temperature (25-55 °C), salt (0-10 g/100 g) and sucrose (30-60 g/100 g) concentrations through response surface methodology. The solution of Fick’s law for unsteady-state mass transfer in a cylindrical configuration was used to calculate the effective diffusivities of water, sucrose and NaCl. Analyses were conducted in triplicate for moisture, sugar and salt contents. Peleg’s model was used to predict the equilibrium condition, which was shown to be appropriate for water loss and solute uptake. For the above conditions of osmotic dehydration, the effective diffusivity of water was found to be in the range of 5.19-6.47 × 10⁻¹⁰ m² s⁻¹, the sucrose effective diffusivity between 4.27-6.01 × 10⁻¹⁰ m² s⁻¹ and that of NaCl between 4.32-5.42 × 10⁻¹⁰ m² s⁻¹. The working conditions that simultaneously optimize these 3 variables were the temperature of 25 °C with a solution composed of 30 g/100 g of sucrose and 10 g/100 g of sodium chloride. This condition provided values of 4.80 × 10⁻¹⁰ m² s⁻¹ for effective diffusivity of water, of 3.21 × 10⁻¹⁰ m² s⁻¹ for effective diffusivity of sucrose and 4.49 × 10⁻¹⁰ m² s⁻¹ for effective diffusivity of sodium chloride.     

A novel approach to evaluate the temperature during drying of food products with negligible external resistance to mass transfer

The paper deals with modeling the convective drying process. A relevant and reliable mathematical model that captures the history and distribution of temperature is presented. The attention is focused on the simultaneous heat and mass transfer occurring during drying where dry and hot air flows about the food. In the present study, external resistance to mass transfer is considered negligible. As a result, the drying curve is almost independent of the boundary conditions, which means that drying is diffusion-controlled. The main connotation of present study regards to undertake analytical procedure to establish the novel model for practical applications. The results show that the temperature evolution can be evaluated from an advanced analytical solution in a quick and efficient manner. The model is validated with the literature experimental data obtained for carrot and mango slabs. A good agreement is obtained between the model predictions and the available experimental results.     

Vacuum drying kinetics of Asian white radish (Raphanus sativus L.) slices

In this study, radish slices were dried as single layers with thickness of 4 and 6 mm in the ranges of 40-60 °C of drying air temperature in a laboratory scale vacuum dryer. The effect of drying air temperature and slice thickness on the drying characteristics was determined. Moisture transfer from radish slices was described by applying the Fick's diffusion model, and the effective diffusivity changes between 6.92 × 10⁻⁹ and 14.59 × 10⁻⁹ m²/s within the given temperature range. Effective diffusivity increased with increasing temperature. An Arrhenius relation with activation energy values of 16.49 and 20.26 kJ/mol for the thickness of 4 and 6 mm expressed the effect of temperature and sample thickness on the diffusivity. A non-linear regression procedure was used to fit nine thin-layer drying models available in the literature to the experimental moisture loss data. The models were compared based on the coefficient of determination, mean relative percent deviation, root mean square error, and the reduced chi-square between the observed and predicted moisture ratios. The logarithmic model has shown a better fit to the experimental drying data as compared to other models.     

Osmotic dehydration of pineapple (Ananas comosus) pieces in cubical shape described by diffusion models

To prolong the post-harvest life of agricultural products, one alternative is water removal. Pineapples, for instance, can be peeled, cut into pieces and dried. Conventional drying is an expensive operation due to the phase change of the water from liquid to vapor. Thus, a pretreatment such as osmotic dehydration is normally used. The main objective of this article is to describe the osmotic dehydration of pineapples cut in a cubical configuration, using the three-dimensional analytical solution of the diffusion equation and an algorithm optimization. Three models were proposed to describe the experiments with two concentrations of the solution of water and sucrose: 40 and 70 °Brix. One model that used several terms of the series that represents the analytical solution with boundary condition of the third kind well described the kinetics of water and solid migration, and enabled to predict the mass distributions at any given time.     

Modelling the mass transfer during convective, microwave and combined microwave-convective drying of solid slabs and cylinders

In the present work, the mass transfer characteristics, namely moisture diffusivity and moisture transfer coefficient, of slab and cylindrical potato samples were evaluated by adopting the analytical model proposed by Dincer and Dost [Drying Technology, 13,1/2 (1995), 425]. As part of the experimental work, the moisture contents of slab and cylindrical potato samples dried under convective, microwave and combined convective–microwave conditions (air temperature, 30–60 °C; air velocity, 1–2 ms⁻¹; microwave output power, 30–650 W) were measured. From the data collected the drying coefficients and lag factors were calculated and incorporated into the model. The results showed a reasonably good agreement between the values predicted from the correlation and the experimental observations; average error between experimental and predicted results less that 10%. The experimental system exhibited mass transfer Bi numbers in the range 0.038–11.4, thus indicating the presence of finite internal and external resistances. Moisture diffusivity values in the range 0.13×10⁻⁸ to 24.22×10⁻⁸ m²s⁻¹ were calculated.     

Dependence of the effective diffusion coefficient of moisture with thickness and temperature in convective drying of sliced materials. A study on slices of banana, cassava and pumpkin

Several studies have indicated that effective diffusion coefficients of slices apparently vary with the thickness of the samples. Even though the effective diffusion coefficients have been observed to be dependent on the square of the slice thickness, a theoretical explanation to this behavior is not available to date. A theoretical model is formulated herein, in order to correlate effective diffusion coefficient of moisture in the slices with the slice thickness. Experiments are carried out for drying of slices of different thicknesses of banana, cassava and pumpkin in order to evaluate the effective diffusion coefficients. The model is found to describe the variation of the effective diffusion coefficient with slice thickness very satisfactorily. A possibility of the estimation of the axial and radial diffusion coefficients of moisture in the slices is also outlined.     

Modelling the growth of Listeria monocytogenes in fresh green coconut (Cocos nucifera L.) water

The behaviour of Listeria monocytogenes in the fresh coconut water stored at 4 °C, 10 °C and 35 °C was studied. The coconut water was aseptically extracted from green coconuts (Cocos nucifera L.) and samples were inoculated in triplicate with a mixture of 5 strains of L. monocytogenes with a mean population of approximately 3 log₁₀ CFU/mL. The kinetic parameters of the bacteria were estimated from the Baranyi model, and compared with predictions of the Pathogen Modelling Program so as to predict its behaviour in the beverage. The results demonstrated that fresh green coconut water was a beverage propitious for the survival and growth of L. monocytogenes and that refrigeration at 10 °C or 4 °C retarded, but did not inhibit, growth of this bacterium. Temperature abuse at 35 °C considerably reduced the lagtimes. The study shows that L. monocytogenes growth in fresh green coconut water is controlled for several days by storage at low temperature, mainly at 4 °C. Thus, for risk population this product should only be drunk directly from the coconut or despite the sensorial alterations should be consumed pasteurized.     

Diffusivity,shrinkage and simulated drying of litchi fruit (Litchi Chinensis Sonn.)

Litchi (Litchi Chinensis Sonn.) is an important commercial fruit in Thailand and Vietnam. Litchi fruit is consumed both as fresh and dried products. Also most of the export of litchi is in the form of dried whole litchi fruit. Thermo-physical properties and drying model of litchi fruit is important for optimum design of litchi dryer. This paper presents moisture diffusivity, shrinkage and finite element simulated drying of litchi fruit. The moisture diffusivities of litchi were determined by minimizing the sum of square of deviations between the predicted and experimental values of moisture content of thin layer drying under controlled conditions of air temperature and relative humidity. The components in the form of cylinder for seed and seed stalk and slab for seed coat, shell and flesh were dried in thin layers at the air temperatures of 50, 60, 70 and 80 °C and relative humidity in the range of 10–25%. The mean diffusivity of flesh, seed and shell of litchi fruit increased with temperature and was expressed by the Arrhenius-type equation, but the diffusivities of seed coat and seed stalk were independent of temperature. The moisture diffusivities of seed coat and seed stalk were much lower than those of the other parts of the litchi. The shrinkage of litchi fruit has also been determined experimentally and it was expressed as a function of moisture reduction. A two-dimensional finite element model has been developed to simulate moisture diffusion in litchi fruit during drying. Shrinkage of the flesh and different component diffusivities of litchi during drying were also taken into account. The finite element model was programmed in Compaq Visual FORTRAN version 6.5. This finite element model satisfactorily predicts the moisture diffusion during drying. Moisture contents in the different components in the litchi fruit during drying were also simulated. This study provides an understanding of the transport processes in the different components of the litchi fruit.     

Analysis of chemical and structural changes in kiwifruit (Actinidia deliciosa cv Hayward) through the osmotic dehydration

Osmotic dehydration experiments of kiwifruit (Actinidia deliciosa cv Hayward) were carried out in order to apply a nonlinear irreversible thermodynamic model. Samples were immersed into 65% (w/w) sucrose aqueous solution at 30 °C during 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 250, 320, 400, 720, 1440 min. Some physical-chemical parameters were measured in fresh, treated and reposed (24 h at 30 °C) samples. It was possible to apply the enthalpy-entropy compensation coupled to a nonlinear thermodynamic model, obtaining the apparent bulk modulus and explaining the elastic answer of the tissue throughout the osmotic process. The osmotic dehydration also produces losses in the native compounds of kiwifruit such as citric acid and Calcium and Potassium.     

Determining the effective diffusion coefficient of water in banana (Prata variety) during osmotic dehydration and its use in predictive models

The objective of this study was to develop a suitable method for determining the effective diffusion coefficient of water in banana (Prata variety) from experimental data of osmotic dehydration (OD) and using this coefficient for predicting dehydration of the same sample under other situations. Different methods were compared in order to determine the best coefficient to be used in the predictive models. The analytical solution of the diffusion equation allowed estimating averaged values of coefficients between the initial moisture and the average sample moisture at a given instant. The numerical method allowed estimating how the effective diffusion coefficient varies with the moisture. The models prediction ability were validated using a dehydration data set not used for estimating the diffusion coefficients. The use of the diffusive model with a coefficient that depends on the moisture content has the best predictive ability, because it takes into account that the coefficient decreases during the OD.     

椰子水多糖的结构和体外生物学活性分析

采用气相色谱-离子迁移谱（GC-IMS）和化学计量法,研究了成熟椰子水在−18 ℃冷冻0、1、2和3个月（CW0、CW1、CW2和CW3）后挥发性物质的变化。结果表明：GC-IMS能够从成熟椰子水中鉴定出29种挥发性有机物,包括13种醇类、6种酯类、6种醛类、2种酮类、2种酸类物质。经冷冻后,挥发性物质的总量（峰值体积）发生了显著的降低和散失。随着冷冻时间的延长,酸类化合物峰体积逐渐增强并在冷冻第2个月后达到最大值,而后降低。醇、酯、醛类物质峰体积逐渐上升并在冷冻第三个月后达到最大值,酮类物质峰体积逐渐降低,并在冷冻2个月之后达到最小值。主成分分析（PCA）和正交偏最小二乘判别分析（OPLS-DA）均能在不过拟合的情况下对4种椰子水进行判别;进一步从鉴定出的挥发性物质中,根据可变重要性投影（VIP）值>1选取9个关键标志物,在聚类热图分析中分别实现对4种椰子水的聚类和有效区分,其中乙酸乙酯（D、M）、异丁醛、乙醛、己酸乙酯、2-丁酮、乙酸（M）可作为椰子水不同冷冻时长的阶段标志物。研究结果为不同冷冻时间下椰汁的GC-IMS快速鉴别提供了依据。     

Optimization of the antioxidant capacity of thyme (Thymus vulgaris L.) extracts: Management of the convective drying process assisted by power ultrasound

Food properties change during processing, altering the quality of the final product. Sometimes, the important causal relationships are not well known and thus process management is difficult. This is especially true when chemical changes can occur as in the case of the drying of bioactive materials. The aim of this work was to develop a management tool for the thyme drying process, assisted by power ultrasound, to allow the appropriate values of the operating conditions that maximize the antioxidant capacity (AC) of the dried thyme extracts to be determined. For this proposal, the thyme drying process was analyzed at different drying air temperatures (T) (40–80 °C), drying air velocities (v_a) (1–3 m/s) and levels of power ultrasound (US) (0, 6.2, 12.3, 18.5 kW m⁻³). The essential oil was extracted by means of a supercritical fluid extraction method, and its AC was measured by FRAP. The drying velocity and the AC of the dried thyme extracts were both influenced by the magnitude of the air velocity and temperature, and also by power ultrasound. Artificial neural networks were developed to formulate and solve the optimization problem. The developed management tool allowed the optimal conditions of the process to be established, thereby maximizing the AC values in function of the raw materials, process characteristics and room air conditions.