A Comparison of Some Mathematical Models Used for the Prediction of Mass Transfer Kinetics in Osmotic Dehydration of Fruits

Mass transfer in osmotic dehydration of fruits at atmospheric pressure has been modeled either by a phenomenological approach using Crank's model (which is a Fick's law solution) or empirically, using models developed from polynomial equations, mass balances, or relations between process variables (i.e., Magee's, Azuara's, and Page's models). For all of these models, experimental data are required to determine the values of their adjustable parameters for specific processing conditions. From a wide variety of published data, the parameters for moisture loss (ML) and solid gain (SG) were calculated for the above-mentioned models, and a comparison of their correlation capability was made. Azuara's and Page's models yield better correlations (with mean absolute errors less than 1.26% for ML and 0.46% for SG) than Magee's and Crank's models (with mean absolute errors of up to 2.98 and 1.68% for ML and SG, respectively).     

Artificial Neural Network Modeling of Osmotic Dehydration Mass Transfer Kinetics of Fruits

Artificial neural network (ANN) models were developed for the prediction of transient moisture loss (ML) and solid gain (SG) in osmotic dehydration of fruits using process kinetics data from the literature. ANN models for ML and SG were developed based on data over a broad range of operating conditions and ten common processing variables: temperature and concentration of osmotic solution, immersion time, initial water and solid content of the fruit, porosity, surface area, characteristic length, solution-to-fruit mass ratio, and agitation level. The trained models were able to accurately predict the outputs with associated regression coefficients (r) of 0.96 and 0.93, respectively, for ML and SG. These ANN models performed much better than those obtained from linear multivariate regression analysis. The large number of process variables and their wide ranges considered along with their easy implementation in a spreadsheet make them very useful and practical for process design and control.     

Artificial Neural Network Modeling of Osmotic Dehydration Mass Transfer Kinetics of Fruits

Artificial neural network (ANN) models were developed for the prediction of transient moisture loss (ML) and solid gain (SG) in osmotic dehydration of fruits using process kinetics data from the literature. ANN models for ML and SG were developed based on data over a broad range of operating conditions and ten common processing variables: temperature and concentration of osmotic solution, immersion time, initial water and solid content of the fruit, porosity, surface area, characteristic length, solution-to–fruit mass ratio, and agitation level. The trained models were able to accurately predict the outputs with associated regression coefficients (r) of 0.96 and 0.93, respectively, for ML and SG. These ANN models performed much better than those obtained from linear multivariate regression analysis. The large number of process variables and their wide ranges considered along with their easy implementation in a spreadsheet make them very useful and practical for process design and control.     

果蔬渗透脱水过程动力学研究

结合植物组织结构与流体传输过程机理建立了渗透脱水过程的一维质量传递数学模型。模型以植物细胞为传输过程的基本单元，考虑了各组分在细胞内、细胞外、通过细胞膜及胞间连丝的质量扩散，和由于体积收缩而导致的集流传输。以土豆为实验物料，在40℃恒温条件下，采用40％（质量百分比）的蔗糖溶液作为渗透液，进行渗透脱水实验，得到的实验结果与模拟结果十分接近，验证了模型的有效性。通过数值模拟可详细描述渗透脱水过程中土豆细胞内外水和蔗糖的质量浓度分布。并就能源与生产效率方面对“渗透-干燥”与“无预处理干燥”过程作了比较。     

OSMOTIC DEHYDRATION OF PINEAPPLE

The effects of sugar type, sugar concentration, immersion time and temperature on the mass transfer of osmotic dehydration were studied using pie shape slices (7 mm thick with its center cork thrown away) of fresh pineapple (Queen variety, 90% maturity). The dehydration process was performed using two type of sugar as an osmotic agent (glucose and sucrose), three levels of sugar concentration (50, 60, and 70%), three levels of temperature (30, 50, and 70 °C), and three levels of immersion time (3, 6, and 9 hours). Following the osmotic dehydration process, the pineapple was dried at 70 °C for 48 hours. The mass transfer was then calculated and analyzed statistically. Sugar type, concentration, temperature, and length of immersion, have a significant effect on the mass transfer of osmotically dehydrated pineapple. The highest mass transfer of pineapple was found by using sucrose at the concentration of 70%, temperature 50 °C and 9 hours of immersion time.     

Mass Transfer during Osmotic Dehydration in a Multicomponent Solution Rich in Grape Phenolics with Antioxidant Activity

Osmotic dehydration has been assessed as an operation for obtaining solid foodstuffs supplemented with grape phenolics. However, mass transfer in multicomponent osmotic solutions during OD needs to be described appropriately if the infusion of target solutes, in this case phenolics with antioxidant activity, is to be better controlled. The effective diffusion coefficients of moisture, total phenolics, and the major individual phenolics of low-molecular-weight (caftaric acid, coutaric acid, caffeic acid, coumaric acid, ferulic acid, and rutin) were evaluated during the OD of a model food with a concentrated red grape must. An increase in the concentration of soluble solids above 50° Brix decreased the level of penetration of phenolics in the model food.     

Mass Transfer during Osmotic Dehydration in a Multicomponent Solution Rich in Grape Phenolics with Antioxidant Activity

Osmotic dehydration has been assessed as an operation for obtaining solid foodstuffs supplemented with grape phenolics. However, mass transfer in multicomponent osmotic solutions during OD needs to be described appropriately if the infusion of target solutes, in this case phenolics with antioxidant activity, is to be better controlled. The effective diffusion coefficients of moisture, total phenolics, and the major individual phenolics of low-molecular-weight (caftaric acid, coutaric acid, caffeic acid, coumaric acid, ferulic acid, and rutin) were evaluated during the OD of a model food with a concentrated red grape must. An increase in the concentration of soluble solids above 50° Brix decreased the level of penetration of phenolics in the model food.     

ANN-Based Models for Moisture Diffusivity Coefficient and Moisture Loss at Equilibrium in Osmotic Dehydration Process

Equations were developed using artificial neural networks to predict water diffusivity coefficient (D_e) and moisture loss at equilibrium point (ML_∞) in order to get the moisture loss (ML) at any time in osmotic dehydration of fruits. These models mathematically correlate nine processing variables (temperature and concentration of osmotic solution, water and solid composition of the fruit, porosity, surface area, characteristic length, solution-to-fruit mass ratio, and agitation level) with D_e and ML_∞. Models were developed using a wide variety of data from the literature and they were able to predict D_e (r = 0.98) and ML_∞(r = 0.94) in a wide range of variable conditions. With these two parameters known, ML can be calculated using Crank's solutions of Fick's second law. The wide range of processing variables considered for the formulation of these models, and their easy implementation in a spreadsheet, using a set of equations, makes them very useful and practical for process design and control.     

ANN-Based Models for Moisture Diffusivity Coefficient and Moisture Loss at Equilibrium in Osmotic Dehydration Process

Equations were developed using artificial neural networks to predict water diffusivity coefficient (D _e ) and moisture loss at equilibrium point (ML _∞) in order to get the moisture loss (ML) at any time in osmotic dehydration of fruits. These models mathematically correlate nine processing variables (temperature and concentration of osmotic solution, water and solid composition of the fruit, porosity, surface area, characteristic length, solution-to-fruit mass ratio, and agitation level) with D _e and ML _∞. Models were developed using a wide variety of data from the literature and they were able to predict D _e (r = 0.98) and ML _∞(r = 0.94) in a wide range of variable conditions. With these two parameters known, ML can be calculated using Crank's solutions of Fick's second law. The wide range of processing variables considered for the formulation of these models, and their easy implementation in a spreadsheet, using a set of equations, makes them very useful and practical for process design and control.     

Effect of Blanching by Ohmic Heating on the Osmotic Dehydration Behavior of Apple Cubes

The effect of blanching by ohmic heating (OH) on the damage to apple tissues and subsequent osmotic dehydration kinetics was investigated. Apple cubes were heated ohmically to various blanching scales. Heating temperature and duration were, respectively, 60–95 ± 2°C and 0–6 min. After cooling, the treated samples were put into sucrose solutions (70 °B) for the osmotic dehydration (OD). The equilibrium state of osmotic dehydration was estimated using the Azuara model. Ohmic heating leads, even for short treatments, to significant changes in the cellular structure of apples and to the enhancement of mass transfer during osmotic dehydration.     

Assessment of Osmotic Process in Combination with Coating on Effective Diffusivities during Drying of Apple Slices

The effect of carboxymethyl cellulose (CMC) coating on the mass exchanges during the osmotic dehydration of apples and its effect on the quality of final product were studied. Coating semi-rings of apple with CMC solution (1%) was found to prevent solute uptake and to reduce salt diffusion coefficient from 4.35 × 10^-10 m²/s to 2.86 × 10^-10 m²/s. However, coating did not significantly affect the diffusivity of water. The effective diffusivity of salt and consequently solids gain were found to be depended on the concentration of CMC solution in the range of 0-1%. Increasing the concentration of CMC further from 1% had no effect on the mass exchanges during the osmotic process. Maximum performance ratio, defined as water loss/solids gain, and the lowest solids diffusion was observed for coated samples (with 1% CMC solution) treated with an osmotic solution containing glucose syrup (50%) and NaCl (2%).     

Mathematical modeling of moisture and solute diffusion in the cylindrical green bean during osmotic dehydration in salt solution

In this study, mass transfer during osmotic dehydration of cylindrical cut green beans in salt solution was investigated. The osmotic solution concentrations used were 10%, 20% and 26.5% (w/w) NaCl, osmotic solution temperatures used were 30 °C, 40 °C and 50 °C, the solution-to-green bean mass ratio was more than 20:1 (w/w) and the process duration varied from 0 to 6 hr. A two-parameter mathematical model developed by Azuara et al. (1992) was used for describing the mass transfer in osmotic dehydration of green bean samples and estimation of the final equilibrium moisture loss and solid gain. Effective radial diffusivity of moisture as well as solute was estimated using the analytical solution of Fick's second law of diffusion in the cylindrical coordinates. For above conditions of osmotic dehydration, moisture and salt effective diffusivities were found to be in the range of 1.776 × 10⁻¹⁰-2.707 × 10⁻¹⁰ m²/s and 1.126 × 10⁻¹⁰-1.667 × 10⁻¹⁰ m²/s, respectively. Moisture and solute distributions as a function of time and location in the radial direction were plotted by using the estimated equilibrium moisture and solute concentrations and also moisture and solute diffusivities.     

Osmotic Dehydration of Apple Cylinders: I. Conventional Batch Processing Conditions

Osmotic drying was carried out, with cylindrical samples of apple cut to a diameter-to-length ratio of 1:1, in a well-agitated large tank containing the osmotic solution at the desired temperature. The solution-to-fruit volume ratio was kept greater than 30. A modified central composite rotatable design (CCRD) was used with five levels of sucrose concentrations (34–63°Brix) and five temperatures (34–66°C). Kinetic parameters weight reduction (WR), moisture loss (ML), solids gain (SG) were considered. A polynomial regression model was developed to relate moisture loss and solids gain to process variables. A conventional diffusion model involving a finite cylinder was also used for moisture loss and solids gain, and the associated diffusion coefficients were computed. The calculated moisture diffusivity ranged from 8.20 × 10^?10 to 24.26 × 10^?10 m²/s and the solute diffusivity ranged from 7.82 × 10^?10 to 37.24 × 10^?10 m²/s. Suitable ranges of main parameters were identified for OD kinetics further study.     

Osmotic Dehydration of Apple Cylinders: I. Conventional Batch Processing Conditions

Osmotic drying was carried out, with cylindrical samples of apple cut to a diameter-to-length ratio of 1:1, in a well-agitated large tank containing the osmotic solution at the desired temperature. The solution-to-fruit volume ratio was kept greater than 30. A modified central composite rotatable design (CCRD) was used with five levels of sucrose concentrations (34-63°Brix) and five temperatures (34-66°C). Kinetic parameters weight reduction (WR), moisture loss (ML), solids gain (SG) were considered. A polynomial regression model was developed to relate moisture loss and solids gain to process variables. A conventional diffusion model involving a finite cylinder was also used for moisture loss and solids gain, and the associated diffusion coefficients were computed. The calculated moisture diffusivity ranged from 8.20 × 10^-10 to 24.26 × 10^-10 m²/s and the solute diffusivity ranged from 7.82 × 10^-10 to 37.24 × 10^-10 m²/s. Suitable ranges of main parameters were identified for OD kinetics further study.     

Enthalpy-Entropy Compensation and Water Transfer Mechanism in Osmotically Dehydrated Agar Gel

Enthalpy-entropy compensation and water transfer in osmotically dehydrated agar gel were studied by carrying out experiments at 30, 40, and 50°C in a 60% (w/w) sucrose solution. An additional experiment was carried out at the isokinetic temperature (T_B = 14°C) to confirm the physical meaning of T_B. When osmotic dehydration (OD) was carried out at the isokinetic temperature, the diffusion coefficient remained constant (≈0.54 × 10^?10 m²/s) during the entire process and the weight loss reached a limit (≈0.277 g/g) when the process was performed at T_B. Leffler's criterion indicated that diffusion mechanism was entropically controlled given the internal resistance developed during OD. Results were confirmed by the linear relationship found between the relaxation time and entropy variation according to the Adam and Gibbs equation.     

Osmotic Dehydration of Apple Cylinders: III. Continuous Medium Flow Microwave Heating Conditions

Continuous flow osmotic drying permits a better exchange of moisture and solids between the food particle and osmotic solution than the batch process. Osmotic drying has been well studied by several researchers mostly in the batch mode. Microwave heating has been traditionally recognized to provide rapid heating conditions. Its role in the finish drying of food products has also been recognized. In this study, the effects of process temperature, solution concentration on moisture loss (ML), solids gain (SG), and mass transport coefficients (k_m and k_s) were evaluated and compared under microwave, assisted osmotic dehydration (MWOD) versus continuous flow osmotic dehydration (CFOD). Apple cylinders (2 cm diameter, 2 cm height) were subjected to continuous flow osmotic solution at different concentrations (30, 40, 50, and 60°Brix sucrose) and temperatures (40, 50, and 60°C). Similar treatments were also given with samples subjected to microwave heating. Results obtained showed that solids gain by the samples was always lower when carried out under microwave heating, while the moisture loss was increased. The greater moisture loss strongly counteracted solids gain in MWOD and thus the overall ratio of ML/SG was higher in MWOD than in CFOD.     

Osmotic Dehydration of Apple Cylinders: II. Continuous Medium Flow Heating Conditions

Mass transfer of apple cylinders during osmotic dehydration was quantitatively investigated under continuous medium flow conditions. The influences of the main process variables (solution concentration, operation temperature, contact time, and solution flow rate) were determined. A second-order polynomial regression model was used to relate weight reduction (WR), moisture loss (ML), solids gain (SG), and mass diffusivity (D _m and D _s ) to process variables. The conventional diffusion model using a solution of Fick's unsteady state law involving a finite cylinder was applied for moisture diffusivity and solute diffusivity determination. Diffusion coefficients were in the range of 10^?9–10^?10 m²/s, and moisture diffusivity increased with temperature and flow rate, increased with solution concentration (> 50°Brix), and decreased with increasing solution concentration (< 50°Brix), but solids diffusivity increased with temperature and concentration and decreased with increasing flow rate. A continuous-flow osmotic dehydration (CFOD) contactor was developed to be a more efficient process in terms of osmotic dehydration efficiency: time to reach certain weight reduction (T _w ) and moisture loss (T _m ) were shorter than that of conventional osmotic (COD) dehydration processes. Effectiveness evaluation functions used in this study could be widely applied to osmotic dehydration system evaluation.