Mathematical modelling and simulation of mass transfer in osmotic dehydration processes. Part III: Parametric study (original) (raw)
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Possibility of Using Pseudo-Diffusion Approach to Model Mass Transfer in Osmotic Dehydration
Transactions of the ASAE, 1998
O smotic dehydration is a water removal process performed by immersing cellular tissues, such as fruits and vegetables, in concentrated osmotic solutions. The process involves at least two simultaneous, counter-current flows or fluxes: the solute in the osmotic solution penetrates into the tissue; and water flows from the tissue to the solution. The process is carried out at relatively low temperature and does not involve a phase change of water as in other dehydration processes, such as air drying and freeze drying. The main advantages of osmotic dehydration include minimized heat damage and less discoloration of fruits (Ponting et al., 1966; Contreras and Smyrl, 1981), increased retention of volatile compounds and pigments (Flink and Karel, 1970), and improved texture quality of rehydrated products (Shipman et al., 1972). Cellular tissues can be considered as individual cells embedded in a continuous cell wall matrix. The porous cell walls form channels for flow and the individual cells, which can contain up to 90% of tissue water (Nobel, 1983), function as material sources or sinks. The individual cells are separated from the cell wall by a cell membrane, which allows water to pass through easily but acts as a barrier to solutes to some degree depending on the characteristics of the solutes. The space occupied by the individual cells is generally referred to as intracellular volume and that occupied by the cell wall and free space as extracellular volume. Mass transfer in osmotic dehydration is complicated. When tissues first come in contact with an osmotic solution, the solutes in the solution penetrate into the tissue along the extracellular volume. The penetration of solutes induces a chemical potential difference of water across the cell membranes, and the chemical potential difference drives the water out of the intracellular volume into the osmotic solution through the extracellular volume. The amount of out-flowing water is proportional to the amount of solute that penetrates into the tissue. In osmotic dehydration, however, the volume of the out-flowing water is much larger than that of incoming solute. This inequality results in a non-zero bulk flow velocity from the tissue to the solution, and, therefore, results in shrinkage of the material. For solute penetration, this bulk flow acts as a resistance and sharpens the concentration gradient. This results in a larger diffusion flux even though the total flux is very small (Yao and Le Maguer, 1997a,b). The complicated mass transfer in osmotic dehydration is often modeled by a so called "pseudo-diffusion" approach, in which the heterogeneous material is assumed to be homogeneous and an unsteady-state second-order diffusion equation is used to find an approximate solution of mass transferred. An effective diffusivity is used to account for the effect of the cell membrane, bulk flow, and tissue shrinkage. The effective diffusivity is determined by regressing the experimental data. The majority of modeling in osmotic dehydration employs this approach because of its simplicity (
Osmotic Dehydration: An Analysis of Fluxes and Shrinkage in Cellular Structure
Transactions of the ASAE, 1996
A comprehensive analysis of fluxes and shrinkage in cellular structure immersed in osmotic solution was carried out. A relation between shrinking velocity and bulk flow velocity (volume average velocity) was developed for a shrinking body through volume change. Equations were derived to relate fluxes based on stationary frame and shrinking velocity frame, as well as based on the total interface area and true flow channel in cellular tissue. Computer simulations were carried out to show the trend and relative magnitude of diffusion, bulk flow and net fluxes of potato tissue slice immersed in 0.535 kmol/m^ mannitol solution. It was shown that the net volume flux ratio of water to mannitol was about 60 most of the time, but could be as high as 450 at the beginning of the process. In addition, the bulk flow transported about 90% of water removed in osmotic dehydration and washed back about 60% of mannitol penetrating by diffusion. Therefore the bulk flow should be considered in describing mass transfer in osmotic dehydration.
Comparative Study of Mass Transfer in Wet and Dry Osmotic Dehydration
The differences in the external osmotic medium, dry or dissolved osmotic agent and its concentration (constant or variable) can significantly influence the kinetics of mass transfer. The objective of this work was to compare water and solute transport during the osmotic dehydration of strawberry pieces under different external conditions, wet or dry osmotic agent, with varying types of sugar (sucrose, fructose and isomaltulose). The evolution of the liquid phase concentration as well as the net fluxes under the different scenarios was described and modelled. Results showed that mass transfer kinetics were higher when the concentration of the external medium was variable, in the wet process slightly
A simple model to predict mass transfers in dehydration by osmosis
Zeitschrift f�r Lebensmitteluntersuchung und -Forschung A, 1997
The curves of dehydration by osmosis of 1 cm apple cubes have been simulated assuming the existence of two diffusional species. The diffusivity value of the two species, water and sucrose, was obtained by using a numerical method of non-linear regression analysis. The influence of the solution conditions (temperature and sucrose concentration) on the absorption rate was evaluated. Two sets of experiments were carried out: experiments at 70°Brix and different solution temperatures (30, 40, 50, 60 and 70°C) on the one hand, and experiments at 50°C and different solution concentrations (30, 50 and 70°Brix) on the other. The proposed diffusive model is able to explain 98% of the total variance. This model is also applicable to the simulation of dehydration by osmosis for other food products.
Food and Bioproducts Processing, 2016
The aim of this study was to model both the dynamic and equilibrium mass transfer periods for water, osmotic solute and food solids interchange between product and solution during an osmotic dehydration (OD) process. The OD model is able to represent situations where concentration of osmotic media changes during the process or where interfacial resistance to mass transfer cannot be neglected. Water and solute are considered to move within the product by a diffusion mechanism based on Fick's second law, while external convective mass transfer is considered in the fluid. The state-space form of the model is analytically solved for one-dimensional mass transfer in products with flat slab, infinite cylinders and sphere geometries. The developed theory was applied to the analysis of equilibrium and OD dehydration curves of carrot slices obtained at 40 • C in sodium chloride solutions with and without stirring and different ratios between solution volume and product mass. Water and NaCl diffusivities were identified in the narrow ranges of 6.0-7.6 × 10 −10 m 2 /s and 3.5-4.1 × 10 −10 m 2 /s, respectively, demonstrating the applicability of the proposed model under a wide range of operating conditions.
Mass transfer in cellular tissues. Part II: Computer simulations vs experimental data
Journal of Food Engineering, 1992
The kinetics of equilibration of potato tissue with sucrose solutions was studied. The model developed in a companion paper and based on the internal cellular structure of the plant material was found to be a powerful tool to monitor the changes that occur in the potato tissue, and helps in understanding the phenomena involved in the osmotic process. The proposed model was able to represent the mass transport phenomena successfully. This conclusion relies on the observed good agreement between the predicted and the experimental sucrose and water contents of potato slices. From the results of the simulations, it seems that the water permeability coeJgicient is dependent on the boundary layers that exist at the sur$ace of the plasmalemma membrane. This study has also shown that it is not possible to obtain a good agreement between predicted and experimental data for sucrose content in potato tissue considering only the difision phenomenon.
Multicomponent Diffusion Applied to Osmotic Dehydration
2014
Conclusions: The values of concentration obtained by the simulation proved to be convergent and consistent with the experimental results, which validates the application of FEM to model the osmotic dehydration process. The simplex optimization method, coupled with the functions of desirability, proved to be an effective tool in the search of the primary parameters involved in the diffusion process during the osmotic dehydration of melon pieces.
Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions
Biophysics and Medical Physics Computing, 2014
Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed. Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations
Osmotic Dehydration: Dynamics of Equilibrium and Pseudo-Equilibrium Kinetics
International Journal of Food Properties, 2010
A true equilibrium process usually takes very long to achieve and is very difficult, therefore, a pseudo-equilibrium process is often employed. Several methods exist for predicting pseudo-equilibrium conditions and their accuracies vary. Dynamic equilibrium and pseudo-equilibrium moisture loss (ML) and solids gain (SG) during osmotic dehydration of apple cylinders at different temperature (40, 50, and 60°C) and concentrations (30, 40, 50, and 60°Brix) were evaluated in this study. Pseudo-equilibrium achieved depended on product and processing conditions. Higher concentrations increased the pseudo-equilibrium ML and decreased SG. Two kinds of pseudo-equilibration appear to exist, one for the liquid, which is reached in about 24 h, depending on sample size, the other for the solid matrix, which takes much longer to achieve. Solute penetration in to the product is a much slower process during osmotic dehydration equilibration.
The Osmotic Migration of Cells in a Solute Gradient
Biophysical Journal, 1999
The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.