Anisotropic diffusion during osmotic dehydration of celery stalks in salt solution
Introduction
Osmotic dehydration is widely used for partial removal of water from plant tissues by immersion in a hypertonic (osmotic) solution. The difference between the osmotic pressure in the material and solution gives rise to simultaneous counter-current water diffusion from the food to the solution and solute diffusion into the food. Osmotic dehydration has many advantages such as: improving the organoleptic food properties such as color, flavor, or aroma and texture; increasing the product storage time; energy saving compared to other drying techniques; simple process equipment and reducing the processing time due to the absence of phase change. This process is considered to be as a pre-process for conventional drying systems (Lewicki and Lenart, 2015).
The rate of mass transfer in osmotic dehydration is affected by concentration and temperature of the osmotic solution (Herman Lara et al., 2013, Rastogi and Raghavarao, 1994, Rastogi and Raghavarao, 1997), agitation (Mavroudis et al., 1998), food to osmotic solution volume ratio (Da Conceicao Silva et al., 2012), food structure (porosity, etc.), shape and size (Ruiz Lopez et al., 2010, Sirousazar et al., 2009, Van Nieuwenhuijzen et al., 2001), nature and molecular weight of the osmotic solute (Lenart and Flink, 1984, Tsamoa et al., 2005) and pressure (Fito, 1994, Rastogi and Niranjan, 1998, Rastogi and Raghavarao, 1996). Fickian diffusion model is usually used for modeling of mass transfer during drying and osmotic dehydration of solids. In some researches, the dehydration process was carried out in high solution to material volume ratio in one dimensional (Abbasi-Souraki et al., 2012, Abbasi-Souraki et al., 2013a, Abbasi-Souraki et al., 2013b) and multidimensional systems (Abbasi-Souraki and Mowla, 2008, Da Silva et al., 2014, Ruiz Lopez et al., 2010). Some researches were also carried out in low solution to material volume ratio and thus varying solution concentration in one dimensional (Singh et al., 2007, Telis et al., 2003) and multidimensional systems (Khin et al., 2006, Ruiz Lopez et al., 2010). Solutions of the Fickian diffusion equation with different boundary conditions have been developed, comprehensively, by Crank (1975).
In some agricultural products, internal textures could be different from the longitudinal direction compared with the lateral direction of growth (Fernando et al., 2011), and considering the same properties for all directions of the product (isotropic structure), could potentially lead to misleading predictions. In this regard, different methods have been used by various authors for taking into account the anisotropic nature of the food products. Rossello et al. (1997) and Abbasi-Souraki and Mowla (2008) studied the drying behavior of cylindrical green beans. In their research, the anisotropic structure of green bean samples has been taken account, by defining different diffusivities in the radial and axial directions. Fernando et al. (2011) estimated the axial and radial moisture diffusivities of anisotropic banana, cassava and pumpkin by using the drying curves of samples with different thicknesses. Zhang et al. (2011) calculated the salt diffusivities, in x and y directions, for anisotropic grass carp muscles by measuring the salt content of muscles in different points. Pacheco Aguirre et al. (2014) estimated the axial, radial and angular effective diffusivities of anisotropic cylindrical carrot samples. At first, the axial and radial diffusivities were obtained using the effect of increasing the length of samples on the drying curves, and then the angular diffusivity was obtained using the drying curves of samples with equal length and different cut angles.
The objectives of this research were to study the dehydration behavior of celery stalks during osmotic dehydration in salt solution and developing a mathematical model for explaining the anisotropic mass transfer in this foodstuff during dehydration. Experiments were carried out by dehydration of different cuts of celery stalks in salt solutions of different concentrations and temperatures in a batch osmo-reactor. Due to the asymmetric structure of the celery stalks, two types of geometries, cylindrical and cubical, were considered for mathematical modeling of the dehydration process. By fitting the experimental data to the models, effective diffusivities in different directions were estimated.
Section snippets
Materials
In this work, fresh and green celery from Rasht, situated in the north of Iran, was used as raw material. Celeries were purchased from the same supplier to maximize reproducibility of results. Because of homogeneity of the samples, care was taken when selecting the samples, to take celeries with approximately the same shape, color and degree of ripening. Ends and leafy tops of bunches of celeries were removed and only the middle portions, were used to produce the required samples. Then celeries
Mathematical modeling
A number of celery stalks are immersed in a limited volume of solution, and the solution is well stirred. If the volume of the solution in which the bodies are immersed is not large enough to neglect the amount of solute taken up or moisture extracted from the solid, then the concentration in the liquid will change as diffusion proceeds. By stirring the solution well, time would be the only parameter affecting the concentration of the solute in the fluid. The unsteady-state one-dimensional mass
Estimation of the equilibrium water loss and solid gain
Equilibrium values of water loss (WL∞) and solid gain (SG∞) were predicted by fitting the linear form of Azuara model to the experimental data, according to Eqs. (22), (23), respectively. Table 2, Table 3 show the equilibrium water loss (WL∞) and solid gain (SG∞) values as well as the regression coefficients R2 and RMSE for two cuts of celery stalks at nine combinations of three concentrations and temperatures. The high values of regression coefficient and low values of RMSE confirm the
Conclusions
Mass transfer during osmotic dehydration of celery stalks in a batch osmo-reactor was investigated. The two-parameter model developed by Azuara et al. (1992) was used to evaluate the equilibrium values of moisture loss and solute gain by the samples. Due to the asymmetric structures of celery stalks, cubical and cylindrical geometries were selected for mathematical modeling of mass transfer during osmotic dehydration of the samples. Effective diffusivities in x or y direction in the cubic
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