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Cárdenas-Bailón, et al. Emir. J. Food Agric ● Vol 31 ● Issue 9 ● 2019 655 of cylindrical potato samples in a tunnel dryer. McLaughlin and Magee, (1998) predicted potato spheres dehydration in a fluidized bed dryer successfully by using the Fick ́s second law incorporating a Fourier number accounting for shrinkage. Hatamipour and Mowla, (2002) were able to correlate carrots volume depletion during dehydration in a fluidized bed dryer with humidity content of the sample. More recently, Zielinska and Markowsky, (2007) correlated the shrinkage data with moisture content by a linear equation during carrot cubes dehydration in a spouted bed dryer. They found that coefficients of the linear equation are highly influenced by blanching, and effective moisture coefficients resulted lower when shrinkage was considered than when no shrinkage was taken into account. Białobrzewski et al., (2008) worked out a mathematical model to depict heat and mass transfer during carrot cubes dehydration in a spout fluidized bed dryer using Lagrange–Eulerian formulation, in which solid particles were considered as a discrete phase. The mathematical model considered the heterogeneous volume depletion of the carrot cubes. However the model failed to predict drying kinetics accurately since errors of more than 50% were reported and model requires numerical solving of three linked equations making it unpractical for a direct application. Arevalo-Pinedo et al., (2010) evaluated effective moisture diffusion coefficients considering both shrinkage and no shrinkage of carrot slices in a vacuum dryer using Fick ́s second law for a slab and they found that the effective moisture diffusion coefficients were higher when no shrinkage was considered. Also, Zielinska and Markowsky (2010) developed two models based on Fick’s second law to predict dehydration kinetics of carrot cubes in a spout bed dryer and found that volume depletion should be considered in order to obtain trustworthy values of effective moisture diffusivity in carrots. These authors found that if volume depletion is not considered during mathematical modeling of dehydration kinetics, then the effective moisture diffusivity in carrots can be miscalculated at the starting and final dehydration stage. Aversa et al., (2011) evaluated shrinkage during drying of eggplant disks in a moisture analyzer finding a non-linear dependence of food volume with moisture content. Brasiello et al., (2013) developed two mathematical models considering volume depletion effect describing eggplant dehydration. The models are both modified diffusion equations that consider different changes of eggplant slice structure during drying. In the foremost model a diffusion coefficient variable with the humidity content is considered whereas in the second model an unreal convective term was introduced. Both models were capable to describe the analyzed dehydration processes. Aprajeeta et al., (2015) studied volume depletion and porosity changes along with coexisting heat and mass transport during potato slices dehydration in a convective cabinet dryer. They studied the influence of volume depletion and porosity on heat and mass transfer and modeled the data without much success. Brasiello et al., (2017) analyzed the evolution of moisture content profiles inside cylindrical samples of eggplant during dehydration using magnetic resonance imaging taking into account shrinkage effects. As can be seen from the above reports, considering shrinkage effect is essential to build suitable mathematical models to depict dehydration kinetics of food products. Also, models should be practical and relatively easy to apply and should provide accurate prediction of drying kinetics. Based on this, the aim of this work was to build a mathematical model with base on Fick ́s second law, both considering shrinkage effect and neglecting it, to predict drying kinetics of carrot cubes in a two stage dehydration process using a semipilot spouted bed dryer in the first step and a lab scale spout-fluidized bed dryer in the second stage, as well as to evaluate the effect of drying parameters on product quality (β-carotene content, rehydration ratio and both pectin methyl esterase PME and peroxidase POD residual activity as thermal degradation indicators). The methodology developed in the present work can be applied to any food product.

Shrinkage modeling, drying kinetics and quality assessment of carrot cubes dried in a two stage spouted bed drying process