THEORY A mathematical model describing the drying behavior of beet slices was developed based on data from an air-drying experiment which measured average moisture content and temperature. The model was based on application of Fick's law for unidimensional moisture flow in the falling drying rate period. The mathematical model and the data generated from the kinetic studies of temperature-and moisture-sensitive red beet pigments (betanine and vulgaxanthin-I) were combined in a computer program to simulate and predict beet pigment retention, as a function of the process variables. Predicted and actual experimental pigment retention agreed well, which indicates this approach's potential for simulating deterioration of beet pigments during air-drying.
Moisture changesFick's law for unidimensional moisture flow in the region 0 G x Q L was applied:(1) where D = diffusion coefficient, cm* /set; L = slab thickness, cm; m = moisture content, g water/g solids; t = time, set; and x = distance from the surface of slab, cm.Considering the boundary conditions:1NTRODUCTION m = mi t = 0 for all X A MARKED and intensified interest in natural food colorants, which was initiated by consumer awareness and health aspects of some artificial dyes, has arisen in recent years. Dehydrated and red beet juice concentrates are applicable as water-soluble, natural-source red pigments in many food systems (Pasch et al., 1975; von Elbe and Maing, 1973; von Elbe et al., 1974). m = m, x = 0,L; for all t > 0where mi = initial moisture content, g water/g solids and me = equilibrium moisture content, g water/g solids, the moisture distribution (m,) and the average moisture content (m) for the first falling rate period can be expressed as (in analogy to potato drying, AguiIera et al., 1975):The degradation of the beet pigments in mixture, juice, and powder was investigated thoroughly (Aurstad and Dahle, 1973; Kepelman and Saguy, 1977a, b; Pasch and von Elbe, 1975, Saguy et al., 1978a; Sapers and Hornstein, 1979; Wiley et al., 1979). However, very little attention has been given to the feasibility .of predicting and simulating beet pigment retention, based on the combined approach of kinetic studies and drying behavior (i.e., time, temperature, and moisture content relationships).Moreover, the complications encountered during the drying process, because of moisture distribution, temperature changes, and other related parameters, prevented attempts to solve the problem. 4 m, = m, +-(mi -me) n 2n+l ----TX] exp [-$ (T2+1)2 Dt] L (2) Ee 8-1 mcm, z: -exp [-mi-me 71* n=O (2n+l)* x2 (2L:+lY Dt) (3)For E c 0.6, Eq (3) reduces to:The purpose of this investigation was to develop a mathematical/kinetic model for predicting the losses of the main red beet pigments (betanine and vulgaxanthin-I) during airdrying. The specific objectives were as follows:(1) To investigate the rate of betanine and vulgaxanthin-I losses as a function of dynamic moisture and temperature changes during drying;(2) To develop a mathematical/kinetic model describing the losses of the ...