Mathematical modeling of the drying process of Yuyo leaves: kinetic and thermodynamic parameters

To mitigate the high perishability of Yuyo leaves (Amaranthus viridis L.) and revalorize them as a gluten-free agro-industrial raw material, this research determined the kinetic and thermodynamic parameters of their convective hot-air drying at 50, 60, and 70 °C. The evaluation of eight thin-layer mathematical models showed that the Page equation presented the best overall predictive fit. This two-parameter model systematically minimized absolute dispersion indices, recording the lowest sum of squared errors (SSE ≤ 0.0634) and mean squared errors (MSE 0.0022 at 50 °C; 0.0027 at 60 °C; 0.0023 at 70 °C), coupled with high coefficients of determination (R2 ≥ 0.97). The rate constant (k) confirmed thermal dependence, increasing from 0.01002 to 0.01846 min-1, while the exponent remained constant (n = 1.1), suggesting geometric uniformity during leaf shrinkage. Complex four-parameter formulations presented analytical redundancy due to overfitting. Analysis of variance (ANOVA) and Tukey's test (p < 0.05) determined that dehydration is an endothermic (ΔH* = 25.4 to 25.2 kJ.mol-1), endergonic, and non-spontaneous process (ΔG* = 89.6 to 93.6 kJ.mol-1), characterized by a transition toward a higher local structural order of the residual water within the plant tissue (ΔS* = -198.7 to -199.2 J.mol-1. K-1).