Mathematical Modeling for Cactus Pear Juice Concentration Kinetics and a Study of the Physicochemical Changes During the Concentration Process

Cactus pear juice was concentrated by applying a rotary vacuum evaporator at different temperatures (50°C, 60°C, 70°C, and 80°C). The kinetics of the juice concentration based on the change in total soluble solid content was investigated by applying five mathematical models. The modeling of this process was essential to accurately describe the evolution of total soluble solids and to identify the most suitable model for predicting concentration behavior. The constants of the mathematical models were estimated with nonlinear regression and according to the determination of three statistical parameters: the coefficient of determination ( R 2 ), the adjusted R 2 (adj R 2 ), and the root mean square error (RMSE); it was revealed that the model known as Weibull distribution is the best descriptive one ( R 2 > 0.980, adj R 2 > 0.971, and RMSE < 2.12). The activation energy for the concentration process was estimated at 254.09 kJ/mol. To study the effect of the vacuum concentration on physicochemical characteristics and on bioactive compounds, several parameters were determined, namely, total soluble solid content, moisture, pH, acidity, viscosity, ascorbic acid, phenolic compounds, betalains, antioxidant activity, and reducing power. The results showed a significant increase in acidity (from 0.037 to 0.129 g citric acid eq/100 mL) and viscosity (from 0.048 to 0.275 Pa·s), after juice concentration. Bioactive compounds were concentrated along with the increase in °Bx value (from 15 to 60°Bx), with betalains reaching up to 59.66 mg/100 g, total phenolic compounds up to 246.74 mg GAE/100 g, and ascorbic acid up to 39.36 mg/100 g in the juice concentrates. However, statistical evaluation of the results made for the reconstituted juices from juice concentrates revealed that the bioactive compounds and the antioxidant activity of the cactus pear juice were better preserved when applying the lowest temperatures (50°C and 60°C).