A combined mathematical model to represent transpiration, respiration, and water activity changes in fresh cape gooseberry (Physalis peruviana) fruits

Abstract

In this work, a combined respiration and transpiration model is proposed for fresh cape gooseberry fruits, also considering changes in water activity (aw) and moisture content. Initially, a correlation of parameters was obtained from experimental data to determine the kinetics of O2 consumption and CO2 production for cape gooseberry fruits at different temperatures. From the data on the change in gas concentration, a parameter adjustment was made evaluating three kinetic models to represent respiration: 1) Power-Law Chemical kinetics (PL), 2) Simple Michaelis–Menten kinetics (MM), and 3) Michaelis–Menten with uncompetitive inhibition by CO2 (MMU). The temperature-dependence was considered in the three models by integrating an Arrhenius equation in the kinetic parameters. Afterward, a combined model was obtained to describe the fruit transpiration, coupling the moisture sorption isotherm (logistic model), and including the temperature-dependence and the most suitable respiration kinetics. It was determined that with the MMU kinetics it was possible to obtain a high goodness of fit with the experimental behaviour for the changes in the O2 and CO2 concentrations (R2adj. = 0.964 and 0.981). The MM kinetics had an acceptable fit (R2adj. = 0.940 and 0.941), while the PLK model could not explain the observed behaviour (R2adj. = 0.247 and 0.647). It was found that a logistic model appropriately described the relationship between the fruit moisture content and aw (R2adj. = 0.998). A close relationship was determined between the fruit's transpiration and its respiration rate, the change in the water activity, and the surrounding temperature and relative humidity (R2adj. = 0.998). As the temperature decreased, and as the relative humidity increased, the change in water activity and the transpiration rate decreased. Through the parameters established for each model, it is possible to predict the behaviour of processes such as respiration, transpiration, and changes in aw to configure a storage and packaging system by proposing the gas balance equations (O2, CO2, and water vapour) that allow obtaining favourable gas levels for the preservation of the fresh fruits.