Mathematical modelling of vacuum cooling of leafy vegetables using bidirectional conjugate model combining heat and mass transfer with leaf structural deformation

Abstract

The numerical model is an effective solution to regulate the uneven temperature distribution, water loss, and structural shrinkage of leafy vegetables during vacuum cooling (VC). Nevertheless, the developed models mainly concentrate on the heat and mass transfer of leafy vegetables during the cooling, ignoring the structural deformation and its interaction with heat and mass transfer. For a better understanding of the cooling process, a macroscopic bidirectional coupled thermo-hydro-mechanical (THM) model was developed to describe the VC of leafy vegetables using spinach as a representative case. The simulations, validated by the experimental results, accurately predicted the changes in vapour pressure, weight loss, evaporation rate, moisture concentration, and shrinkage of the leafy vegetable, as well as the cooling gradients of the stem, blade, midvein, and lateral veins. Results showed that the cooling of the blade was easier, but the cooling gradient of the blade was lower than that of the leaf stem, with a maximum temperature gradient of stem, veins, and blade after cooling being 2.09 °C. Reducing the cooling end pressure could shorten the cooling time to the desired cooling temperature and minimise the water loss. Sensitivity analysis revealed that porosity significantly affected the changes in temperature, moisture concentration, and shrinkage. Notably, water evaporation was the primary reason for the shrinkage of the leaf tip and edge, but the contraction of the solid matrix cannot significantly aggravate further water evaporation. These findings highlight the potential of the THM model to promote the commercialisation of VC for leaf vegetables.