A new mathematical model for water uptake during soaking of grains

There are very few models in the open literature for predicting the water uptake characteristics of grains. Peleg’s equation (1988) is a widely used empirical model that does not involve important soaking parameters to describe water uptake. Other existing models have been developed based on the diffusion theory. However, these existing models are strongly connected to experimental data for predicting the equilibrium moisture of the grain (maximum water uptake with time). In practice, the soaking of grain involves many physical parameters such as time, temperature, the viscosity of the soaking medium, the density of grain and soaking medium, diffusion coefficient, and solid loss from the grain (for example alpha-galactosides). However, there is no documentation of a model involving these physical parameters. This present work proposed a generalized mathematical model for predicting water uptake of grain (cowpeas) using non-dimensional analysis. The proposed model was successively applied to predict the soaking of cowpeas via the simplification of the model using six data points from experimental works in the literature. In predicting the soaking characteristics of different cowpeas, a good agreement was observed when the proposed model was compared with existing experimental data in the literature. This work presents a novel way of predicting water uptake in cowpeas using non-dimensional analysis which can be applied by food scientists and food engineers to model the water uptake for other grains. However, the physics of soaking, particularly as the porous structure of the grain evolves, could be analyzed using fractal mathematics. This approach should be considered for future studies to capture the complex, irregular dynamics of the process more accurately.