A Variable Diffusivity Model for the Drying of Spherical Food Particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R value greater than 98.6% for all temperatures. Nomenclature A coefficient 1 for effective diffusivity equation, m/s B coefficient 2 for effective diffusivity equation, dependent on equation type C coefficient 1 for Arrhenius type equation, m/s D coefficient 2 for Arrhenius type equation, m/s Deff effective diffusivity, m/s M moisture content, kg water/kg dry matter Me equilibrium moisture content, kg water/kg dry matter M0 initial moisture content, kg water/kg dry matter MR dimensionless moisture ratio R gas constant, JKmol R coefficient of determination, % r radius, m T temperature, °C t time, s WMR dimensionless weighted moisture ratio