MATHEMATICAL MODELLING AN ACTIVE COMPONENT RELEASE FROM SWELLING POLYMER-COATED GRANULE

A mathematical model of an active component release from swelling polymer-coated granule is proposed. The model predicts the degree of an active component release and the size of the capsule at any given time. The model is based on two differential equations of molecular diffusion with corresponding boundary conditions. The first equation describes the transfer of water through the polymer coating layer into the capsule. The second equation characterizes the diffusion of an active component through the coating layer into the environment. The boundary conditions vary depending on the release process period: impregnation of the coating layer with water, dissolution of the fertiliser solid core surrounded by a saturated solution and a decrease in the concentration of the solution inside the capsule after the total dissolution of the solid core. Unlike well-known models, this model takes into account the dependence of the release rate of an active component on the moisture content of the coating layer. Additional relationships allow to calculate the current volume and radius of the capsule, pressure and tensile stress inside the shell. The model also makes it possible to predict the onset of uncontrolled release of an active component when the critical value of the tensile stress and rupture of the shell is reached. Urea granules with an acrylic polymer elastic coating were obtained in a spouted bed laboratory apparatus in order to verify the adequacy of the mathematical model. Urea release experiment was carried out in water under static conditions. The dependences of the degree of urea release and the radius of granules on the process time are obtained. Comparison of the calculated and experimental data showed their good agreement. The standard deviation for the degree of urea release was 0.011 and for the granule radius it was 0.027 mm.