Mathematical modelling of water absorption and evaporation in a pharmaceutical tablet during film coating

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature.