# (164e) Modelling of Water Absorption By a Pharmaceutical Tablet

Authors:
UCL
University College London
Aqueous film coating is a crucial step in the manufacture of solid-dosage drugs in pharmaceutical industries. It is well understood that the shelf life of pharmaceutical tablets depends on the amount of humidity to which they are exposed during the coating process, the handling of the intermediate coated product and the packaging. Understanding, and being able to predict the mechanisms of water absorption onto and into tablets, is therefore important, to avoid accelerating the degradation mechanisms caused by high water content.

Mathematical models that efficiently simulate the overall coating process have already been developed. Recent models permit calculating the size of the spray droplets before impact, simulating the tablet movement inside the coater and predicting coating uniformity. However, there is little, if any, fundamental understanding of the sorption phenomena at the point of contact between the coating droplet and the porous tablet. This information is essential to perform a full-system global optimisation and determine the optimal design of the tablet.

This work aims to define and describe the driving forces that play a role in water-based coating sorption after impingement on a porous substrate. We aim to demonstrate two mathematical models. The first takes into account the spreading and sorption phenomena, whereas the second predicts the evaporation rate of the water absorbed in the porous matrix of the tablet. The ambient conditions; such as temperature, pressure and humidity, are set to be similar to the conditions present inside a pan-coater.

The spreading sorption model is divided into two separate phases: the kinematic phase and the capillary phase. During the first, inertial forces govern the spreading, while during the second, capillary forces become dominant. To acquire results for the kinematic phase, we developed a 1D model that solves the energy balance equation for the first milliseconds after impact. The results for the capillary phase come from the solution of the Navier Stokes equation, obtained using the lubrication approximation theory.

For the second model, of the evaporation process, we adopted a model for the second drying stage of a slurry droplet inside a spray dryer. During this stage, we 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. The dry core represents the surface of the tablet, while the wet core represents the wetted areas inside the tablet.

The information provided by these mathematical models, is important to understand the spreading, absorption and evaporation phenomena and predict the moisture content inside the tablet after the impingement of a liquid coating droplet. We implemented the models in gPROMS, employing the Modelbuilder modelling platform. The results (droplet height, spreading and wetting front profile) are in good agreement with recent experimental data and CFD simulations.

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