Mathematical modelling of dissolvable surfaces in fluid flow with applications to pharmaceuticals (BLYTHM2_U26EMP)

How a dissolvable solid surface interacts with a fluid presents a highly complex nonlinear free-boundary problem. The rate of dissolution of the surface depends on various factors including the local flow velocity field and the surface geometry, both of which are evolving in time. These features make mathematical modelling of the problem highly challenging.

It is well known that the dissolution of a soluble particle placed into a liquid is promoted by inducing motion within the fluid. Experiments carried out by Huang et al. (2015) showed that hard candy bodies immersed in a high-speed laminar flow adopt a characteristic terminal form prior to being fully depleted.

A similar terminal form is reached irrespective of the initial shape of the body. Based on these observations Huang et al. hypothesised that the body reaches a stable shape-flow state. This project is driven by the desire to understand how rapidly tablets/drugs of different compositions dissolve in a liquid, the primary motivation coming from the pharmaceutical industry.

Oour goal is to develop flow models of solid surface dissolution in simplified geometries. In the simplest scenario we ignore flow completely and consider the dissolution of a flat or circular particle in a quiescent liquid. Building up the complexity we will examine flow over an initially flat surface with a view to developing model equations that are amenable to analysis and which provide a simplified system for efficient numerical experiments.

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