Mathematical modelling of dissolvable surfaces in fluid flow with applications to pharmaceuticals (BLYTHM2_U26EMP)
Key Details
- Application deadline
- 31 January 2026 for International, 31 March 2026 for Home
- Location
- UEA
- Funding type
- Self-funded
- Start date
- 1 June 2026
- Mode of study
- Full-time
- Programme type
- PhD
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Project description
Primary supervisor - Prof Mark Blyth
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. Various flow conditions will be scrutinised, including low-speed flow (Stokes flow) and high-speed flow, where boundary-layer theory will be used to make progress. Full-scale CFD simulations will be carried out to assess the accuracy and predictive power of the simplified flow models.
Entry requirements
The standard minimum entry requirement is 2:1 in Mathematics.
Funding
This project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found here.
A bench fee is also payable in addition to the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.
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References
Huang, J. M., Moore, N. J. & Ristroph, L. (2015) Shape dynamics and scaling laws for a body dissolving in fluid flow, Journal of Fluid Mechanics, 765.
Jiang, Y. & McDonald, N. R. (2022) Dissolution of plane surfaces by sources in potential flow, Physica D, 133549.