Supervisors: Dr. Radu Cimpeanu (Maths), Dr. Ellen Luckins (Maths)

Summary:

Interfacial fluid flows around obstacles and through porous materials are key to numerous applications, including filtration, decontamination and manufacturing. For instance, resin must be injected into a porous mesh, without trapping air bubbles, to manufacture composite materials. Interfacial flows are difficult to model and simulate accurately, and in porous media the multiple disparate lengthscales further complicates matters. However, this multi-scale setting also provides beautiful mathematical modelling opportunities. In this project we will develop and use hybrid modelling approaches for moving fluid-fluid interfaces around obstacles, incorporating analytical and computational techniques, to investigate questions such as minimising defects in composite manufacturing.

Background:

Hybrid continuum modelling techniques, incorporating both rigorous asymptotic analysis and detailed numerical simulations, have recently been used to make significant advances in the field of interfacial flows [1,2]. Theoretical progress may be made for porous media interfacial flows by adapting and specialising asymptotic homogenisation (averaging) techniques [3]. This project seeks to combine these approaches in a novel and exciting way, generating a state-of-the-art modelling and direct numerical simulation framework that can also incorporate data-driven elements.

There is potential to explore a variety of specific applications of this work throughout the PhD project which lies at the intersection of interests of enthusiastic specialists with rich experience in both fundamental research and knowledge transfer, and their growing research groups. In addition to the composite materials manufacturing scenario [4], we might look at problems motivated by the chemical decontamination of porous building materials, in the aftermath of a chemical weapons attack [3]. Collaborators at Adjacency (composite material manufacturers) and DSTL (chemical decontamination experts) could provide supervision support through their domain-specific expertise, contribute with experimental data, and ensure access to networks of practitioners in the relevant industrial space.

Relevant references:

[1]	Alventosa, L.F., Cimpeanu, R., & Harris, D.M. (2023). Inertio-capillary rebound of a droplet impacting a fluid bath. Journal of Fluid Mechanics, 958, A24.
[2]	Tomlin, R.J., Cimpeanu, R., & Papageorgiou, D.T. (2020). Instability and dripping of electrified liquid films flowing down inverted substrates. Physical Review Fluids, 5(1), 013703.
[3]	Luckins, E., Breward, C.J., Griffiths, I.M., & Wilmott, Z. (2020). Homogenisation problems in reactive decontamination. European Journal of Applied Mathematics, 31(5), 782-805.
[4]	Modelling and Control of Resin Transfer Moulding, HetSys CDT Study Group with Industry 2022 Report.