Modelling interfacial flows in porous media: a hybrid asymptotic-computational approach

Interfacial fluid flows around solid obstacles and through porous materials are important in numerous applications, including carbon sequestration, materials science, filtration, 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 complicate matters.

In this project we will develop and use hybrid modelling approaches for moving fluid-fluid interfaces around obstacles, incorporating mathematical modelling, state-of-the-art asymptotic methods and high-fidelity numerical simulations, to investigate questions like how to minimise air trapping during composite material manufacturing.

Supervisors

Primary: Dr Ellen Luckins, Maths
Dr Radu Cimpeanu, Maths

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Project details

Hybrid continuum modelling techniques, incorporating both dedicated 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 asymptotic homogenisation (averaging) techniques [3]. This project will aim to combine and further develop these approaches, incorporating uncertainty quantification and data-driven components at the model level.

There is potential to explore a variety of specific applications of these types of flows during the PhD project. 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) may provide supervision support through their domain-specific expertise, experimental data, and practitioner networks.

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] Wray, A.W., Cimpeanu, R., & Gomes, S.N. (2022), Electrostatic control of the Navier-Stokes equations for thin films, Physical Review Fluids 7, L12200.

[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.