Research and scholarship
Research and scholarship
My primary research is in fluid mechanics. My research interests lie in continuum mechanics of problems related to industry, biology and physiology, and specifically, problems involving fluid-structure interaction and free boundaries. I am interested in mathematical modelling and in using asymptotic and numerical techniques to solve these problems. I have investigated problems involving the role of surfactants in thin-film fluid dynamics such as in drop spreading and foam drainage. I have also investigated problems in pulmonary mechanics involving lung airway reopening, cough manoeuvres and mucus transport.
My current research in thin-film fluid dynamics investigates the role of thermosviscous and thermocapillary effects, and phase change (solidification) in spreading and draining flows. The focus is on understanding the mechanisms underlying fingering instabilities observed in real flows, such as in lava flows.
I am also involved in the mathematical and computational of medical and biomedical problems. I am conducting Computational Fluid Dynamics (CFD) modelling and simulation of mechanical thrombectomy – an interventional medical procedure related to the removal of blood clots in the brain either by suction or using a mechanical device. The focus is to investigate the 3-way coupling between the blood flow, blood clot deformation and suction or mechanical device, to address important clinical problems. This work is in collaboration with the School of Pharmacy and Bioengineering at Keele and clinicians at the Royal Stoke University Hospital.
I am also involved in the mathematical modelling of in vitro/in vivo tissue engineering with researchers at the School of Pharmacy and Bioengineering at Keele and the Robert Jones and Agnes Hunt Orthopaedic hospital in Oswestry. Projects related to this include the mathematical modelling of the regeneration of cartilage and bone defects, such as in the knee, after cell therapy. The focus is in understanding the role of growth factors in facilitating the regeneration or repair process.
I currently supervise 1 PhD student:
Jatinder Pannu (start 2023) – The role of solidification in the spreading of molten flows.
Past PhD students:
Joe Goddard (2014) - Fingering instabilities in gravity and surfactant-related thin
film flows.
Abdulghani Alharbi (2016) - Numerical solution of thin-film flow equations using adaptive moving mesh methods.
Ghanim Algwauish (2019) - The non-Newtonian and non-isothermal spreading of liquid domes using mathematical and numerical methods.
Kelly Campbell (2020) - Mathematical modelling of cartilage and bone defect healing after cell implantation.
Hani Alahmadi (2021) - Non-Newtonian and non-isothermal effects in the gravity-driven draining of a vertically-aligned thin liquid film.
