Fluid Mechanics

Fluid mechanics is the study of how fluids move. Newtonian fluids are described by the Navier–Stokes equations, and there are various formulations for non-Newtonian fluids. Modelling approaches may include direct numerical simulations, asymptotic approaches, and the solution of model problems in simplified domains.

Fluid mechanics modelling can be used to help understand a wide range of problems. Problems brought to Mathematics in Medicine Study Groups which have involved such modelling are listed below.


Understanding patterns of retinal haemorrhage
Richard Bonshek (Manchester Royal Eye Hospital, Central Manchester University Hospitals)
Targeting stem cells following i.v. injection using magnetic particle based approaches
Prof Alicia El Haj (Institute for Science & Technology in Medicine, Keele University)
Mr Thomas Kwan (ISTM, Keele University)
Mathematical modelling of airway smooth muscle cell proliferation and apoptosis in asthma
Dr Charlotte Billington (Division of Therapeutics & Molecular Medicine, University of Nottingham)
Prof Ian Hall (Therapeutics and Molecular Medicine, University of Nottingham)
Dr Anthony Holmes (NC3Rs)
Mathematical modelling of the normal swallow
Mrs Carol Fairfield (Department of Clinical Language Sciences, University of Reading)
Definition of a periodicaly distributed 'porosity gradient' in functionally graded materials to be used as bone scaffolds
Dr Carmen Torres-Sánchez (Mechanical Engineering, Heriot-Watt University)
Comparing placentas from normal and abnormal pregnancies
Dr Alexander Heazell (Maternal and Fetal Health Research Centre, University of Manchester)
Sodium flux during haemodialysis
Dr Sushrut Waikar (Renal Division, Brigham and Women's Hospital)
Intramantle pressure gradients favoring hydrocephalus development following disruption of integrin-matrix interactions
Dr. Miles Johnston (Sunnybrook Health Sciences Centre)
Solid–fluid interaction in force and energy transmission in shaken baby syndrome
Dr Donal McNally (Institute of Biomechanics, University of Nottingham)
Multiscale modelling of bioreactors for growing bone tissue
Mr Norazharuddin Abdullah (Engineering Science, University of Oxford)
Dr Diganta Das (Chemical Engineering, Loughborough University)
Modelling of the growth of engineered orthopaedic tissue in zero force and variable load environments
Dr Nikolay Nikolaev (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University)
Mr Henk Versteeg (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University)
Prof David Williams (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University)
Measuring intra-disc pressures in the spine from MRI images
Ms Angela Darekar (University of Southampton)
Dr Hamid Rassoulian (Medical Physics Group, Southampton University Hospitals NHS Trust)
Continuous non-invasive blood-pressure measurements
Dr Tony Birch (Neurological Physics Group, Southampton University Hospitals NHS Trust)
Photonic and microfluidic strategies for bioanalysis applications
Dr Tracy Melvin (Optoelectronics Research Centre, University of Southampton)
Implants for osteochondral repair using cell printing
Dr Jos Malda (University Medical Center, University of Utrecht)
The swollen and sunken optic disc
Mr Alexander Foss (Queen's Medical Centre, University of Nottingham)
Representation of spectrum in the auditory system
Dr Chris Sumner (MRC Institute of Hearing Research, University of Nottingham)
Optimisation of fluid distribution inside a porous construct
Dr Sarah Cartmell (Institute of Science and Technology in Medicine, University of Keele)
Mr Vipin Michael (Institute of Science and Technology in Medicine, University of Keele)
How can we model the water transport through the kidney?
Dr Susan Franks (Computational Toxicology, Health and Safety Laboratory)
In vivo delivery of gene therapy to tumours
Dr Kerry Fisher (Clinical Pharmacology, University of Oxford)
Dr Len Seymour (Clinical Pharmacology, University of Oxford)
Using micro-nanostructures to deliver genes and drugs to skin for immunotherapeutic applications
Dr Mark Kendall (The PowderJect Centre for Gene and Drug Delivery Research, University of Oxford)
Modelling the development and formation of biofilms
Prof Judith Armitage (Department of Biochemistry, University of Oxford)
Ions in solutions and protein channels
Prof Robert Eisenberg (Department of Molecular Biophysics and Physiology, Rush University Medical Center)
Bacterial proteins that knock out cell defences: Cruise missiles or cannonballs?
Dr Gail Preston (Department of Plant Sciences, University of Oxford)
Post-reattachment retinal detachment
Alistair Fitt (School of Mathematics, University of Southampton)
Drug release from polymer coated stents
Simon Kennedy (Physiology and Pharmacology, University of Strathclyde)
Atherosclerotic plaque rupture
Prof Alan Moody (Academic Radiology, University of Nottingham)
The impact of substrate on the measurement of DNA complex morphology
Dr Stephanie Allen (School of Pharmaceutical Sciences, University of Nottingham)
Hydrocephalus shunts: Modelling pressure and volume changes in the brain
Dr Roger Bayston (School of Medical and Surgical Sciences, University of Nottingham)
Odontogenic cysts: Comparing the growth of radicular cysts and keratocysts
Dr Gabriel Landini (The School of Dentistry, University of Birmingham)
The effect of ureteric stents on urine flow: Is there a better shape?
Mr Stuart Graham (Institute of Urology and Nephrology, University College London)
Curvature of the spine: Hydrostatic pressure as an indicator of scoliosis
Ms Susan Bibby (Physiology Laboratory, University of Oxford)
Dr Jill Urban (Physiology Laboratory, University of Oxford)
Mathematical modelling of profiled haemodialysis
Dr Steve Baigent (Centre for Nonlinear Dynamics and Its Applications, University College London)
Prof Robert Unwin (Middlesex Hospital)
Effects of a new anti-tumour drug, fibrinogen E-fragment, in vivo: differential effects on the outer versus the inner areas of tumours
Prof Claire Lewis (Medical School, University of Sheffield)
Blunt traumatic aortic injury
Dr Mike Neale (Transport Research Laboratory, Crowthorne)
Magnetically-targeted drug and gene delivery
Dr Jon Dobson (Department of Biomedical Engineering and Medical Physics, University of Keele)


Retinal Haemorrhage Follow-Up Meeting 2014
ASM Growth in Asthma Follow-up Meeting 2012
Neurons Follow-up Meeting 2010