From October 2026 to 2031, I have been appointed N M Rothschild & Sons Professor of Mathematics and Director of the Isaac Newton Institute for the Mathematical Sciences at the University of Cambridge. Email sent to my UCL email address will still be monitored as usual.
RESEARCH AREA: COMPLEX FLUIDS
I'm interested in fluids that don't behave like the standard (air, water, honey) Newtonian model. This field has wide-ranging industrial applications - including plastics manufacture and the processing of toothpaste. I work on a variety of flow scenarios including particles suspended in a viscous fluid (for example, with my recent Ph.D. student Adam Townsend below and recent postdoc Jurriaan Gillissen); polymeric liquids (for instance, with my first Ph.D. student Sally Everitt); instabilities in elastic liquids (including work with my recent Ph.D. student Hugo Castillo Sanchez and a collaboration with Suzanne Fielding at Durham on shear-banding instabilities, and work with my current student Xintong Ji), and the doubly-complex question of particles suspended in a viscoelastic fluid with recently completed Ph.D. student Liam Escott and new student Luke Debono. Some of these systems also have applications in forensic science, which I'm studying with my current Ph.D. student Gareth Jenkins with sponsorship from Dstl.
Recent and current funded projects include:
SUM4Products: Scale-Up Mathematics for Formulated Products, an EPSRC-Funded Network+ which will bring mathematical modelling to the UK formulations sector. Find out more on the SUM4Products project website.
Shear-thickening fluids for cryopreservation in which we began an exploration of whether interactions between particles in suspension could inhibit the growth of ice crystals. This work was led by Asymptote and funded by Innovate UK.
Complex ORAL health products (CORAL): Characterisation, modelling and manufacturing challenges. Here we worked with UCL Engineers and commercial sponsor GSK to investigate the rheology of three-phase suspensions in a viscoelastic matrix, with application to toothpastes. This work was funded by EPSRC.
Extensional Rheology Matters, a small project funded by EPSRC in which I aimed to develop tools to assess whether extensional flow components are important in a given flow situation.
RESEARCH GROUP
Research Students
Xintong Ji: Theoretical analysis of Stokes flow through sharp-cornered geometries. Awaiting viva (2026), UCL
Gareth Jenkins: A mathematical model for the transfer of forensic trace evidence. Awaiting viva (2026), UCL
Luke Debono, PhD (2026): Hookean dumbbells to flat elastic particles: Theory, computation and rheology, UCL
Liam Escott, PhD (2022): The rheology of weakly-viscoelastic multiphase systems using a cell model, UCL
Hugo Castillo Sanchez, PhD (2019): Channel flow instabilities of complex fluids, UCL Adam Townsend, PhD (2017): The mechanics of suspensions, UCL
Thomas Brickell, MPhil (2012): General two-dimensional linear flows of particle suspensions, UCL
Sally Everitt, PhD (2004): Bubble dynamics in polymeric foams, University of Leeds
Postdocs
Complex oral health products:
Jurriaan Gillissen. 2017-2020.
Shear-thickening for cryopreservation: Adam Townsend, 2016.
Instabilities in polymer processing:
Mehmet Sahin, 2005-2007;
Tim Reis, 2007-2008.
Innovation Research Associate
SUM4Products: Matthew Shirley (University of Cambridge) 2027-2029.
Non-technical articles Case study for the Royal Society on how a supportive employer can support a mother on her return to work. Blog post and TV news interview commenting on the award of the Fields Medal to a female mathematician for the first time. The D'Hondt Method Explained: brief explanation of an easier way to understand the allocation of seats at the European elections Interview in International Innovation, issue 191: "What is mathematics?", August 2015 (Research Media, UK, pp48-51), ISSN 2054-6254. Joint article on the award of the Abel Prize to a female mathematician for the first time.
