Applied Mathematics · University of Southampton
Lecturer (Assistant Professor) in Mathematical Modelling, working on the mathematics of transport: how heat, mass, charge and momentum move through fluids, batteries and engineered surfaces.
I am a Lecturer (Assistant Professor) in Mathematical Modelling in the School of Mathematical Sciences at the University of Southampton, where my research focuses on industrial modelling for sustainability.
I develop analytical and asymptotic methods for transport phenomena (coupled problems of fluid flow, heat and mass transfer, and electrochemistry) arising in engineering and energy applications. Much of my work turns problems that would ordinarily demand large numerical simulation into explicit formulae: results that expose the physics, and that engineers can actually use.
Before joining Southampton in October 2024, I was a Chapman Fellow in the Department of Mathematics at Imperial College London (2022–24). From 2018 to 2022 I was a postdoctoral researcher in the Mathematical Institute at the University of Oxford, working with Professors Jon Chapman and Colin Please on multi-scale modelling of lithium-ion batteries within the Faraday Institution's Multi-scale Modelling project. I hold a PhD in Applied Mathematics from Imperial College London (2017), supervised by Professor Demetrios Papageorgiou, for which I was awarded an EPSRC Doctoral Prize Fellowship, and a BA in Mathematics from Trinity Hall, University of Cambridge.
Together with several of my long-standing collaborators, I am a member of the Red Lotus Project, an international consortium on surface engineering for heat transfer, sustainability and energy harvesting.
I am currently accepting applications from prospective PhD students.
Three threads run through my work, tied together by a common toolkit: matched asymptotic expansions, complex analysis, and mixed boundary-value problems. Mathematics in service of physical insight.
Exact and asymptotic solutions for the coupled transport of momentum, heat and mass. Slip flows over superhydrophobic and structured surfaces, thermocapillary (Marangoni) stresses on curved menisci, conjugate heat transfer, and electrohydrodynamics: multiscale mixed boundary-value problems solved with matched asymptotics and complex-variable methods.
Physics-based modelling of lithium-ion batteries: asymptotic reduction of electrochemical models of porous electrodes, electrode heterogeneity and particle-size distributions, and nonlinear impedance spectroscopy for parameter identification. Current work extends to thermal ratings of power cables and energy harvesting from waste heat.
The thermal management of high-power electronics: microchannel and superhydrophobic-surface cooling, longitudinal-fin heat sinks, grooved heat pipes, and thermal spreading and contact resistance. Explicit formulae for Nusselt numbers and flow resistance that replace expensive conjugate simulations in design.
Longitudinal-fin heat sinks are a workhorse of electronics cooling, but predicting their performance normally requires numerical simulation of the conjugate heat transfer between fin and fluid. Using matched asymptotic expansions in the limit of small fin spacing, this paper derives explicit formulae for the velocity and temperature fields and the Nusselt number (including the effect of clearance above the fin tips), accurate enough to replace numerical solution across much of the design space.
A new architecture for pumping weakly conducting liquids with no moving parts. A periodic array of asymmetrically spaced electrode pairs generates Maxwell stresses on the interface between two layered fluids; the asymmetry produces a net flow whose direction is controlled purely through the applied potentials. A small-period asymptotic analysis yields closed-form solutions for the electric field, the flow and the pumping speed, together with estimates of the power required.
Standard (linear) impedance spectroscopy cannot uniquely identify the parameters of physics-based battery models: different parameter sets produce identical spectra. By modelling the response to moderately large sinusoidal currents, this work derives explicit formulae for the second-harmonic impedance of a full cell and shows that the nonlinear content breaks these degeneracies, validated against time-series simulations to ~11 mV accuracy. Nonlinear EIS becomes a practical, fast diagnostic for battery parameterisation.
After a lithium-ion battery is discharged and left at rest, its voltage keeps drifting for hours, far longer than standard models predict. This paper shows the phenomenon is a signature of heterogeneity: a distribution of particle sizes in the electrodes continues to exchange lithium internally long after the current stops. A many-particle extension of the Doyle–Fuller–Newman model reproduces experimental relaxation quantitatively across discharge rates, with implications for how models should be validated.
Superhydrophobic surfaces reduce drag by letting liquid glide over gas-filled grooves, but in cooling applications the heat itself deforms the menisci and drives thermocapillary stresses that can destroy the benefit. Solving the coupled three-dimensional problem with asymptotic and conformal-mapping techniques, this paper derives slip lengths capturing both effects simultaneously, showing that heating always degrades slip and by how much, essential accounting for any thermal application of these surfaces.
A single-author Rapids paper presenting remarkably simple asymptotic formulae for flow in channels patterned with longitudinal ridges and arbitrarily protruding menisci, with no restriction on how far the gas–liquid interface bulges into or out of the liquid. The slip-length formula stays accurate over a very wide range of geometries, giving a design tool for drag-reducing surfaces that previously required full numerical computation.
My first JFM paper, and a foundational analysis of convective heat transfer in microchannels with ridged superhydrophobic walls. Perturbing about a flat interface, the coupled hydrodynamic and thermal problems are solved analytically via eigenfunction expansions and dual-series equations, yielding Nusselt numbers as explicit functions of the geometry, and revealing that the effect of meniscus curvature is captured, to excellent accuracy, by just two terms of the expansion.
Collaborations span applied mathematics, mechanical engineering and electrochemistry, across three continents. Selected collaborators below. Many of these collaborations run through the Red Lotus Project, a consortium of academic, industry and government partners working on surface engineering for heat transfer and energy harvesting.
University of Southampton
Tufts University
Imperial College London
Imperial College London
University of Oxford
University of Oxford
University of Oxford
Technion
University of Tokyo
Journal publications, organised by research theme. See also Google Scholar and ORCID. ★ marks the highlighted papers above.
I have co-supervised ten PhD, Masters and undergraduate research students across Imperial College London, the University of Oxford and Tufts University, in applied mathematics and mechanical engineering. I am currently accepting PhD applications in mathematical modelling of transport phenomena and energy systems.
For research enquiries, collaboration, or PhD supervision:
School of Mathematical Sciences · University of Southampton · Southampton SO17 1BJ, UK