Dr Toby Lawrence Kirk

BA (Cantab), MSc (London), PhD (London)

Status

Postdoctoral Research Associate

Research groups

Oxford Centre for Industrial and Applied Mathematics

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Highlighted publications

Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries

Kirk, T Please, C Chapman, S Journal of The Electrochemical Society volume 168 (16 Jun 2021)

Thermocapillary stress and meniscus curvature effects on slip lengths in ridged microchannels

Kirk, T Karamanis, G Crowdy, D Hodes, M Journal of Fluid Mechanics volume 894 (04 May 2020)

Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

Kirk, T Journal of Fluid Mechanics volume 839 (01 Feb 2018)

Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

Kirk, T Hodes, M Papageorgiou, D Journal of Fluid Mechanics volume 811 315-349 (07 Dec 2016)

Teaching

B5.4 Waves and Compressible Flow (Tutor, 2020-21)

C5.6 Applied Complex Variables (Tutor, 2019-20, 2020-21)

Research interests

Toby is currently a Postdoctoral Research Assistant in the Oxford Mathematical Modelling Battery Group in the Mathematical Institute at the University of Oxford, and part of the Multi-Scale Mathematical Modelling Fast Start Project of the Faraday Institution. His current research is using asymptotic methods to account for electrode heterogeneity in lithium-ion battery models.

He earned his PhD in fluid dynamics under Prof. D. T. Papageorgiou at Imperial College London, studying modern micro-structured (i.e. superhydrophobic) slip surfaces. Using asymptotic and complex methods, he investigated their possible implications for viscous flows, convection, and the nonlinear interfacial dynamics of thin films.

His research interests include:

Asymptotic methods
Lithium-ion batteries
Applied complex analysis
Fluid dynamics
Nonlinear waves

Recent publications

Modelling electrode heterogeneity in lithium-ion batteries: unimodal and bimodal particle-size distributions

Kirk, T Evans, J Please, C Chapman, S SIAM Journal on Applied Mathematics volume 82 issue 2 625-653 (14 Apr 2022)

Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles

Yariv, E Kirk, T IMA Journal of Applied Mathematics volume 86 issue 3 490-501 (22 Apr 2021)

Stability of falling liquid films on flexible substrates

Alexander, J Kirk, T Papageorgiou, D Journal of Fluid Mechanics volume 900 (13 Aug 2020)

Effect of surface curvature on contact resistance between cylinders

Mayer, M Hodes, M Kirk, T Crowdy, D Journal of Heat Transfer volume 141 issue 3 (04 Feb 2019)

Spreading and Contact Resistance Formulae Capturing Boundary Curvature and Contact Distribution Effects

Hodes, M Kirk, T Crowdy, D Journal of Heat Transfer volume 140 issue 10 (11 Jun 2018)

Prizes, awards, and scholarships

EPSRC Doctoral Prize (2017)