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Thomas Barker

Dr Thomas Barker


School of Mathematics

+44 29225 13201
Abacws, Room 5.07, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Available for postgraduate supervision


Research Group

Applied Mathematics

Research Interests

Granular flow, Continuum mechanics, Fluid dynamics, Geophysical flow modelling, Non-Brownian suspensions

Hi, I'm a Lecturer in Applied Mathematics. I teach 2nd Year Vector Calculus and 4th Year Theoretical Fluid Dynamics. My research is focused on modelling granular flows such as debris avalanches, subsea landslides and pharmaceutical powder processing. I use a combination of Continuum Mechanics theory, Numerical Solutions of PDEs and Discrete Particle Simulations to understand and predict these important and widespread physical processes












At present my main research areas are:

Modelling granular flows in industry: Think of all the foods, cleaning chemicals and medicines around your home that are made from powders and grains. Each of these products or ingredients originate from industry or agriculture and have come to you via processing, mixing and transport. To optimise this journey, and to ensure reliable outcomes, accurate models for flowing granular materials are required. One aspect which needs to be tackled is that real grains differ in size, density and shape even within a single sample.

Three-dimensional granular flow rheology: Once the restriction to 2D flow is lifted, many new 'types' of material deformation are possible. This in turn hugely expands the possible connections between stress and strain-rate. Formulating constitutive relations for flowing granular material in 3D could therefore be very difficult - requiring many experimental measurements for model fitting. Thankfully, this complexity can be greatly reduced by employing key concepts originating in statistical thermodynamics and differential geometry

Submarine landslides: Earthquakes, sedimentation and the motion of glaciers can each trigger landslides on the ocean bed. Whilst most often harmless, extreme events can damage sub-sea communication cables and in the worst cases cause devastating Tsunami waves. Due to the huge differences in scale between the grains of seabed rock and the typical ocean depths, modelling of these processes relies on the use of multiscale frameworks connecting together mathematical descriptions appropriate at different length scales

Suspension flow dynamics: When grains and fluids mix there can be many distinct, and often messy, outcomes. An important subset of these is the case of fully immersed mobile grains, for which the combined system of grains+fluid is known as a suspension. Because the grains can move relative to the fluid, forces acting on the mixture can affect the two phases independently. Good models for suspension flow dynamics can be useful to cement mixers, cake makers and toothpaste manufacturers, who all rely on the good mixing of granulated powders with water to reliably achieve high quality final products


During 2019-2021 I completed a Postdoctoral Research Associate position at The University of Edinburgh developing models for Pyroclastic Density Currents (hot, fast and very dangerous granular avalanches on volcanoes). For this I employed Multiphase Fluid Dynamics alongside Discrete and Fluid-Coupled Particle Simulations 

Before this I completed my PhD and first Postdoc position at The University of Manchester studying mathematical models for Granular Flow. This included Non-Newtonian Flow Simulations, Linear Stability Analysis including assessing Well-Posedness, and proposing new models based on Dimensional Analysis and Small-Scale Laboratory Experiments

My undergraduate MPhys in Physics was also at The University of Manchester where I specialised in Viscous Fluid Flow, Nonlinear Dynamics and Statistical Physics. My thesis was titled ‘Cellular Automata Modelling of Granular Segregation’


I welcome interest from prospective PhD students and postdoctoral researchers who are keen to work in the areas of:

  • Granular materials
  • Suspension flow
  • Geophysical process modelling
  • Industrial applications
  • Non-Newtonian fluids
  • Numerical methods for continuum mechanics