# Industrial and Applied Maths Seminars

The Industrial and Applied Maths (IAM) seminar series will be hosted by academics in the School of Mathematical Sciences at the University of Nottingham.

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## The Fluid Mechanics of Carbon Sequestration

**Wednesday 10 ^{th} October 2018**

**Speaker:** Andy Woods, University of Cambridge

**Time:** 13:00 - 14:00

**Location:** Room A31, Clive Granger Building, University Park Campus

In this talk I will describe some of the challenges of CO2 sequestration in subsurface permeable rock, including modelling the dispersal of the CO2 in heterogeneous aquifers, the challenge of monitoring this sub-surface flow using measurement at the surface and some of the fluid mechanical processes which can arise if the CO2 migrates back to the man’s environment. The talk will be illustrated with both mathematical and experimental models of the processes.

## Beyond homogenisation: large-deviation theory applied to the advection-diffusion of passive scalars

**Wednesday 24 ^{th} October 2018**

**Speaker:** Jacques Vanneste, University of Edinburgh

**Time:** 16:00

**Location:** Room A17, School of Mathematical Sciences, University Park Campus

A standard application of homogenisation theory is to the coarse-graining of the advection-diffusion equation which governs the dispersion of passive scalars in periodic fluid flows. It leads to a diffusion equation involving an effective diffusivity. This captures the enhancement of dispersion caused by the fluid flow and predicts that a localised release of scalar leads to a Gaussian concentration distribution in the long-time limit. This prediction fails in the tails of the distribution which are typically non Gaussian. I will describe how the theory of large deviations generalises homogenisation to provide a complete form of the concentration distribution, including its tails. This requires the solution of a family of eigenvalue problems which generalise the cell problem of homogenisation. The use of large deviations in this multiscale context has a broad appeal which I will illustrate with applications to cellular flows, to dispersion on networks, and to diffusion in perforated media.

## Nanoscale bubbles and drops, and coupled dynamics of solid-liquid-vapour systems with mass transfer

**Wednesday 31 ^{st} October 2018**

**Speaker:** David Sibley, University of Loughborough

**Time:** 16:00

**Location**: Room A17, School of Mathematical Sciences, University Park Campus

The dynamics of droplets on surfaces has received vast attention theoretically due to the interest in the moving contact line problem, and due to applications in inkjet printing, creation of super-hydrophobic surfaces, efficient irrigation methods and more. To accurately describe the shape and motion of droplets on the nanoscale, techniques from statistical mechanics much be employed to go beyond classical sharp-interface/Navier-Stokes models. Here we briefly introduce the density functional theory (DFT) of fluids method to calculate a density profile, with information that may be passed to an interfacial Hamiltonian (thin-film) model to explore dynamics of both normal and terraced droplets (which may be caused at temperatures close to freezing). We will also discuss equilibrium nanoscale bubble profiles using similar methods. In the second part of the talk, we will explore a complex non-conserved regime where a droplet of liquid spreads over a solid and in the presence of a vapour, all of the same material (such as ice-water-water vapour). We consider dynamics where vapour can condense to liquid which in turn can freeze to solid throughout a droplet spreading process, and indeed vice-versa. By developing a thin-film model capturing phase-change, surface tension, density contrast, and interfacial potentials, a rich phase diagram will be explored---and complex dynamics such as layered solid growth driven by forces at the contact lines described.