The mathematics of multiphase flows with applications

Programme theme

This is an INI Satellite programme that will be held at the University of East Anglia (UEA) in Norwich, UK. UEA is part of the Norwich Research park which also includes the Quadram Institute for food and intestinal re- search, the John Innes Centre for Plant Science, and the Norfolk & Norwich University Hospital. The purpose of the programme is to bring together theoreticians, computational modellers, and experimentalists to discuss the mathematical modelling of multiphase flows.

Multiphase flows comprise fascinating phenomena characterised by the interaction of different phases or compo- nents of matter: gas, liquid and solid. Deep theoretical understanding of the dynamics of multiphase flows is of fundamental importance to a huge variety of natural phenomena and industrial processes. Some examples are vis- cosity and density stratified flows, flows with phase changes (e.g. melting, evaporation), aerated and bubbly flows, suspensions and colloids, hydroelasticity, and flows involving capsules, particles and cells. Applications in Natural Science include disease transmission (e.g. for airborne respiratory infections such as COVID-19), coating flows including clinical applications of 3D printing for artificial limbs, blood flow in the cardiovascular system, biofilms, cavitation bubbles in plants and trees, and volcanic flows and soil erosion. Industrial and engineering applications include the transportation of Liquid Natural Gas (LNG) [R1], aircraft wing icing, renewable energy generation, heat and mass transfer devices, wave impacts on floating structures, and chemical reactions and combustion.

Under certain conditions multiphase systems can be treated as complex homogeneous fluids with specific thermo- dynamic properties and equations of state. In other situations it is appropriate to treat each phase as being distinct, in which case the interfacial boundaries between phases must be accurately tracked as the flow evolves, and interac- tions between phases and phase changes must be properly accounted for. Strong nonlinearity and coupling between phases is also a prevalent feature.

Multiphase flows pose many fascinating mathematical challenges. They exhibit complex spatiotemporal phenom- ena that span disparate length scales and time scales, and operate with complex multi-physics components. Addi- tional challenges stem from such features as singularity formation and topological transitions. An ability to make accurate predictions demands sophisticated modelling techniques and analytical approaches (e.g. asymptotic anal- ysis and stability analysis), as well as computational modelling and Direct Numerical Simulations (DNS). Modern DNS embraces continuum approaches such as volume-of-fluid and boundary-integral methods, as well as discrete approaches such as molecular dynamics and Lattice-Boltzmann methods. These offer powerful numerical tools but they work on a case-by-case basis parametrically and they are computationally expensive. Physical insight and breakthroughs in understanding requires judicious use of DNS combined with predictions from simplified models that operate with a small parameter set and that are amenable to mathematical analysis.

The programme will be organised as follows:

2nd-5th    July 2024: Summer School for Early Career Researchers 
8th-12th   July 2024: Programme workshop: New Directions in Multiphase Flows
15th-26th July 2024: In-residence research programme

The entire programme will be held at the University of East Anglia in Norwich. It will follow a similar format to programmes that are held at the Isaac Newton Institute in Cambridge. Participants at the in-residence part of the programme will be given a desk and other facilities, and there will be a regular series of research seminars.