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 research, 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 components 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 viscosity 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, 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 thermodynamic 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 interactions 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 phenomena that span disparate length scales and time scales, and operate with complex multi-physics components. Additional 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 analysis 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 (further details below)
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.
ECR Summer School
The Summer School for Early Career Researchers is aimed at PhD students, postdoctoral researchers and lecturers at an early stage of their career. The school will consist of a number of taught sessions covering various apsects of multiphase flow as follows:
Introduction to control and some applications to interfacial flows (Dr Susana Gomes, University of Warwick)
Falling liquid films are typical interfacial flows which exhibit an interesting range of behaviours, from flat films to travelling waves and chaotic-looking interfaces. They are a canonical problem in fluid dynamics and have a range of industrial applications, including coatings or microchip cooling. In these applications, we would therefore want to control them to have a desired interface shape. I will introduce some results in control theory (from linear control theory applicable to ODEs to nonlinear optimal control problems) and show how to adapt these to be applied to nonlinear PDE models for the interface of these films. We’ll discuss robustness of controls across models, and finally show how they perform in direct numerical simulations of the Navier—Stokes equations for the full problem.
Using asymptotics to probe the nonlinear dynamics of multilayer flows (Prof. Demetrios Papageorgiou, Imperial College, London)
Immiscible multilayer flows are challenging due to nonlinearities in both the governing equations
(Navier-Stokes systems) and the free surfaces/interfaces that must be determined as part of the solution.
Nonlinear deflections can lead to singular effects such as dewetting and topological transitions.
This set of lectures will explore, from first principles, the powerful use of multiscale asymptotic analysis
in deriving physically relevant reduced order models. The models will be analysed and computed with
emphasis placed on the supported intricate nonlinear phenomena that would be extremely hard to access
using direct numerical simulations. Multiphysics effects such as external electric and magnetic fields, surfactants are also amenable to analysis and key elements will be presented.
Multiphase Flows at Small Scales: Beyond Navier-Stokes (Prof. James Sprittles, University of Warwick)
The conventional Navier-Stokes modelling paradigm gives remarkably accurate results for a wide range of fluid flow phenomena. However, when layers of fluid become sufficiently thin, additional physics, conventionally neglected, becomes prominent. In this talk, I will introduce some of this additional physics and explain how it can be incorporated into a computational modelling framework that `goes beyond’ the traditional Navier-Stokes setup. Specifically, gas kinetic effects, disjoining pressure and thermal fluctuations will be shown to have a dominant effect on a number of commonly observed and technologically-relevant flows, such as the collision dynamics of liquid droplets and the stability of thin liquid films.
Interface-resolved Simulations of Multiphase and Evaporating Flows with OpenFOAM (Dr Mirco Magnini, University of Nottingham)
This session will provide an introduction to the most established techniques for the direct numerical simulation of two-phase flows, with a specific focus on the Volume Of Fluid method and on the opensource simulation toolbox OpenFOAM. The session will cover the key ingredients for accurate interface-resolved simulations, from interface advection, to surface tension and phase-change. Hands-on sessions will provide an opportunity for participants to practice benchmark flow configurations using OpenFOAM and a custom solver for flows with phase change, installed in a self-contained virtual machine running a linux operating system.
At the interface between analytical approaches and high performance computing in fluid mechanics (Dr Radu Cimpeanu, University of Warwick)
During this session we will explore how analytical techniques can work hand in hand with accurate numerical methods in order to enhance both the range of validity and efficiency of each strategy. Rather than disparate individual approaches, we will instead try to position ourselves at the centre of large scale evolving communities, building an interdisciplinary skillset along the way. We will (perhaps unsurprisingly) tackle interfacial flow problems that enable both meaningful analytical progress via modelling and asymptotic techniques, and hands-on numerical work using the volume-of-fluid method. The session will be highly interactive, with framework code provided and group work encouraged. We will spend ample time also discussing elements of good practice in this space, from version control to how to build, maintain and disseminate sustainable software for the applied mathematical community. No prior experience required, but a setup with (and working knowledge of) a UNIX-based operating system could be quite useful - if not already in place, this will be a good opportunity to meet new colleagues as part of the group discussions and practical elements of the session.
Analytical methods for multiphase flows (Prof. Darren Crowdy, Imperial College, London)
Compared to single-phase flows, analytical methods for multiphase flows interacting across an interface are rare, even in two-dimensional model prob- lems where many tools (e.g. conformal mapping) that are useful in single-phase problems fail. These summer school lectures will survey some of the analytical methods for multiphase flows that do exist, including novel numer- ical schemes based on them, with special focus on recent examples pertaining to problems of current interest in modern multiphysics applications. The aim of the lectures is to spur interest in developing new mathematical tools and approaches for modelling multiphase flows.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme The mathematics of multiphase flows with applications, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
Subscribe for the latest updates on events and news
INI is a creative collaborative space which is occupied by up to fifty-five mathematical scientists at any one time (and many more when there is a workshop). Some of them may not have met before and others may not realise the relevance of other research to their own work.
INI is especially important as a forum where early-career researchers meet senior colleagues and form networks that last a lifetime.
Here you can learn about all activities past, present and future, watch live seminars and submit your own proposals for research programmes.
Within this section of the website you should find all the information required to arrange and plan your visit to the Institute. If you have any further questions, or are unable to find the information you require, please get in touch with the relevant staff member or our Reception team via our contact pages.
INI and its programme participants produce a range of publications to communicate information about activities and events, publish research outcomes, and document case studies which are written for a non-technical audience. You will find access to them all in this section.
The Isaac Newton Institute aims to maximise the benefit of its scientific programmes to the UK mathematical science community in a variety of ways.
Whether spreading research opportunities through its network of correspondents, offering summer schools to early career researchers, or hosting public-facing lectures through events such as the Cambridge Festival, there is always a great deal of activity to catch up on.
Find out about all of these endeavours in this section of the site.
There are various ways to keep up-to-date with current events and happenings at the Isaac Newton Institute. As detailed via the menu links within this section, our output covers social media streams, news articles, a regular podcast series, an online newsletter, and more detailed documents produced throughout the year.
“A world famous place for research in the mathematical sciences with a reputation for efficient management and a warm welcome for visitors”
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
INI has a vital national role, building on many strengths that already exist in UK universities, aiming to generate a new vitality through stimulating and nurturing research throughout the country.During each scientific programme new collaborations are made and ideas and expertise are exchanged and catalysed through lectures, seminars and informal interaction, which the INI building has been designed specifically to encourage.
For INI’s knowledge exchange arm, please see the Newton Gateway to Mathematics.
The Institute depends upon donations, as well as research grants, to support the world class research undertaken by participants in its programmes.
Fundraising activities are supported by a Development Board comprising leading figures in academia, industry and commerce.
Visit this section to learn more about how you could play a part in supporting INI’s groundbreaking research.
In this section you can find contact information, staff lists, maps and details of how to find INI’s main building in Cambridge.
Our administrative staff can help you with any queries regarding a prospective or planned visit. If you would like to discuss a proposed a research programme or other event, our senior management team will be happy to help.