Multi-phase flows occur when two or more different phases or types of fluid are brought together. They are seen to occur in a vast range of both physical and industrial type systems. Such systems are, to name but only a few, in processing, production and transportation of foods, oil, gas, waste and slurries; in energy production from evaporators, condensers, pumps and turbines; in natural systems such as geophysical and geochemical flows, reservoir extraction / filtration, biological and biochemical flows. In such systems the point at which different phases meet is termed an interface and this interfacial area gives rise to a host of complex rheological phenomena due to stresses that occur. Phenomena such as suspension dynamics, wetting, jamming, coalescence, break-up, collision and capillarity are all heavily interface dominated flows and are not readily mathematically easy to predict in typical engineering scenarios.

In these cases numerical computer simulations have proved an invaluable tool in successfully understanding, diagnosing, predicting and optimising systems. A growing current state of the art class of numerical computer simulation methods used for engineering multi-phase flow is called the lattice Boltzmann method. However, in this promising method, a drawback is the large amounts of resources that are spent smoothing and broadening interfaces in order to resolve and calculate the necessary flow details. This severely restricts the physical representative size of a simulation and the range of industrially useful applications that can benefit from this type of predictive modelling which is often needed to avoid long development delays.

This programme of research will develop brand new techniques for the numerical lattice Boltzmann methods in order to apply the mathematically correct stress jump boundary conditions in a sharp exacting manner. This will free up expensive computational resources which means (i) that existing simulations can be modified to take a fraction (estimated at up to 4 times less) of the time and memory, (ii) that a new range of larger more physically representative, accurate and industrially relevant multi-phase flows can be modelled. To ensure the correctness of the newly developed techniques they will be tested against known data and compared against the present day techniques in order to demonstrate the significant enhancements expected to be achieved through this research.

The types of research that will use the techniques developed in this research work will predominantly be multi-phase related but it is noted that the techniques developed will apply to any transport phenomena that involves stress boundaries within the lattice Boltzmann methods. For example the junction of an open fluid flowing into a porous media model contains a stress jump. More specifically this research will go on to be applied to the explicit modelling of emulsions and suspension. These are flows that contain a large number of particles with multiply interacting interfaces dominating the emergent complex rheological behaviour. Such flows are prevalent in the foods, drinks, creams, pastes, bio-fluids (blood) and other processing industries and the modelling tools developed here will lead to improved constitutional theories of non-Newtonian fluids, knowledge transfer and process optimisation for many years to come.

Potential Impact:
The research proposed addresses important methodological advancements in multi-phase fluids modelling for soft matter materials that will enable improved scientific understanding to guide design, characterisation and optimisation for a myriad of sectors. There is broad and palpable relevance to not only academic (as detailed separately) but also a range of industry sectors such as food, pharmaceuticals, personal care, health care, functional materials, biotechnology, display technology, geological/environmental remediation or extraction/storage, nuclear and energy storage. Many of these industries feature in the Research Councils themes and priorities such as those in Manufacturing the Future, Energy, Healthcare Technologies and Mathematical Sciences.

There is substantial potential for impact on the successful completion of this research programme which will lead to new predictive modelling mechanisms. Taking an example from the pharmaceuticals, foods or personal care product sectors: it can take six plus years to develop new product lines yet due to dynamic environmental and health regulations and evolving market demands, it can require product reformulation at short notice. Despite these sectors being technologically advanced it is still often the case that even small ingredient changes/substitutions can cause existing formulations and processes to fail having expensive consequences. Such scenarios might be avoided if product formulation of such soft matter were more firmly grounded with scientific understanding provided uniquely through advanced modelling of the type this proposed research aims to establish.

The ability to rationally design soft matter materials and the processing of soft matter materials can lead to shorter lead times, lower associative costs and may also lead to new methods/products that may otherwise never come to market. Avenues to these industry sectors will be pursued through our current establish teaching and research links to companies that have both strong UK and international operations and directly involve the manufacture and processing of soft matter materials (Nestle Uk, PepsiCo UK, Warburtons, Mars, Unilever, Premier Foods).

Many areas of the economy could benefit from the systematic development through our modelling paradigm rather than design by trial and error. Some specific examples include new display technology using liquid crystals or dielectrophoretically controlled inks; enhanced cell scaffolds used in tissue engineering for health; novel food gel phases and colloidosomes that deliver specific health benefits; new energy storage materials - batteries and fuel cells; optimised extraction/storage/clean-up of material in geological reservoirs; safe processing and treatment of nuclear products; and patient specific diagnosis with design of clinical interventions. So many of these conceptual ideas will benefit from the resolved scientific understanding that this research seeks to complete.