The movement of solid-liquid suspensions in pipes and vessels is a generic complex problem which is commercially challenging and technically important. Industrial applications are numerous, e.g. chemicals, consumer goods, food, pharmaceuticals, oil, mining, river engineering, construction, power generation, biotechnology and biomedical. Despite such large markets, industrial practice and processes are neither efficient nor optimal because of a severe lack of fundamental understanding of these flows. Such flows involve complex phenomena on a wide range of scales as flow conduits generally vary from the micron scale to the centimetre scale, and vessels vary from the millilitre scale to the cubic metre scale. Flows may be turbulent or viscous and the carrier fluid may exhibit complex non-Newtonian rheology. Particles occur in various shapes, sizes, densities, bulk and surface properties which exacerbates the complexity of the problem. The design of processes for conveying or processing solid-liquid suspensions requires information about particle behaviour such as particle trajectory, radial migration across streamlines, particle velocity distribution, and solids distribution. There are, however, huge practical difficulties in imaging solid-liquid flows and measuring local fluid and solid velocities, since little of the available instrumentation is applicable. Mixtures of practical interest are often concentrated and opaque so that flow visualisation is impossible, and particles may be deformable, breakable or prone to aggregation. Such complex phenomena are presently difficult to predict. They have hampered fundamental research and the development of rigorous holistic modelling strategies and, as a result, work has generally followed a piecemeal empirical approach. This proposal will use a multiscale approach to study the flow of solid-liquid suspensions including fluids of complex non-Newtonian rheology and particles with complex properties: (i) experimentally via a unique and accurate Lagrangian technique of positron emission particle tracking, which can measure local 3-D phase velocities as well as phase distribution in opaque systems; and (ii) by developing and validating novel modelling approaches to predict such flows including detailed interactions between particles, fluid and walls. A number of advanced modelling techniques will be used including principally the Discrete Element Method (DEM), Computational Fluid Dynamics (CFD), Smooth Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Coarse-Grained Molecular Dynamics (CGMD). None of these methodologies on its own, however, is able to effectively model these complex flows as they all enjoy strengths as well as weaknesses. We will, therefore, exploit the strengths of each technique by assembling these methods in an efficient hybrid fashion to produce an integrated multiscale modular framework to be made available free of charge within the unique and well-known open source code DL_MESO. Thus, we will evaluate the best hybrid approaches and develop a paradigm for modelling these complex flows by mapping the model hybrids against flow characteristics. The use of a hybrid modelling methodology and a multiscale approach to include concentrated turbulent flows, fluids of non-Newtonian rheology, particles of complex shapes and properties will produce a quantum leap advance in the modelling of these complex flows. In the medium to long-term, the findings from this work should improve the competitiveness of the UK solid-liquid processing technologies. Our industrial and academic partners, however, will be able to draw immediate benefits through engagement with the project.

This user-need CDT will equip graduates with the skills needed by the UK formulation industry to manufacture the next generation of formulated products at net zero, addressing the decarbonisation needs for the sector and aligning with this EPSRC priority. Formulated products, including foods, battery electrodes, pharmaceuticals, paints, catalysts, structured ceramics, thin films and coatings, cosmetics, detergents and agrochemicals, are central to UK prosperity (sector size > £95bn GVA in 2021) and Formulation Engineering is concerned with the design and manufacture of these products whose effectiveness is determined by the microstructure of the material. Containing complex soft materials: structured solids, soft solids or structured liquids, whose nano- to micro-scale physical and chemical structures are highly process dependent and critical to product function, their manufacture poses common challenges across different industry sectors. Moving towards Net Zero manufacture thus needs systems thinking underpinned by interdisciplinary understanding of chemistry, processing and materials science pioneered by the CDT for Formulation Engineering at the University of Birmingham over the past twenty years, with a proven delivery of industrial impact evidenced by our partner's letters of support and three Impact Case Studies ranked at 4* in the recent Research Excellence Framework in 2021. A new CDT strategy has been co-created with our industry partners, where we address new user-led research challenges through our theme of Formulation for Net Zero ('FFN0), articulated in two research areas: 'Manufacturing Net Zero (MN0)', and 'Towards 4.0rmulation'. Formulation engineering is not taught in first degree courses, so training is needed to develop the future leaders in this area. This was the industry need that led to the creation of the CDT in Formulation Engineering, based within the School of Chemical Engineering at Birmingham. The CDT leads the field: we won for the University one of the 2011 Diamond Jubilee Queen's Anniversary Prizes, demonstrating the highest national excellence. The UK is a world-leader in Formulation; many multinational formulation companies base research and manufacture in the UK, and the supply of trained graduates, and open innovation research partnerships facilitated by the CDT are critical to their success. The CDT receives significant industry funding (>£650k pa), supported by 31 industry partners including multinationals: P&G, Colgate, Unilever, Diageo, Devro, Fonterra, Samworth Bros., Jacobs Douwe Egberts, Nestle, Pepsico, Mondelez, GSK, AZ, Lonza, Novartis, BMS, BASF, Celanese, Croda, Innospec, Linde/BOC, Origen, Imerys, Johnson Matthey, Rolls-Royce/HTRC, JLR Lucideon and SMEs: Aquapak, CALGAVIN and ITS/StreamSensing. Intra and cross cohort training is central to our strategy, through our taught programme and twice-yearly internal conferences, industry partner-led regional research meetings, student-led technical and soft skills workshops and social events and inter CDT meetings. We have embedded diversity and inclusion into all of our projects and processes, including blind CV recruitment. Since 2018 our cohorts have been > 50% female and >35% BAME. We will co-create training and research partnerships with other CDTs, Catapult Centres, and industry, and train at least 50 EngD and PhD graduates with the skills needed to enhance the UK's leading international position in this critical area. The taught programme delivers a common foundation in formulation engineering, specialist technical training, modules on business, entrepreneurship and soft skills including a course in Responsible Research in Formulation. We have obtained promises of significant industry and University funding, with 67 offers of projects already. EPSRC costs will be 44% of the cash total for the CDT, and ca. £27% of the whole cost when industry in-kind funding is included.

A vital challenge for modern engineering is the modelling of the multiscale complex particle-liquid flows at the heart of numerous industrial and physiological processes. Industries dependent on such flows include food, chemicals, consumer goods, pharmaceuticals, oil, mining, river engineering, construction, power generation, biotechnology and medicine. Despite this large range of application areas, industrial practice and processes and clinical practice are neither efficient nor optimal because of a lack of fundamental understanding of the complex, multiscale phenomena involved. Flows may be turbulent or viscous and the carrier fluid may exhibit complex non-Newtonian rheology. Particles have various shapes, sizes, densities, bulk and surface properties. The ability to understand multiscale particle-liquid flows and predict them reliably would offer tremendous economic, scientific and societal benefits to the UK. Our fundamental understanding has so far been restricted by huge practical difficulties in imaging such flows and measuring their local properties. Mixtures of practical interest are often concentrated and opaque so that optical flow visualisation is impossible. We propose to overcome this problem using the technique of positron emission particle tracking (PEPT) which relies on radiation that penetrates opaque materials. We will advance the fundamental physics of multiscale particle-liquid flows in engineering and physiology through an exceptional experimental and theoretical effort, delivering a step change in our ability to image, model, analyse, and predict these flows. We will develop: (i) unique transformative Lagrangian PEPT diagnostic methodology for engineering and physiological flows; and (ii) innovative Lagrangian theories for the analysis of the phenomena uncovered by our measurements. The University of Birmingham Positron Imaging Centre, where the PEPT technique was invented, is unique in the world in its use of positron-emitting radioactive tracers to study engineering processes. In PEPT, a single radiolabelled particle is used as a flow follower and tracked through positron detection. Thus, each component in a multiphase particle-liquid flow can be labelled and its behaviour observed. Compared with leading optical laser techniques (e.g. LDV, PIV), PEPT has the enormous and unique advantage that it can image opaque fluids, and fluids inside opaque apparatus and the human body. To make the most of this and image fast, complex multiphase and multiscale flows in aqueous systems, improved tracking sensitivity and accuracy, dedicated new radiotracers and simultaneous tracking of multiple tracers must be developed, and new theoretical frameworks must be devised to analyse and interpret the data. By delivering this, we will enable multiscale complex particle-liquid flows to be studied with unprecedented detail and resolution in regimes and configurations hitherto inaccessible to any available technique. The benefits will be far-reaching since the range of applications of PEPT in engineering and medicine is extremely wide. This multidisciplinary Programme harnesses the synergy between world-leading centres at Birmingham (chemical engineering, physics), Edinburgh (applied maths) and King's College London (PET chemistry, biomedical engineering) to develop unique PEPT diagnostic tools, and to study experimentally and theoretically outstanding multiscale multiphase flow problems which can only be tackled by these tools. The advances of the Programme include: a novel microPEPT device designed to image microscale flows, and a novel medical PEPT validated in small animals for translation to humans. The investigators' combined strengths and the accompanying wide-ranging industrial collaborations, will ensure that this Programme leads to a paradigm-shift in complex multiphase flow research.

This application requests funds to continue and develop the EngD in Formulation Engineering which has been supported by EPSRC since 2001. The EngD was developed in response to the needs of the modern process industries. Classical process engineering is concerned with processing materials, such as petrochemicals, which can be described in thermodynamic terms. However, modern process engineering is increasingly concerned with production of materials whose structure (micro- to nano- scale) and chemistry is complex and a function of the processing it has received. For optimal performance the process must be designed concurrently with the product, as to extract commercial value requires reliable and rapid scale-up. Examples include: foods, pharmaceuticals, paints, catalysts and fuel cell electrodes, structured ceramics, thin films, cosmetics, detergents and agrochemicals. In all of these, material formulation and microstructure controls the physical and chemical properties that are essential to its function. The Centre exploits the fact that the science within these industry sectors is common and built around designing processes to generate microstructure:(i) To optimise molecular delivery: for example, there is commonality between food, personal care and pharmaceuticals; in all of these sectors molecular delivery of actives is critical (in foods, to the stomach and GI tract, to the skin in personal care, throughout the body for the pharmaceutical industry);(ii) To control structure in-process: for example, fuel cell elements and catalysts require a structure which allows efficient passage of critical molecules over wide ranges of temperature and pressure; identical issues are faced in the manufacture of structured ceramics for investment casting;(iii) Using processes with appropriate scale and defined scale-up rules: the need is to create processes which can efficiently manufacture these products with minimal waste and changeover losses.The research issues that affect widely different industry sectors are thus the same: the need is to understand the processing that results in optimal nano- to microstructure and thus optimal effect. Products are either structured solids, soft solids or structured liquids, with properties that are highly process-dependent. To make these products efficiently requires combined understanding of their chemistry, processing and materials science. Research in this area has direct industrial benefits because of the sensitivity of the products to their processes of manufacture, and is of significant value to the UK as demonstrated by our current industry base, which includes a significant number of FMCG (Fast Moving Consumer Goods) companies in which product innovation is especially rapid and consumer focused. The need for, and the added value of, the EngD Centre is thus to bring together different industries and industry sectors to form a coherent underpinning research programme in Formulation Engineering. We have letters of support from 19 companies including (i) large companies who have already shown their support through multiple REs (including Unilever, P+G, Rolls Royce, Imerys, Johnson Matthey, Cadbury and Boots), (ii) companies new to the Centre who have been attracted by our research skills and industry base (including Bayer, Akzo Nobel, BASF, Fonterra (NZ), Bristol Myers Squibb and Pepsico).

The overall aim of this new CDT is to generate a body of highly-trained, doctoral scientists and engineers expert in the emerging and economically important area of metamaterials and possessing the skills, knowledge and professional attributes required to meet the challenges of employment in industry, academia and other commercial or governmental spheres. We will provide students with a detailed understanding of metamaterials from fundamental theory right through to prototype device design. At the same time they will be formally trained in the wider professional and personal skills such as innovation, engagement, commercial awareness and, importantly, leadership. Metamaterials are widely recognized as one of the most significant recent technical discoveries, highlighted as a top-ten insight of the last decade by Science Magazine. They are also set to become a major economic factor. In 2011 the global market for metamaterials was worth $256M, and is predicted by BCC Research to grow to $760M million by 2016, and to reach almost $2 billion by 2021. While products based on metamaterials are appearing (e.g. metamaterial antennas in mobile handsets and spacecraft; heat-assisted magnetic recording; transparent conductors for displays; surface bound data transfer and noise barriers etc.), the UK must ensure that future developments in these areas are strongly underpinned at the fundamental research level and also supported by highly skilled practitioners. The Government report on "Technology and Innovations Futures: UK Growth opportunities for the 2020s" (2010) lists 'metamaterials' and 'carbon nanotubes and graphene' as two key advanced materials areas. The UK's Ministry Of Defence (MOD) regards metamaterials as a key emerging technology, specifically listing advanced optical materials, advanced materials, bio-inspired technologies, and micro and nano technologies, as key areas, all topics that are of direct relevance to this CDT proposal. We note the comment from Professor Young's (Dstl) letter of support: "Dstl fully supports your proposal as a timely and unique vehicle for training future scientists, engineers and leaders for the benefit of the wider UK defence and security sector." Our cohort-based training will also help fulfil one of Minister David Willets' key aims "To create a more educated workforce that is the most flexible in Europe." To meet this last aim and to stimulate future UK work in this fast moving materials area we will establish a new CDT in a broad range of metamaterials research with PhD training that has an embedded engagement with industry. We will, together with our collaborators from industry, governmental laboratories and universities overseas, strengthen the synergy between physicists and material engineers, building on our pre-existing excellence in metamaterials and functional materials research. The research focus will be on EPSRC's Physical Sciences theme, specifically the sub topics "Photonic Materials, Metamaterials" (one of only three "Growth" research areas for this theme), and "Plasmonics" (a "Maintain" area). In addition, our CDT is relevant to the EPSRC's grand challenges of "Nanoscale Design of Functional Materials", and "Quantum Physics for New Quantum Technologies". There is also significant overlap with the EPSRC ICT "Growth" research areas of "RF and microwave communications" and "RF and microwave devices", which also encompass THz devices. Our team of 33 academics are addressing key and topical challenges across a range of internationally competitive metamaterials research: from microwave metasurfaces to carbon nanotubes, from graphene plasmonics to spintronics, magnonics and magnetic composites, from terahertz photonics to biomimetics. With the recent recruitment of two world leading theoreticians in transformation optics plus new work in acoustics, we shall combine depth and breadth of metamaterial research linked to industrial and Government laboratory researchers