Over the past several decades there has been persistent and broad interest in the elucidation of drop impact problems. In the present work, we propose an integrated experimental, numerical, and analytical investigation of droplet impact on fluid interfaces with a focus on three-dimensional effects. Arguably, the required algorithms and associated computing power needed to accurately investigate 3D impacts are only just starting to mature in recent years due to the highly multi-scale nature of the fluid flow and strongly non-linear interfacial deformations. Similarly, recent advances in visualization and flow measurement have now made such investigations possible in the lab. Our ambitious project brings together a diverse set of young leaders in fluid dynamics to tackle this exciting and pressing research topic, and develop new transformative frameworks to study this challenging set of problems with cutting-edge tools and methodologies. Droplet-liquid impacts are fundamental to a range of industrial applications such as spray cooling, fuel injection, agricultural applications such as pesticide spray, and rain droplet impact, infectious disease transmission, manufacturing applications such as inkjet printing and droplet-based 3D printing, and environmental applications such as oil spill remediation. The bulk of prior work on droplet-liquid and droplet-solid impact focuses on axisymmetric, normal impacts due to the relative simplicity of experimental characterization and visualization and reduced computational demands. In practice, non-axisymmetric droplet-interface impacts are far more common and thus broadening the current understanding to include explicit three-dimensional effects is of critical and timely importance to unlocking and advancing applications. The objective in each constituent study will be focused on delineating parametric thresholds between the impact regimes of rebound, coalescence, and splashing. These efforts will be accompanied by the development of reduced-order models (guided and benchmarked by experiment and high-fidelity simulation) to extend the practical applicability of our results. The highly collaborative research program proposed herein will fully span low-energy to high-energy impacts under a single framework and allow the development of a single, consistent, physical picture for droplet impacts on liquid layers of the same fluid, with an unprecedented focus on three-dimensional effects, the role of the ambient gas, and the depth of the fluid layer. The research outputs are anticipated not only to include the specific scientific discoveries, but also benchmarked and documented experimental and computational tools and datasets to strengthen the broad global research efforts in the area. Moreover, the PIs will jointly develop new experimental and simulation data visualization activities related to the proposed work for the promotion of science, outreach purposes, and access initiatives in both the UK and USA. Several established artists have agreed to participate in visualisation of fluids events, open studio sessions and competitions, which will be organised by the PIs, building on their collective record of success in scientific visualisation.

The generation of small sizes of liquids in forms of jets or droplets has a significant impact on our daily life in many levels. When an electric field is applied to a liquid meniscus formed out of a nozzle, electric charges are accumulated on the liquid surface producing stress. This electrically-driven stress deforms the meniscus into a cone shape known as Taylor cone and due to the singularity at the apex, a fine jet, much smaller than the nozzle in size is produced (electrojetting). This jet then breaks up into droplets due to Rayleigh instability. Understanding the physical mechanisms of this phenomenon has been the focus of scientists and engineers due to its use in a variety of technical applications, such as electrospray mass spectrometry and electro-hydrodynamic printing. The collapse of cavities on free liquid surfaces is another interesting phenomenon, in which effects such as momentum focusing can lead to the production of diminutive droplets and aerosols. This phenomenon has been exploited in applications such as wastewater treatment, drug delivery in microfluidics, crop spraying and inkjet printing. While both phenomena described above produce small droplets, each one of these has limitations that prevent it from producing submicron droplets of complex fluids with high viscosity and density. Our proposal then aims to comprehensively study, for the first time, the behavior of both cavity collapse jetting and electrojetting to provide deep insights into the dynamics of the micro-droplets emerged when both phenomena are combined. This would then allow us to develop a novel printing technique based on the knowledge acquired throughout our study. We will also develop a predictive theoretical model for the droplet size and its speed based on the operation conditions and the physical properties of the liquids. The ultimate goal of the project is to use the proposed printing method to fabricate high performance piezoelectric devices as evidence of the applicability and the effectiveness of the technique. The current available droplets generation techniques can produce droplets comparable to the nozzle size. Small and thin nozzles are more prone to clogging and breaking and more difficult to manufacture. This has hindered the implementation of these technologies in a variety of applications, in which the high-resolution printing of highly particle-loaded inks (>5000 cP) is required. This project aims to solve this problem by proposing a novel technique that capable of printing highly viscous functional materials with small sizes (< 1 micron), surpassing the range of sizes and materials offered by the current printing systems in the market. A preliminary data shows that the new technique can produce jets that are up to 100 times smaller than the nozzle in size (no need for small nozzles) and printing frequency that is one order of magnitude higher than the traditional natural electrojetting pulsation technique (fast printing). The proposed system offers also a solution to the problem of electrojetting on non-conductive surfaces. Depositing subsequent charged drops with the same polarity on nonconductive surfaces is problematic because this creates a repulsion force between the droplets leading to splashing and hence poor printing. This is because the nonconductive surface does not permit the charges within the drops to dissipate. However, the flexibility of the proposed system could allow us to neutralize the charges of the subsequent droplets, which will solve the problem and ensure high-resolution printing even on non-conductive surfaces. This will push forward the implementation on applications such as high-resolution printed electronics, manufacturing microlenses by depositing liquid crystals micro/nano droplets and many other applications that depends on printing complex fluids and active materials with high resolution such as additive manufacturing of tissues and organs.

The spreading of liquids over solid objects is a familiar and every day occurrence. For example: raindrops smashing into windscreens; stones being thrown into ponds; a chocolate fountain coating a strawberry. In all these cases, there is a maximum speed at which the liquid can traverse (or 'wet') the object and going beyond this speed creates easily observable effects such as the the disintegration of the raindrop into smaller drops or a patchy coating of the strawberry. Remarkably, despite the seemingly innocuous nature of these everyday phenomena, at present there exists no theory or computational model capable of predicting, and hence controlling, the maximum speed of wetting. In addition to the academic curiosity of these events, they form the basis of a remarkable array of technological applications and natural processes. In particular, the coating of thin layers of liquid which subsequently solidify is a ~$100 billion (and ever-increasing) market which is key to the manufacture of products ranging from solar cells, to alleviate energy and environmental crises, to emerging capabilities to print electronic circuits. In these industries, an ability to create optimal designs is currently limited by our knowledge of the underlying physics. This project will underpin exploration of the aforementioned phenomena and innovation within industry by exploiting a synergy between computational models embedded within software and cutting-edge experimental analysis. The computational and experimental aspects are particularly ambitious as (a) the wetting of solids is a strongly multiscale problem, requiring resolution from almost-molecular scales right up to engineering application scales, and (b) the process is inherently three-dimensional, meaning that simplifications leading to reductions in computational complexity are impossible and high performance computing techniques must be implemented. This project exploits recent advances in (a), by the Investigators, in order to tackle the problems associated with (b) for the very first time. New knowledge of how liquids spread over solid surfaces will be initially focussed on industrial coating problems, where the challenge is to wet a solid with a liquid as fast as possible without entraining air. Initial progress will be guided and enhanced by a collaboration with 3M (famous for products such as Post-it and Scotchgard), a multinational corporation with ~$30 billion sales annually from manufacturing solar cells, paints, anti-reflective coatings, adhesives, etc. For them, a computational model provides a fast and cost-effective way to achieve understanding of the physical mechanisms at play in order to optimise the coating process. Breakthroughs achieved in this project will have impact within related fields of research. Within industry, this involves working with Trijet, a leading consulting firm on emerging drop-based technologies, who will translate our advances to improve the control of inkjet printing technologies that are being used in everyday applications of fluids, e.g. in the automotive industries and in the printing of high-value metallic inks such as silver for printed electronics. Furthermore, our advances could have impact in other fields, such as climate science, where similar flow structures are observed when a liquid drop impacts a bath of the same liquid, as occurs when a raindrop impacts the ocean. Here, our understanding of how trapped gas between the drop and the ocean is entrained into the latter could feed into climate models, where this is a key parameter.

The scientific discipline of fluid dynamics is primarily concerned with the measurement, modelling and underlying physics and mathematics of how liquids and gases behave. Almost all natural and manufactured systems involve the flow of fluids, which are often complex. Consequently, an understanding of fluid dynamics is integral to addressing major societal challenges including industrial competitiveness, environmental resilience, the transition to net-zero and improvements to health and healthcare. Fluid dynamics is essential to the transition of the energy sector to a low-carbon future (for example, fluid dynamics simulations coupled with control algorithms can significantly increase wind farm efficiency). It is vital to our understanding and mitigation of climate change, including extreme weather events (for example in designing flood mitigation schemes). It is key to the digitisation of manufacturing through 3d printing/additive manufacturing and development of new greener processing technologies. In healthcare, computational fluid dynamics in combination with MRI scanning provides individualised modelling of the cardio-vascular system enabling implants such as stents to be designed and tested on computers. Fluid dynamics also shows how to design urban environments and ventilate buildings to prevent the build-up of pollutants and the transmission of pathogens. The UK has long been a world-leader in fluid dynamics research. However, the field is now advancing rapidly in response to the demand to address more complex and interwoven problems on ever-faster timescales. Data-driven fluid dynamics is a major area where there are rapid advances, with the increasing application of data-science and machine learning techniques to fluid flow data, as well as the use of Artificial Intelligence to accelerate computational simulations. For the UK to maintain its competitive position requires an investment in training the next generation of research leaders who have experience of developing and applying these new techniques and approaches to fluids problems, along with professional and problem-solving skills to lead the successful adoption of these approaches in industry and research. The University of Leeds is distinctive through the breadth, depth and unified structure of its fluid dynamics research, coordinated through the Leeds Institute for Fluid Dynamics (LIFD), making it an ideal host for this CDT. The CDT in Future Fluid Dynamics (FFD-CDT) will build on the experience of successfully running a CDT in Fluid Dynamics to address these new and exciting needs. Our students will carry out cutting-edge research developing new fluid dynamics approaches and applying them across a diverse range of engineering, physics, computing, environmental and physiological challenges. We will recruit and train cohorts of students with diverse backgrounds, covering engineering, mathematical, physical and environmental sciences, in both the fundamental principles of fluid dynamics and new data-driven methodologies. Alongside this technical training we will provide a team-based, problem-led programme of professional skills training co-developed with industry to equip our graduates with the leadership, team-working and entrepreneurial skills that they need to succeed in their future careers. We will build an inclusive, diverse and welcoming community that supports cross-disciplinary science and effective and productive collaborations and partnerships. Our CDT cohort will be at the heart of growing this capability, integrated with and within the Leeds Institute for Fluid Dynamics to deliver a dynamic and vibrant training and research environment with strong UK and international partnerships in academia, industry, policy and outreach.