The breakup of liquid jets into droplets has been the focus of study for more than two centuries. The fast production of microjets and microdroplets has gained additional importance beyond its pure scientific interest motivated by their application in microfluidics devices and in some modern digital technologies, such as 2D and 3D-Printing. Most current studies of this topic aim to improve the control over the position, number and directionality of droplets and their satellites. The objective of this project is two-fold: (i) we will investigate and exploit self-stimulation (resonance) of liquid jets for a better control of the breakup frequency and length; and (ii) once we are able to extract the most unstable (most efficient) frequency we will study the generation of single drops from a continuous liquid jet by means of intermittent pressure pulses. A liquid jet/column will break up into droplets due to the action of surface tension. In continuous inkjet applications the breakup of a jet (or column) of ink is induced and controlled by applying external perturbations in the pressure (or velocity) of the fluid via piezoelectric elements. If the frequency and amplitude of these perturbations are within the so-called 'most unstable modes' range, droplets of uniform size will be obtained. Although these frequencies are roughly predicted by the Rayleigh/Weber equations, in practice this still requires much adjustment and fine tuning; this fine tuning is an empirical process that has to be repeated when different fluids, or inks, are used, which is both limiting and time consuming. We propose to detect and exploit self-stimulated modes in which the system tunes itself to its most unstable frequency by means of feedback. This, by definition, is the most efficient breakup. In this part of the project, mechanisms for self-stimulation will be investigated. The clear advantage of this approach is that the fine tuning is not needed and the breakup frequency can be readily found for a wide range of fluids (within a reasonable operating regime). The second part of the project, the generation of single drops from an otherwise unperturbed jet will be investigated. These single drops could be used for precise deposition, on demand, of small volumes of fluids for a variety of applications (e.g. Inkjet Printing). Moreover, it is envisaged that within these drops single particles (or cells, or other immiscible liquids in emulsion, etc.) can be trapped in real time and selectively delivered to a specific target. These 'particles' may be functional materials, chemical reactants, cells, etc. which are normally dispersed in a carrier fluid on purpose (e.g. fluids with the correct nutrients to sustain life, or functional materials in 'latent' mode) or unintentional and undesired (e.g. solid pollutants). These two overlapping and complementing studies would increase the predictability and reproducibility of the velocity and volume of droplets, and as a consequence these would increase reliability, efficiency and quality of printing technologies.

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.

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 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.