Industrial inkjet technology involves the generation, manipulation and deposition of very small drops of liquid (typically 20-50 um diameter) under digital control. The UK is recognised internationally as a leader in this area. Inkjet technology already dominates the desktop printing market. In commercial printing, it is rapidly becoming established for short-run applications and has, in only a few years, conquered a market previously occupied by conventional screen-printing equipment, where its great flexibility and inherent scalability give significant advantages. If higher printing speeds and greater quality can be achieved, then it will also be able to move into large-volume commercial printing. Apart from these printing applications, novel opportunities for inkjet deposition are also beginning to be exploited commercially in the manufacturing of high-value, high precision products (e.g. flat-panel displays, printed/plastic electronics, photovoltaic cells for power generation). By extending the existing benefits of inkjet methods (e.g. flexible, digital, non-contact, additive) to attain the speed, coverage and material diversity of conventional printing and manufacturing systems, we can transform inkjet from its present status as a niche technology into a group of mainstream processes, with the UK as a major player. But in order for this transformation to happen, we need a much better understanding of the science underlying the formation and behaviour of very small liquid drops at very short timescales, and to widen the range of materials which can be manipulated in this way, especially to allow fluids with high solids content (i.e. colloidal fluids) to be deposited. This cross-disciplinary programme of research is strongly supported by a consortium of nine UK-based companies and will bring together established research groups from three major UK universities to study three themes focused on key aspects of the industrial inkjet process: the formulation, rheology and jetting behaviour of colloidal printing fluids; understanding and controlling dynamic micro-scale drop impact, spreading and fixing; and development and validation of an advanced process model for industrial inkjet. Within these themes we aim to: develop a theoretical and practical understanding of how to make stable high solid-content colloids suitable for inkjet deposition, and how they behave in an inkjet system and on the substrate; explore post-impact processes that determine the structure and functionality of the printed features, including surface morphology, chemistry and surface treatment, fluid dynamics of wetting and the interaction of successively printed materials; and develop a set of models, validated by precise measurements and underlying physical theory, to describe all aspects of the formation and ultimate fate of ink drops. Industrial beneficiaries will include companies in the fields of inkjet printing and digital manufacturing, as well as other companies involved in the precise manipulation of small liquid droplets: examples of sectors include pharmaceuticals, agrochemicals, combustion, coating application, materials processing, and particle technology. Academic beneficiaries, apart from researchers working directly on inkjet technology, will include those in the fields of rheology, fluid mechanics, microfluidics, materials science and surface engineering.

This project concerns uncertainties in the predictions made by models. A model is a description of a real process, using mathematical equations. Usually, a computer is used to compute or solve these equations to produce the model predictions. We think of these as the outputs of the model. The model also has inputs of various kinds, which are numbers to put into the equations. For example, a model to forecast the weather is based on very complex equations describing the movement of the air at various altitudes, the formation of clouds, and so on. The numbers to be put into the model include the current state of the atmosphere, the temperature of the air at different locations and altitudes, physical constants used in the equations, and so on. Any model is an imperfect representation of reality, and its predictions are imperfect. The predictions can be wrong because the equations are wrong, they have the wrong numbers in them, or the computer program is solving them inaccurately. In practice, all of these imperfections are present to some degree. As a result, we may expect the true real-world value corresponding to the model output to be close to the model prediction, but there is uncertainty about its precise value.The objective of this project is to develop tools to manage the uncertainty in model outputs. One of the hardest tasks is simply to quantify the uncertainty / just how close to the output do we expect the true value to be? To answer this we must first quantify the uncertainty in the model inputs and the model structure. Then we must determine how these uncertainties feed through into uncertainty about the model output. The latter task can be very difficult. The usual approach is a method known as Monte Carlo, in which we take randomly sampled values of the inputs and run the model for each set of sampled inputs. The collection of outputs we obtain from these runs provides a random sample that tells us how much uncertainty there is in the model output. However, this method typically requires very many model runs, and if the model takes some minutes, hours or even days to run, then this is impractical.Methods have been developed to allow much more efficient determination of uncertainty in model outputs. These methods are quite well understood theoretically, and have been used in a number of serious applications. Nevertheless, they are not yet ready for routine use. Further work is needed to identify robust and reliable ways to implement them in a wide range of modelling situations, to tackle the large numbers of inputs, outputs and data sources that arise in many models, and to construct suitable links between the model outputs and the real-world variables that they are designed to predict. We seek funding for this work, which will turn the theory into usable tools, thereby providing a basic technology for the developers and users of models.The same underlying approach, known as Gaussian process emulation, can be adapted to address many other problems associated with complex models. These include sensitivity analysis (how much of the output uncertainty can be attributed to each source of input uncertainty?), calibration (using observations of the real-world phenomenon to reduce uncertainty about the inputs, and hence to reduce uncertainty in outputs), and the dynamic version of calibration known as data assimilation. The Bayesian approach handles all these tasks in a unified framework that addresses all sources of uncertainty. This project will produce a toolkit for these techniques and others, specified in a standard format (Universal Modelling Language), so that others can use the methods. We will also produce some substantial case studies to exemplify the techniques.

Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.

Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.

Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.