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Inkjet printing

Simulation software assists leading UK inkjet companies in technology development

Industry background
Inkjet printing is a rapidly advancing technology. A recent industry report (Smithers-Pira, “Future of Inkjet Printing to 2017: Global Market Forecasts”) predicts that the total market value of inkjet printing will more than double from its 2012 value of $30 billion to around $70 billion by the year 2017. Inkjet technology uses one of two methods for generating ink droplets. Continuous-inkjet produces a continuous stream of droplets from the surface-tension-driven break-up of a liquid jet; this method is used for high-speed, lower-quality printing. Drop-on-demand printing provides higher quality printing through individually generated droplets.

Impact summary
Leeds mathematicians have developed experimentally verified simulation software for predicting jet ejection and droplet break-up in industrial inkjet applications. The software allows users to assess the effects of changes to nozzle design, jet modulation and the properties of printing fluids. Print head manufactures Xaar Technologies and Domino use the software to reduce the costs of developing new print-head designs and inks by reducing the need for physical experimentation. 

The Leeds group has also used the software to assist international companies to develop new inkjet applications, including: the manufacture of pharmaceuticals (GlaxoSmithKline), where this has enabled them to greatly extend the range of tablet products that can be manufactured using this technology, and; new spray coating technologies (AkzoNobel).

Underpinning research
In 1995 Mathematicians from Leeds (together with collaborators from Cambridge) developed a new algorithm for modelling the flow of viscoelastic fluids. Instead of employing

traditional computational flow dynamic methods, the partial differential equations describing the evolution of the viscoelastic stress, mass and momentum are solved in the co-deforming Lagrangian frame of the fluid.

Mathematicians at Leeds continued to develop and refine the numerical code implementing this Lagrangian method from 1995 to 2005, applying it to the modelling of polymers solutions and melts, polymer foams and particulate suspensions. The code uses a mesh embedded in the fluid and so naturally follows the evolution of the fluid surface. This makes it ideal for inkjet studies, where the simulations must determine the position of free surfaces very precisely to be able to predict accurately the break-up of the thin ligands that form behind the main drop in high-speed printing. 

Inkjet simulations
In 2005, a consortium of UK inkjet companies set up a multidisciplinary research project “Next Generation Inkjet Technology” with the universities of Cambridge, Leeds, Oxford and Manchester, to improve the performance of inkjet printing. A key deliverable in the project was the development of simulation software for predicting the break-up of inkjets, in both Newtonian and viscoelastic fluids. A code was created capable of simulating the range of different print-head design, drive waveforms and ink formulations used in inkjet printing based on data supplied by the industrial partners.