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PI: Vella, Dominic

Department: Mathematical Institute (BK)

The oscillating drop method is a technique that has the potential to be used to measure the time-dependent surface tension (dynamic  surface tension) and viscosity (bulk and surfactant-driven) of complex fluids from high-speed images of the shape oscillations of drops. This technique would enable measurements to be made at the sub-millisecond timescales that are not accessible using  current techniques. The goal of this proposal is to develop a ""mathematical toolkit"" in partnership with Ricoh Product UK Ltd (a leading company in inkjet printing) to  enable the inkjet industry to better understand the liquids they use through this technique.

We will start by extending the existing linear theory for simple fluids to account for non-uniform surface tension. This will give a new analytical model that can be used to infer the dynamic surface tension - this will be ready to be adapted for Ricoh's products via appropriate code. We will also incorporate the effect of surface viscosity to account for experimental observations that appear to show that the viscosity of droplets (as measured using the drop oscillation method)  seems to depend on concentration, even at concentrations below the critical micelle concentration. (This runs counter to existing theory that the bulk viscosity does not change at such concentrations, so is most easily understood as a surface viscosity.) Experiments will be conducted both in the Oxford Fluids lab and at Ricoh, which will help in validating our model. This work will be the start of the proof of principle and the early-stages of the design of a new measurement technique, which will be used in industrial applications as well as academic research. Regular visits to Ricoh will enhance the promotion of this work for a joined IP licence and a further grant application to the  technology fund scheme; ultimately we aim to develop the first commercial software for measuring dynamic surface tension of complex fluids.

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