Flow of Elastic Liquids

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***The proposal concerns liquids containing a dissolved polymer, which generally makes the liquid elastic as well as viscous. Polymers are often added to liquids to make the material more viscous - paint and ink are examples - but the polymer also makes the liquid elastic, and this additional fluid property can affect a flow. In inkjet printing, for example, the ink's elasticity can cause unwanted satellite droplets. Sometimes the polymer is added solely for the improvement provided by elasticity. Two well-developed applications are: to agricultural spraying because elasticity improves surface deposition of the coating; and to turbulent pipe flow because elastic stresses reduce the driving pressure. The amount of added polymer is often minute but the effect can be dramatic. In turbulent pipe flow, for instance, the addition of 10 parts per million can reduce the required pressure by 50%. Viscosity is an obvious property of a fluid - liquids are referred to as thick or thin - but elasticity is generally much less evident. The most visible manifestation is probably stringiness, as seen with saliva and egg whites. ******This grant application focusses on four flows in which the effect of elasticity is significant. For one of these, polymer is added for a specific benefit: namely, to water jet micromachining to improve resolution or precision. For the other three flows, polymer is an inherent constituent of the test fluids, and so the experimental liquids are elastic as well as viscous. One experiment is flow past a cylinder, carried out under microscopic conditions so that results can help explain how micro-organisms use their flagella to swim in mucus. Another experiment is flow through an array of rods, the array being a model of a fibrous porous medium, with application to fibre-reinforced plastics. The third is stagnation point flow. Because it is component of all the other flows, results from the study will help in explaining the elastic effects observed in those flows.******The primary objective of the program is to understand the role of elasticity in these experimental flows, that is, to identify when the property is operative, to quantify its effect, and to determine how the stresses caused by elasticity alter a flow. The latter three experiments will be conducted with special viscoelastic fluids - liquids which are elastic but have constant viscosities - that will enable elastic effects to be cleanly separated from viscous effects so that the role of elasticity can be assessed. Initial results with the rod arrays, for instance, have indicated that the resistance to flow caused by elasticity alone can be several times the resistance caused by viscosity, demonstrating the importance of elasticity.