Purely elastic instabilities and turbulence in flows of polymer solutions

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Flows of complex fluids (such as polymers, colloids, emulsions, pastes etc.) are abundant in everyday life. One can think of pouring syrup from a bottle or squeezing toothpaste from a tube, but also of fibre-spinning and extrusion - processes used to produce plastic bags, optical fibres, wire coatings, guitar strings etc. Complex fluids, and polymer solutions in particular, often exhibit unexpected behaviour - they do not flow like water. For example, if one rotates a spoon in a cup of tea, the tea is pushed towards the walls of the cup. When, instead, this experiment is repeated with a polymeric liquid, the polymers move towards the spoon producing the so-called rod-climbing effect.What is even more surprising is that flows of polymers can become unstable. One of the famous examples is the melt-fracture phenomenon observed in extrusion of concentrated polymer solutions or melts, which is one of the main elements of polymer processing in industry. There the liquid is pressed through a thin capillary to produce a regular jet of polymers. At low extrusion speeds the jet remains straight and homogeneous, while at larger speeds the flow starts undulating, becomes chaotic and eventually breaks up. These instabilities are one of the main production-limiting factors and have been plaguing technology and industry for years. Their presence is surprising since in Newtonian flows, instabilities and the transition to turbulence are inertia-driven, and are expected to occur when the Reynolds number exceeds some critical value. The Reynolds number characterises the ratio of inertial to viscous effects and is inversely proportional to the fluid viscosity. For extremely viscous polymeric fluids typical Reynolds numbers are very small, far below the critical value. The inertia-driven transition is thus absent and can not explain instabilities in polymeric solutions. Instead, some other mechanism causes destabilisation.The striking properties of polymer solutions and melts arise from the interactions between their microstructure and the flow: long polymer molecules are stretched and oriented by the flow. In the past 20 years, we have begun to understand that flow-induced stretching and orientation of polymers can not only make polymers flow differently than water, but can also destabilise the flow, leading to vortices and random flows. This chaotic motion looks similar to Newtonian turbulence but is not inertial in origin. This new type of turbulence, the so-called elastic turbulence, is poorly understood and little is known about its structure and conditions at which it might appear.The aim of this research programme is to study this new type of turbulence by means of computer simulations and semi-analytical methods recently developed to describe the structure of Newtonian turbulence close to the transition. The motivation to perform this study is three-fold. First, this is a completely new type of turbulence which we have not encountered in Newtonian fluids like water. Since many every-day fluids are non-Newtonian and viscoelastic, it might be that understanding elastic turbulence is even more important than understanding Newtonian one. Secondly, understanding the origin of elastic turbulence might provide a solution to the industrial problems like melt-fracture. Finally, by comparing the two, we may learn something about the mechanism of Newtonian turbulence.