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21 November 2007 Phys. Sc. & Engin. Grad School, Cardiff VISCOELASTIC FLUIDS: A BRIEF DESCRIPTION AND SOME MAIN FEATURES EXTRUDATE SWELL EXTRUDATE SWELL A viscoelastic fluid is extruded from a pipe. The stress A viscoelastic fluid is extruded from a pipe. The stress gradient at the die is responsible for the extensional gradient at the die is responsible for the extensional swelling. swelling. Capturing this gradient, as well as Capturing this gradient, as well as the free surface’s behaviour, is the free surface’s behaviour, is crucial. Extrusion processes in food crucial. Extrusion processes in food and manufacturing industries are and manufacturing industries are the main industrial applications the main industrial applications FILAMENT STRETCHING FILAMENT STRETCHING A viscoelastic fluid is confined A viscoelastic fluid is confined between two plates. When these plates between two plates. When these plates are pulled apart, the fluid stretches. are pulled apart, the fluid stretches. Tracking the free surface and describing Tracking the free surface and describing the necking effect at the centre are the necking effect at the centre are the main challenges. the main challenges. This phenomenon is common in fibre spinning and industrial This phenomenon is common in fibre spinning and industrial processes involving thin films. processes involving thin films. Once the velocity has been computed at all the internal nodes, then the values on the free surfaces are extrapolated along the vertical gridlines. The node is then relocated according to the new velocity by mean of an ALE (Arbitrary Lagrangian Eulerian) approach to obtain the corresponding boundary conditions. None of the surrounding air nodes (dry nodes) is involved; that’s the reason for this approach being called “wet”. The differential equations above have to be inserted in a computer code to obtain simulations. This is done by mean of the Numerical Analysis; among different choices we adopt Spectral Element Methods. First the domain is divided into (Spectral) elements. Pressure HorizontalVelocity VerticalVelocity Numerical Simulation of Free Surface Flow of Viscoelastic Fluids Giancarlo Russo, Cardiff School of Mathematics ( supervised by Prof. Tim Phillips) Modelling the flow: the OLDROYD – B equation The dynamics of the problems described is modelled by mean of the differential conservation laws for mass (2) and momentum (1); moreover, the constitutive equation is required to close the system. For Newtonian fluids this relation is linear, in our case the Oldroyd-B constitutive model (3) will describe a polymer solution. From the continuous to the discrete: the Spectral Element Methods On each spectral element a particular grid is then used to allow high order polynomials as basis functions. Such polynomials are shown in the pictures above in 1-D and 2-D. 1-D expansion 2-D expansion Flow past a cylinder in a planar channel: contours plot Tracking the free surface 1 5 4 3 2 My research project: two problems of industrial relevance VIscoelastic fluids are the most abundant class of fluids on earth. In fact, all the fluids in nature are viscoelastic, even though some of them like water are very well approximated by the (simple, linear) Newtonian law of viscosity. The main characteristic of viscoelastic matter is a partial elastic recovery after a strain has been applied; this can sometimes result in not so obvious effects like the rod-climbing shown here on the right. Since the polymers, which are highly elastic, became the most used fluids in industrial processes, the request for highly accurate simulations of the request for highly accurate simulations of viscoelastic flows grew dramatically. viscoelastic flows grew dramatically.

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