An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids

Doctoral Thesis


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University of Cape Town

An analysis of the flow about a sphere rotating slowly in a Rivlin-Ericksen fluid contained in a stationary outer concentric sphere is presented. An application of the conformal mapping technique is proposed. The technique is used to obtain the radial and axial velocity components for the flow about a disc rotating within an outer oblate spheroidal shell from the solution to the corresponding problem of the flow about a sphere rotating within an outer spherical shell. The results are compared with an existing rigorous analysis for a disc rotating in an infinite sea of the Third Order fluid. They are also used to estimate wall effects in experimental situations. Tangential and radial velocity profiles are measured for the flow about a sphere rotating slowly in a Newtonian liquid. Velocities are determined from enlarged streak photographs of aluminium particles moving in a collimated 'sheet' of light, at several planes throughout the flow field. Similar velocity profiles are measured for the flow of a 1,50% Natrosol 250 H solution about two spheres of different diameters rotating in tanks with different dimensions. A set of velocity distributions is also measured for a sphere rotating in a 0,9% Natrosol 250 H solution; a dye tracer study of the flow about a sphere rotating in this liquid is presented as well. Velocity profiles are presented for the flow of the 1,50% Natrosol solution about a rotating disc and the flow of the 0,9% solution about a second rotating disc of different diameter. Both Natrosol solutions exhibited viscoelastic behaviour in all cases. The Newtonian fluid study is at a Reynolds number of 1,2: all viscoelastic fluid studies are within the range of Reynolds numbers of 0,05 to 1,24. The zero shear viscosities of the Natrosol solutions are measured using the falling sphere method. The non-Newtonian material parameters are obtained by fitting the theoretical curves to the measured velocity data. The values of the elastic and shear thinning parameters for the two fluids obtained in the different geometrical and dynamical systems are compared.