A study was made of the motion of axisymmetrical objects in viscous and viscoelastic fluids within a cylindrical tank with the assumption of negligible inertial effects. A numerical treatment based on the Stokes equations of motion and an optimization technique enabled the details of the velocity and rate-of-deformation fields for a Newtonian fluid to be predicted. The influence of the shape of various bodies, some even with concave surfaces, was examined. The corresponding experiments were carried out with viscous and viscoelastic fluids using a visualization technique. A correlation between the main flow characteristics and the theological behaviour of the fluids was established.Key words." Non-Newtonian fluid, numerical simulation, visualization, rate of deformation, obstacle Analysis of the literatureThe slow flow of an unbounded viscous fluid around 3-dimensional objects was one of the first applications of the Navier-Stokes equations. Several results were obtained in the last century. In particular, Stokes [1] presented the stream function of the uniform flow around a sphere, and results were then obtained for obstacle with shapes that differed more and more from that of a sphere: Oberbeck [2] considered the flow around an ellipsoid, while Sampson [3] proposed analytical solutions of the equation of a creeping axisymmetric flow for several coordinate systems.In the bibliographical analysis presented below we first consider flows of unbounded fluids and secondly, flows in the presence of walls. For both types of boundary conditions we distinguish between Newtonian and non-Newtonian fluids, and consider 3-dimensional isolated and connected obstacles with various shapes. Ellipsoids in unbounded fluidFor small objects with arbitrary and particularly spheroidal shapes, Cox and Brenner [4] proposed a general theory that enables their drag to be predicted. Morin [5] calculated the streamline patterns around the ellipsoid with the smallest drag in Stokes flow, while the optimal profile of the body of given volume with the smallest drag was obtained by Bourot [6]. This profile looks like a prolate spheroid capped by cones. 98OThe more complicated problem of the flow of nonNewtonian fluids around obstacles was broached by Sheppard [7], who attempted to apply the motion of a sphere to measure the viscosity of nitrocellulose solutions as long ago as 1917. The calculation of the hydrodynamic field of viscoelastic fluids flowing around a sphere constitutes the first attempt to consider a more general non-Newtonian flow than simple shear flows. The pioneers were Leslie [8]

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