Effect of finite boundaries on the slow laminar isothermal flow of a viscoelastic fluid around a spherical obstacle

Abstract

This paper contains experimental and theoretical work on a non-viscomethric flow with constant strain for non-Newtonian fluids. An experimental investigation of the laminar isothermal flow of moderately concentrated aqueous solutions of polymers (polyethylene oxide) around a spherical obstacle, which moves along the axis of a cylinder at low Reynolds number, is carried out. The sphere is free from any attachment and falls under the action of gravity. By means of a vizualisation method, velocity distributions are accurately measured and their dependence upon the three dimensionless parameters We (Weissenberg number), Re (Reynolds number) and λ (sphere-cylinder diameter ratio) is studied. A remarkable difference between Newtonian and viscoelastic velocity fields is pointed out. The drag on the sphere is also determined. The effects of finite boundaries are analyzed for a range of sphere-cylinder diameter ratios greater than 0.25. In particular, it is shown that the wall proximity increases the effects due to the fluid elastic behavior, while, on the other hand, it reduces the inertial effect. In order to complete the experimental results, a theoretical analysis is developed for a Maxwell constitutive equation. The lower terms of an expansion in power series of Re and We and simplified boundary conditions are used. The numerical data conveniently represent the experimentally observed phenomena.