THE TIME-DEPENDENT FLOW OF A VISCOELASTIC FLUID AROUND A SPHERE

We apply the finite element method to calculate the time-dependent vel ocity of a sphere falling along the axis of a circular cylinder filled with a viscoelastic fluid. The mesh surrounding the sphere translates along the cylindrical wall. For our calculations, we select an Oldroy d-B fluid with viscometric properties similar to those of the M1 Boger fluid. We then calculate the motion of spheres with variable density as one would in the laboratory. We examine the effect of the Weissenbe rg number and of the geometry upon the essential features of the time- dependent flow. We find that, for a given sphere and a given fluid, th e viscoelastic effects are damped when the radius of the cylinder beco mes much larger than the radius of the sphere. The velocity overshoot decreases when the Weissenberg number increases. We also examine the s ensitivity of the flow to the magnitude of the retardation time.