Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere–wall and sphere–sphere interactions

Abstract

Axisymmetric sphere–wall and two-sphere interactions were examined in a viscoelastic solution composed of polyisobutylene polymer in tetradecane. The Reynolds and Stokes numbers were small, so that inertia played at most a minor role, while the Deborah numbers De were in the range 0.4 < De < 3.5. When single spheres fell away from the solid top of the containing vessel, or toward the bottom, the range of the sphere–wall interaction was reduced in the viscoelastic fluid relative to a Newtonian fluid. The reduced range was more pronounced at higher settling speeds. In addition, the interaction in the viscoelastic fluid was reversible, in that the effect of the wall on a sphere moving away from it was the same as that on a sphere moving toward it. In the experiments with two equal spheres sedimenting along their line-of-centers, the spheres moved together until they touched. The rate at which they moved together was measured for sphere–sphere separations ranging from contact to many diameters, and for separations greater than 2 diameters was in fair agreement with analytic predictions. The average sedimentation rate of the two spheres increased as they moved together, by an amount that was in good agreement with the Newtonian solution at low Reynolds number.