Effect of the Height of a Cylinder on the Rise of a Sphere Through a Rotating Fluid

Abstract

The work is devoted to an experimental study of the dynamics of a light sphere rising in a vertical rotating cylinder filled with fluid. In a rapidly rotating cylinder, the fluid flow is two-dimensional and has a complex multilayer structure. A Taylor-Proudman column forms around the sphere and rotates at an angular velocity that differs from that of the surrounding fluid. The axial motion of the fluid occurs exclusively within the Stewartson shear layer, located at the boundary of the Taylor-Proudman column. In contrast, the motion in the radial direction is attributed to the Ekman shear layer, which is located at the end-walls of the cylinder. Consequently, a rising sphere experiences a greater drag force compared to the case where rotation is absent. The effect of the cylinder height on the sphere velocity in a low-viscosity fluid is experimentally studied. Theoretical predictions indicate that the sphere velocity decreases with decreasing cylinder height, a finding that is corroborated by the present study. It is shown that the velocity of the sphere decreases in accordance with a power law as the rotation rate of the cylinder increases. It appears that the axial velocity is determined by the Ekman number for all cylinder heights that have been investigated.