Motion of a Probe Ball in the Fluid under Centrifugal Acceleration

Abstract

The viscosity of a fluid can be measured by observing the motion of a probe sphere (or ball) in a centrifuge tube filled with this fluid. The hydrodynamic behavior of the probe ball moving in the centrifuge tube has been solved theoretically. We have got the universal relationship (for balls of a given material and size in a given tube) between the terminal ball velocity, the fluid viscosity and the centrifuge acceleration using the only adjustable parameter - the rotational friction coefficient between the ball and the tube. The rotation of the centrifuge tube in the horizontal plane induces an inertia force which is counterbalanced by the friction force acting on the ball. As a result, the ball moves along the tube with some characteristic speed, which is a measure of the viscosity of the fluid. This speed was calculated in the lubrication approximation. The gravitational acceleration causes the ball to move very close to the bottom of the centrifuge tube. In this situation, the gravity is balanced by a levitation force introduced and calculated in the present paper. The origin of this force is the formation of the bubble behind and below the moving ball. The theoretical development on the terminal velocity for the ball moving very near the bottom of the horizontal centrifuge tube is tested by using a specially designed centrifuge for two types of balls and a wide set of viscosity standards. Excellent agreement between theory and experiment suggests that we have developed a new approach to measure high viscosities of fluids at low shear rates which might be especially useful for the investigation of polymer melts.