Experimental Determination of the Virtual Mass Coefficient for Two Spheres Accelerating in a Power Law Fluid

Abstract

The virtual mass coefficient is determined experimentally for the motion of two spheres side by side and in line in a power law fluid. The velocities of the two accelerating spheres and their separation distance was measured as they accelerated under the action of driving weights through a cylindrical column filled with different concentrations of polyacryamaide solution (0.01%, 0.03%, 0.05%, and 0.07% by weight). For comparison purposes, the experiments were repeated with water. Various densities of spheres and separation distances were examined. Within the range of power law indices (0.61–0.834) and Reynolds numbers (1.1–75) examined, the virtual mass coefficient was found to decrease with an increasing Reynolds number for the two spheres moving side by side, and found to be greater than 0.5 when the spheres were touching each other. As the distance between the spheres increased, the virtual mass coefficient was found to decrease and approached the single sphere value of 0.5 when the distance between the spheres was more than ten radii. When the spheres were in line and touching each other, the virtual mass coefficient was found to be less than 0.5, however, when the distance between the spheres increased, the virtual mass coefficient increased and approached the value of 0.5. The virtual mass coefficient was found to be consistent with the shear thinning behavior; for a given Reynolds number, it increased with an increasing power law index.