Freely rising light solid spheres

This paper examines the behavior of spheres rising freely in a Newtonian fluid when the ratio between the density of the spheres and that of the surrounding fluid is about 0.02. High-speed imaging is used to reconstruct three-dimensional trajectories of the rising spheres. From the analysis of the trajectories the magnitudes of the drag and lift forces exerted by the surrounding fluid are deduced. It is argued that the two main contributions to the drag force are (i) a viscous drag that may be estimated from the standard drag curve by evaluating the Reynolds number using the actual value of the velocity, and (ii) an inertial drag that arises essentially by the same mechanisms that cause the lift-induced drag familiar from wing theory. Estimates of both contributions, the latter using visualizations of the wakes of the spheres, give a favorable agreement with the measured drag forces. These findings are closely related to recent numerical results of in the literature on the forces experienced by oblate ellipsoidal bubbles rising in quiescent water.