Rolling and Sliding of Spheres Inside Horizontal Channels

Abstract

Low Reynolds Number rolling and sliding motion of spheres inside cylindrical channels filled with glycerin is investigated. Experimental data are collected for channel/sphere radius ratios $(r_{ch}/r_{sph})$ of 1.6 and 3, where the magnetic sphere is actuated at frequencies between 0.1-50 Hz. Magnetically actuated sphere is rotated clockwise about the y-axis, where the central axis of the cylindrical channel is designated as the z-axis and the distance between the sphere center and the channel axis is measured in x-direction. For $r_{ch}/r_{sph}$ ratio of 3, we observe that the sphere translates in positive z-direction, performing “rolling”. However, at smaller $r_{ch}/r_{sph}$ ratio of 1.6, where the sphere is closely fitted inside the cylindrical channel, as the actuation frequency is increased, transition from rolling to “sliding” in the opposite direction is observed, which describes the motion of a sphere translating in negative z-direction despite its clockwise rotation about y-axis. Further increase in actuation frequency results in saturation of the lateral velocity of sphere due to step-out in both cases. Experimental results are compared to the predictions of the existing analytical models in the literature. A computational fluid dynamics (CFD) model validated against the data found in the literature is utilized to help extending the existing data and interpreting the experimental results.