A numerical and experimental investigation of rolling and sliding motion of rotating spheres inside a cylinder

Official URL: https://dx.doi.org/10.1017/jfm.2021.1144

Rotating spheres in cylindrical channels roll or slide along the channel depending on the physical and geometric conditions. For a thorough investigation of the phenomenon, finite-element modelling is utilized to obtain the resistance coefficients for the motion of a sphere in a cylindrical channel, with an emphasis on near-wall motion. Extracted coefficients are compared with the data in the literature and utilized in exploring the conditions for rolling versus sliding along the channel. Sliding occurs due to the pressure build-up in the nip region between the wall and the rotating sphere in small confinement ratios, whereas rolling occurs when the shearing forces on the sphere are dominant in larger ratios. According to numerical results, a flow reversal takes place in the nip region and reduces the shear as well. Rolling versus sliding is demonstrated in experiments by using magnetic spherical particles, which are rotated by means of an external magnetic field inside cylindrical channels filled with viscous fluids. Faster axial velocities are observed in narrow channels while sliding than in wider channels while rolling for the same rotation rate of the sphere. Experiment observations are compared with the velocities evaluated from the resistance coefficients, showing that the distance between the sphere and the wall, which is dominated by roughness, plays an important role in the velocity of the sphere.