The effects of atmospheric pressure, air concentration in the fluid, and the surface roughness on the solid-sphere motion along a wall

A phenomenological model for describing a slow steady gravity-driven motion of a solid sphere down an inclined wall in a fluid under the conditions when an air (in the case of a fluid with dissolved air) bubble arises in the sphere-wall lubrication layer between the sphere and the wall is proposed. In the case under consideration, both contact and contactless motion of the sphere is possible. The sphere surface roughness and the concentration of the air dissolved in the fluid are taken into account. The relevant experiment studying the sphere motion accompanied by cavitation was carried out. We used fluids with various air concentration including a limiting case of degasified fluid and spheres of various surface roughness. We find a parameter whose constant value specifies a stationary motion of the sphere including a limiting case of degasified fluid. This parameter turns out to be proportional to the difference between atmospheric pressure and one corresponding to the equilibrium concentration of the air dissolved in fluid. The numerical results found were compared with the experimental data of our investigation and a good quantitative agreement was obtained in a certain domain of parameters. A possibility of unsteady motion of the sphere had been shown.