Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Experimental results were obtained on the steady settling of spheres in quiescent media in a range of cylindrical tubes to ascertain the wall effects over a relatively wide range of Reynolds number values. For practical considerations, the retardation effect is important when the ratio of the particle diameter to the tube diameter ( λ) is higher than about 0.05. A new empirical correlation is presented which covers a Reynolds number range Re = 53–15,100 and a particle to tube diameter ratio λ < 0.88. The absolute mean deviation between the experimental data and the presented correlation was 1.9%. The well-known correlations of Newton, Munroe and Di Felice agree with the presented data reasonably well. For steady settling of spheres in a counter-current water flow, the slip velocity remains practically the same as in quiescent media. However, for rising spheres in a co-current water flow, the slip velocity decreases with increasing co-current water velocity, i.e., the wall factor decreases with increasing co-current water velocity. Consequently, the drag coefficient for rising particles in co-current water flow increases with increasing water velocity. The steady settling of spheres in quiescent media in different cylindrical tubes was investigated and a new wall factor empirical correlation is proposed. Wall factor was approximately constant for settling spheres in counter-current water flow, while decreased with increasing co-current water velocity for rising spheres in co-current water flow. Consequently, drag coefficient for rising particles increases with increasing water velocity. [Display omitted]