Wall effects on the rise of single gas bubbles in liquids

Abstract

We report the results of an extensive experimental investigation on the velocity of rise of air bubbles in the size range d_b = 3 - 80 mm in water. Measurements were made in columns with inside diameters D_T = 0.01, 0.02, 0.03, 0.051, 0.1, 0.174 and 0.63 m. The column diameter was found to have a significant effect on the rise velocity of the bubbles. When the ratio of the bubble diameter to the column diameter, d_b/D_T, is smaller than 0.125 the influence of the column diameter on the rise velocity is negligible and the rise velocity is described quite accurately by the Mendelson equation. With increasing d_b/D_T there is a significant reduction of the rise velocity, i.e. there is a significant "wall effect". The wall effect for spherical cap bubbles rising in inviscid flow, obtained for bubble diameters larger than 0.017 m, is described adequately by the Collins relation. The wall effect for bubbles smaller than 0.017 m is described by an empirical relation suggested by Clift, Grace and Weber.