Rise velocity of a swarm of large gas bubbles in liquids

Abstract

This paper develops a procedure for estimation of the rise velocity of a swarm of large gas bubbles in a bubble column operating in the churn-turbulent flow regime. The large bubble swarm velocity is estimated by introducing two correction factors into the classical Davies-Taylor (1950) relation for rise of a single spherical cap bubble in a liquid V_b = 0.71 √ gd_b(SF) (AF). The scale correction factor (SF) accounts for the influence of the column diameter. This correction is given by the Collins relation (J. Fluid Mech., 28, 97-112, 1967) and is a function of the ratio of the bubble diameter d_b to the column diameter D_T. Volume-of-fluid simulations confirm the validity of the Davies-Taylor-Collins relations for a variety of liquid properties. The acceleration factor (AF) accounts for the increase in the rise velocity of a bubble because of its interaction with the wake of a bubble preceding it. By analysis of video recordings of the interactions between two bubbles, both in-line and off-line, it is found that the acceleration factor AF increases linearly as the vertical distance of separation between the two bubbles decreases. Increasing liquid viscosity reduces this wake acceleration effect. With the aid of an extensive data set on the large bubble swarm velocity in columns of 0.051, 0.1, 0.174, 0.19, 0.38 and 0.63 m in diameter a correlation is developed for the acceleration factor. The large bubble swarm velocity is found to be three to six times higher than that of a single isolated bubble.