Rise velocity of single circular-cap bubbles in two-dimensional beds of powders and liquids

An expression for the rise velocity of single circular-cap gas bubbles in two-dimensional (2D) beds consisting of powders or liquids is developed with the aid of experimental data and computational fluid dynamics. Experiments were performed in a two-dimensional rectangular column of width DT=0.3 m by injecting air bubbles in fluidised beds of silica (mean particle size, dp=38 μm) and polystyrene (mean particle size, dp=570 μm) and in water. The rise velocity of single gas bubbles in the size range db=0.015–0.12 m were found to decrease significantly with increasing ratio of bubble diameter to bed width, db/DT. Computational fluid dynamics simulations of single gas bubbles rising in water, carried out using the volume-of-fluid (VOF) method, showed good agreement with experiment and were used to develop a common expression for the rise velocity of single gas bubbles in gas–solid fluidised beds and bubble columns. The 2D circular-cap bubble rise velocity is found to 10–30% lower than that of a 3D spherical-cap bubble having the same equivalent diameter.