Unsteady motion of a single bubble in highly viscous liquid and empirical correlation of drag coefficient

The unsteady motion of single bubbles rising freely in a quiescent liquid with high viscosity was measured using a CCD (charge coupled device) camera. Sequences of the recorded frames were digitized and analyzed using image analysis software and the measurements of the acceleration and steady motion of bubbles were obtained. The total drag coefficient was calculated from the accelerating motion to the steady motion with the added mass force and history force included. In virtue of dimensional analysis, the total drag coefficient of single bubbles is correlated as a function of the acceleration number, Archimedes number and Reynolds number based on the equivalent bubble diameter. The proposed correlation represents very well the experimental data of the total drag force in a wide range covering both unsteady accelerating motion and steady motion. The combined added mass and history force coefficient accounting for the accelerating effect on single bubbles was evaluated and correlated.