Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions

TLDR: In this article, a simple but reliable correlation for a drag coefficient, CD, of single bubbles under a wide range of fluid properties, bubble diameter and acceleration of gravity were developed based on a balance of forces acting on a bubble in a stagnant liquid and available empirical correlations of terminal rising velocities of single bubble.

Abstract: Simple but reliable correlations for a drag coefficient, CD, of single bubbles under a wide range of fluid properties, bubble diameter and acceleration of gravity were developed based on a balance of forces acting on a bubble in a stagnant liquid and available empirical correlations of terminal rising velocities of single bubbles. The proposed CD consists of three equations, each of which corresponds to pure, slightly contaminated and contaminated systems. The effect of a frictional pressure gradient due to a liquid flow is also taken into account by introducing a concept of an effective body acceleration. Terminal rising velocities of single bubbles were calculated using the proposed CD, and compared with measured data under the condition of 10-2<Eo<103, 10-14<M<107 and 10-3<Re<105 where Eo, M and Re are Eotvos, Morton and bubble Reynolds numbers, respectively. As a result, it was confirmed that the proposed CD gives better predictions than available drag coefficient models.