A model for predicting bubble velocity in yield stress fluid at low Reynolds number

Abstract Currently, studies on bubble velocity in yield stress fluids with low Reynolds numbers are lacking. In most engineering applications, such value is often calculated using predictive models developed for viscous fluids. However, these models are only applicable to yield stress fluids in limited conditions because the bubble rise velocity is affected by the yield stress in these fluids significantly. In this study, a velocity field model around a bubble is first developed by performing an infinitesimal analysis of the velocity field in the equatorial plane of the bubble and combining the continuity equation with the constitutive equation of yield stress fluids. Next, a new model is proposed for predicting bubble velocity in yield stress fluids at a low transport rate by integrating the model of velocity field around the bubble with energy conservation equations. Finally, experimental studies are performed to analyze the bubble transport behavior in yield stress fluids at low Reynolds numbers. The experimental results showed that under a low Reynolds number, the bubble rise velocity is dominated by the yield stress of the fluid. Hence, we further validated the proposed bubble velocity prediction model with experimental measurements, which match closely with each other. We conclude that for a Reynolds number less than 0.4, the model developed in this study can be used to predict the bubble velocity in yield stress fluids with high accuracy.