Application of the Modified Force-Coupling Method of Tracing the Trajectories of Spherical Bubbles with Solid-Like and Slip Surfaces

摘要

The force-coupling method (FCM) developed by Maxey and Patel (2001) was modified and applied to trace the trajectories of spherical bubbles with solid-like and slip surfaces. Careful comparison was made to the experimental results of Takemura et al. (2000, 2002a, 2002b). First, the result obtained by use of the original version of the FCM was compared to the experimental results. It was found that the original FCM was not feasible for tracing spherical bubble trajectories. Then, a correction was made to the FCM calculation of the bubble velocity by renormalization in terms of the bubble Reynolds number, which could very well trace the trajectory of the bubble with a solid-like, no-slip surface, but not that of a bubble with a slip surface. Finally, a substantial correction was made to the monopole term of the FCM, which could trace the trajectory of a bubble with a solid-like or slip surface very well even for the Reynolds number up to 20.