Velocity fluctuations resulting from the interaction of a bubble with a vertical wall

The interaction and motion of a spherical bubble with a vertical wall moving in an ideal fluid are analyzed. This case is representative of a bubble that moves at a high Reynolds number and has a small Weber number. Using potential flow theory, the velocity potential is obtained using a double expansion in spherical harmonics. The presence of the wall is approximated by considering the motion of a bubble and its virtual image. The motion equations, obtained considering an energy conservation argument, are solved numerically for a range of initial conditions. The mean and variance of the bubble velocity are calculated. In particular, the bubble velocity variance is obtained as a measure of the bubble velocity fluctuations resulting from the interaction with the wall. The predictions of this model are in good qualitative agreement with some recent experimental results. (c) 2005 American Institute of Physics.