Numerical simulation of a single bubble rising in an ultrasonic standing wave field

The behavior of a single bubble rising in an ultrasonic standing wave field through vertical pipes filled with a quiescent liquid is analyzed numerically using the cubic-interpolated pseudo-particle(CIP)-combined and unified procedure(C-CUP) method. The calculated terminal velocities of bubbles in pipes agree with the experimental results in silicon oil. As the diameter of the bubble approaches the pipe diameter, the shape of the bubble is deformed into a lengthwise ellipse and rising velocity slows due to the pipe wall. The velocities and shapes of single bubbles are obtained for both standing waves formed in the axial direction of pipes and in the radial direction. When ani initial spherical bubble rises through the node of the radially formed standing wave in pipes, it is deformed into a lengthwise elliptical shape by the acoustic radiation force even if the wall effect is small, and the velocity of the bubble is faster than that for when there is no ultrasonic field. In other cases, the average terminal velocity of bubbles is slower than that for when there is no ultrasonic field.