Application of Shadow Visualization to Study the Drag of Toroidal Bubbles

In this work, the ascent of a toroidal bubble created by the injection of a pulsed air jet into water vertically upwards is studied by the shadow method. When using the shadow method, the bubble border on the image is darkened, and the contrast in comparison with the background is increased, which makes it possible to use software processing algorithms to determine the parameters of the ring on each frame. There are experimental results indicating that, in addition to the buoyancy force, the drag force also acts on the toroidal bubble. In this paper, the experimental data on the change in the torus radius as a function of time are compared with a theoretical model constructed with and without taking into account the drag force. It is shown that taking into account the drag force leads to a much better agreement between theory and experiment. The drag force is concluded to act on toroidal bubbles, but its influence decreases with time, i.e., as the bubble rises. The drag coefficient used in the calculations is determined empirically and assumed to be constant.