THE VELOCITY POTENTIAL OF LIQUID CONTAINING SPHERICAL BUBBLES WITH CENTERS LOCATED IN A LINE
A generalization of the method of reflections devoted to calculating the velocity potential of liquid with two spherical bubbles to the case an arbitrary number of bubbles the centers of which are located in a line has been performed. The recurrent relations obtained have been tested. To this end, a comparison of the results of their application to calculating the hydrodynamic interaction force with similar results evaluated by the method of expansion in spherical functions has been done in the cases of two and three bubbles. A good agreement has been obtained. Comparison of efficiency (i.e., consumption of computer time) of the methods of reflections and expansion in spherical functions has been performed. Various distances between the bubbles and different number of the bubbles were considered. It has been shown that if the bubbles are not relatively close to each other (i.e., when the distance between the bubbles is greater than a few of their characteristic diameters) the efficiency of the both methods is approximately the same. With decreasing the distance between the bubbles, the method of expansion in spherical functions becomes more efficient, except for the case of two bubbles.