COLLISION DYNAMICS OF BUBBLE PAIRS MOVING THROUGH A PERFECT LIQUID

Equations are derived describing the inertial motion of a bubble pair through a perfect liquid. The relative bubble motion is driven by an interactional force induced by the centre of mass motion. This force can be derived from a potential that is proportional to s(n)(n greater-than-or-equal-to 3) and that depends on the bubble pair orientation. The path of two bubbles passing each other is investigated. The angle of deflection of the relative velocity in a two-bubble encounter is calculated numerically as a function of the impact parameter, the relative velocity g and the ratio of the centre of mass velocity components c2/c1. The specific conditions necessary for two bubbles to collide are determined. If c2/c1 > 1 there is a region with irregular behaviour of the deflection angle. The collision cross-section is calculated and depends smoothly on g, approximately proportional to g-1, and has a weak dependence on c2/c1.