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 tosⁿ(n3) 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 velocityg and the ratio of the centre of mass velocity componentsc₂/c₁. The specific conditions necessary for two bubbles to collide are determined. Ifc₂/c₁>1 there is a region with irregular behaviour of the deflection angle. The collision cross-section is calculated and depends smoothly ong, approximately proportional tog^–1, and has a weak dependence onc₂/c₁.