Collisions of slightly deformable, high Reynolds number bubbles with short-range repulsive forces

A collision between two bubbles of radii a with an initial relative velocity 2U∞ is studied in the limit, Re≡ρU∞a/μ≫1 and We≡ρU2∞a/γ≪1. Here ρ and μ are the density and viscosity of the liquid and γ is the surface tension of the air–liquid interface. In the absence of colloidal forces, Chesters and Hoffman [Appl. Sci. Res. 38, 353 (1982)] showed that this situation leads to coalescence. The case where there is a nonhydrodynamic repulsive force between the gas–liquid interfaces of the two bubbles that is sufficient to prevent coalescence is considered. Such a force may arise due to ionic salts in aqueous solution or due to surfactants. The analysis shows the bubbles undergo a nearly elastic bounce on an O(a We1/2/U∞) time scale and the repulsive force per unit area must be at least 2γ/a for rebound. Also, experimental observations of bubble collisions in aqueous solutions using high-speed video photography are presented.