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(infinity) is studied in the limit, Re=rhoU(infinity)a/mu much greater than 1 and We=rhoU(infinity)2a/gamma much less than 1. Here rho and mu are the density and viscosity of the liquid and gamma 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(infinity)) time scale and the repulsive force per unit area must be at least 2gamma/a for rebound. Also, experimental observations of bubble collisions in aqueous solutions using high-speed video photography are presented.