Analyses of coalescence and moving common line

The thinning and rupture of a dimpled film formed as a small bubble approaches a small solid spherical particle is analyzed under the influence of disjoining pressure attributable to London-van der Waals forces and electrostatic double layer. Given the radii of bubble and particle and required physical properties, the coalescence time, which is the time required for thinning and rupture of the liquid film, can be calculated as a function of the strength of the London-van der Waals forces and electrostatic double layer.;An analysis is completed to describe the moving apparent common line and dynamic contact angle formed by a draining film. Our premise here is that a common line does not move. As viewed on a macroscale, it appears to move as a succession of stationary common lines are formed on a microscale, driven by a negative disjoining pressure in the receding film. The dynamic contact angle is computed as a function of the static contact angle and the speed of displacement of the apparent common line.;The effects of surface tension gradient on the thinning and rupture of a draining plane parallel liquid film, formed as a small bubble approaches a liquid-gas interface, are investigated under the influence of the London-van der Waals forces. The mass transfer of surfactant to the interfaces is assumed to be adsorption-controlled. The coalescence time is obtained as a function of bubble radius, adsorption coefficient, surface diffusion coefficient, surface viscosities, surface tension and its change rate with concentration of surfactant and the strength of the London-van der Waals forces.