ON THE SLOW MOTION OF AN INTERFACIAL VISCOUS DROPLET IN A THIN LIQUIDLAYER

In order to investigate the influence of the surface viscosity on the type of the how inside and outside a droplet moving in a thin liquid l ayer, it is essential to compute all hydrodynamical parameters which a re important for a better understanding of the hydrodynamical interact ion of the thin liquid film and the droplet in it. In the present pape r, the problem of a translational slow motion of a droplet with a visc ous interface in a liquid layer bounded by viscous liquid-gas interfac es is considered. For low Reynolds and capillary numbers, different va lues of droplet and film bulk viscosity ratios and surface dilatationa l and shear viscosities are used in the frame of Newtonian surface the ology. The problem reduces to two dimensions when using the ''two vort icities-one velocity'' formulation of basic how equations. The model e quations and boundary conditions, which contain second-order derivativ es of the velocity and the vorticity, are solved numerically to provid e information on type of how, pressure distribution and drag coefficie nt. The numerical results reveal the strong influence of the surface v iscosity on the motion of the droplet in the viscous liquid layer when the radius of the droplet is of the same order of magnitude as the th ickness of the liquid film. The presence of the viscous liquid-gas int erface close to the droplet changes the flow pattern inside the drople t considerably when the droplet bulk viscosity is sufficiently higher than the viscosity of the film.