MATHEMATICAL MODELING OF THE EFFECT OF VISCOELASTICITY ON THE FILM DRAINAGE BETWEEN INTERACTING DROPS

A BSTRACT : Mathematical model of the deformation and drainage of film between interacting drops is presented in the case when dispersed or continuous phases are viscoelastic fluids. The model is based on the assumptions of a gentle collision at small Reynolds numbers and small deformation at small capillary numbers. It consists of lubrication approximation in the film and creeping flow equation in the dispersed phase. The equations in the continuous and dispersed phases are coupled by continuity of the velocity and stress boundary conditions at the interface. Generalizations of the Maxwell-type rheological constitutive relation are used to model the viscoelastic effects: upper-convected Maxwell model in the drop and fractional Maxwell model in the film phase. Predictions of the effect of the extra elastic stresses on the film drainage are given.