Numerical simulation of coalescence of viscoelastic drops in Newtonian fluids

Together with break-up and mass transfer, coalescence is an essential process in many industrial and natural fluid/fluid dispersions, governing drop/bubble sizes and thereby the final product properties. Conceptually, coalescence can be split into a hierarchy of sub-processes, characterized by progressively diminishing length scales (Chesters, 1991): The external flow, governing the frequency, strength and duration of the collisions; Film formation and drainage; The destabilization of the film by inter-molecular forces, leading to rupture. Viscoelastic behavior is exhibited by one or both phases in many industrial processes involving dispersions (blending of molten polymers, production of polymer foams, suspension polymerization, polymer coating, etc.). Of the various elements involved in, coalescence sub-process (ii) is especially sensitive to departures from Newtonian rheology - small changes in the stresses exerted on the film translate into large forces per unit volume. Much progress has been made in recent years on the numerical investigation of film drainage and rupture in Newtonian systems under different conditions ( Abid & Chesters, 1994, Rother, Zinchenko & Davis, 1997) but the extension of such investigations to viscoelastic dispersions is still in its infancy. In the present study the drainage of a Newtonian film between axi-symmetrically interacting viscoelastic drops is investigated. The mathematical model is based on the assumption of small deformation, typical for coalescing collisions, and consists of: lubrication approximations of the film flow (solved by a FDM); creeping flow equations in the viscoelastic, Maxwell-type constitutive equations, for the dispersed phase (solved by a FEM). The film and drop-phase equations are coupled by continuity of the velocity and stress boundary conditions at the interface. The outer boundary condition consists of uniform pressure while a prescribed interaction force takes into account the external flow. The effect of the extra elastic stress in the drop phase on the film drainage is investigated and predictions of the rate of drainage presented. As a main result it is found that an increase of the elastic component (increase of Weissenberg number) yields a faster film drainage.