PERTURBATION SOLUTION TO PLANAR FLOW OF A VISCOELASTIC FLUID WITH 2 MOVING FREE BOUNDARIES

The motivation behind the present study lies in a wide variety of poly mer flow applications involving two moving free boundaries. The two-di mensional deformation of an incompressible viscoelastic material, subj ect to an applied pressure difference and/or initial disturbance, is c onsidered. The initial geometry is taken to be that of a rectangle con taining fluid between two parallel plates, with two straight free boun daries. The full nonlinear problem is first formulated. The external p erturbation is assumed to be small, so that equations of motion, const itutive equations, and boundary conditions can be linearized about the equilibrium state. In this case, the resulting constitutive equation for a wide class of viscoelastic fluids becomes Maxwell's equation. Th e equations governing the flow field become of the hyperbolic type, an d an appropriate implicit finite-difference procedure is devised. As a n illustration, we examine the influence of fluid elasticity and that of surface tension by following the evolution of the flow field subjec t to some initial disturbance and slip conditions at the walls. Finall y, ways in which the present work can be extended and generalized are discussed.