Unsteady extrusion of a viscoelastic annular film - I. General model and its numerical solution

The unsteady extrusion of a viscoelastic film from an annular and axisymmet ric die is examined. This moving boundary problem is solved by mapping the inner and outer liquid/air interfaces of the extruded film onto fixed ones, and by transforming the governing equations accordingly. The ratio of the film thickness to its inner radius at the exit of the die is used as the sm all parameter, epsilon, in a regular perturbation expansion of the governin g equations. Forces applied on the film give rise to four dimensionless num bers: Stokes, Capillary, Reynolds and Deborah. When the Oldroyd-B model is used, the dimensionless retardation time also arises. For typical fluid pro perties and process conditions, the Stokes and Deborah numbers are O(epsilo n(0)), i.e. much larger than the other relevant dimensionless numbers. In s uch cases, the base state is significantly deforming with time and it is ca lculated numerically by solving a partial differential system of equations in time and the axial direction. Special attention is required for its accu rate numerical solution. It was found that gravity plays the most important role in the process by accelerating the film, deflecting its inner and out er surfaces towards its axis of symmetry and decreasing its thickness aroun d the middle of its length. For typical values of the De number, its increa se leads to deceleration of the film that has less curved interfaces and mo re uniform thickness along its length. These effects become apparent, if th e St number is of order one; if it is smaller, the effects of fluid elastic ity decrease considerably. For typical values of the Ca and Re numbers, and of the retardation time of the fluid, their influence on the process is sm all. (C) 2000 Elsevier Science B.V. All rights reserved.