The steady annular extrusion of a Newtonian liquid under gravity and surface tension

The steady extrusion of a Newtonian liquid through an annular die and its d evelopment outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surf ace profiles are calculated simultaneously with the other unknown fields, i .e. using the Newton-Raphson iterative scheme. The effects of three relevan t parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on t he shape of the annular film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin annular film res pectively. A one-dimensional model for the extrudate region, valid for thin annular films, is also presented, and its predictions are compared with th e two-dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one-dimensional model predicts satisfacto rily the effects of the Stokes and capillary numbers. Copyright (C) 2000 Jo hn Wiley & Sons, Ltd.