Numerical Simulation of the Film Casting Process

Abstract

Numerical simulations have been undertaken for the film-casting process with viscoelastic fluids. Viscoelasticity is described by an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times, which fits well experimental data for shear and extensional viscosities and the normal stresses measured in shear flow. Non-isothermal conditions are considered by applying the Morland-Lee hypothesis, which incorporates the appropriate shift factor and pseudo-time into the constitutive equation. A one-dimensional model derived from the conservation of momentum is used to approximate the thickness, while the stress free-surface condition is used to approximate the width. The resulting system of differential equations is solved using the finite element method and the Newton-Raphson iterative scheme. The method of solution was first checked against the Newtonian and Maxwell results for different film geometries. The simulations are compared to available experimental data and previous simulations in terms of film thickness, film width, and film temperature. Agreement between the experiments and the current simulations is considered good with subtle differences. Agreement is also considered good between the current one-dimensional simulations and previous two-dimensional simulations for viscoelastic fluids, in terms of width and thickness. The one-dimensional model is advantageous since the algorithm is relatively simple, convergence is almost guaranteed, and the computing time is short.