Calendering of thermoplastics: models and computations

Abstract John Vlachopoulos (JV) started his polymer processing career with the process of calendering. In two landmark papers with Kiparissides, C. and Vlachopoulos, J. (1976). Finite element analysis of calendering. Polym. Eng. Sci. 16: 712–719; Kiparissides, C. and Vlachopoulos, J. (1978). A study of viscous dissipation in the calendering of power-law fluids. Polym. Eng. Sci. 18: 210–214 he introduced the Finite Element Method (FEM) to solve the governing equations of mass, momentum, and energy based on the Lubrication Approximation Theory (LAT). This early work was followed by the introduction of wall slip (with Vlachopoulos, J. and Hrymak, A.N. (1980). Calendering poly(vinyl chloride): theory and experiments. Polym. Eng. Sci. 20: 725–731). The first 2-D simulations for calendering PVC were carried out with Mitsoulis, E., Vlachopoulos, J., and Mirza, F.A. (1985). Calendering analysis without the lubrication approximation. Polym. Eng. Sci. 25: 6–18. In the intervening 35 years, other works have emerged, however our understanding has not been drastically improved since JV’s early works. Results have also been obtained for pseudoplastic and viscoplastic fluids using the general Herschel-Bulkley constitutive model. The emphasis was on finding possible differences with LAT regarding the attachment and detachment points of the calendered sheet (hence the domain length), and the extent and shape of yielded/unyielded regions. The results showed that while the former is well predicted by LAT, the latter is grossly overpredicted. More results have been obtained for 3-D simulations, showing intricate patterns in the melt bank. Also, the transient problem has been solved using the ALE-FEM formulation for moving free-boundary problems. The results are compared with the previous simulations for the steady-state and show a good agreement. The transient simulations capture the movement of the upstream and downstream free surfaces, and also provide the attachment and detachment points, which are unknown a priori. Finding these still remains the prevailing challenge in the modeling of the calendering process.