Mathematical simulation of the calendering process for non-Newtonian polymers

Abstract

This paper mathematically studies calendering with a tangent hyperbolic model to simulate non-Newtonian polymers. The constitutive equations based on Lubrication Approximation Theory (LAT) are first non-dimensionalized and then simplified. The simplified equations describing the flow inside the calender are solved (a) analytically using the perturbation method and (b) numerically using MatLab built-in routine “BVP4c” method. The first case obtains an analytical expression for velocity, pressure gradient, and final sheet thickness with the help of the perturbation method, while BVP4c and Runge-Kutta methods are used to calculate the velocity, pressure, pressure gradient, and mechanical quantities numerically. The power-law index and Weissenberg number influence on pressure, pressure gradient, and velocity profiles of fluid being calendered are shown with graphs. The pressure inside the calender decreases as the power-law index and Weissenberg number increase. The force function and final sheet thickness decreases as the power-law index and Weissenberg number increases.