Mathematical simulation of the calendering process for non-Newtonian polymers. (July 2022)

• Record Type: Journal Article
• Authors: Javed, Muhammad Asif; Nasir, Sarah; Ali, Nasir; Arshad, Sabeen
• Is Part Of: Journal of plastic film and sheeting. Volume 38:Number 3(2022)
• Page Start: 369
• Page End: 395
• Publication Date: 2022-07
• Subjects: Calendering -- tangent hyperbolic fluid model -- Runge-Kutta method -- perturbation method -- velocity profile -- pressure; City planning -- Bibliography -- Periodicals; 668.495
• DOI: 10.1177/87560879211066900
• Languages: English
• ISSNs: 8756-0879

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.