Forward Roll Coating of a Williamson’s Material onto a Moving Web: A Theoretical Study

Author:

Zahid M.1,Siddique I.2ORCID,Saleem S.3ORCID,Al-Zubaidi A.3,Rana M. A.4,Zafar M.4

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan

2. Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan

3. Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

4. Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

Abstract

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg’s number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate.

Funder

King Khalid University

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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