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# Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating

by 1,*, 1,*, 2 and
1
School of Mathematics & Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2
3
Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan
*
Authors to whom correspondence should be addressed.
Polymers 2020, 12(10), 2285; https://doi.org/10.3390/polym12102285
Received: 28 August 2020 / Revised: 24 September 2020 / Accepted: 25 September 2020 / Published: 6 October 2020
This article presents a mathematical model and theoretical analysis of coating of a thin film of non-Newtonian polymers as they travel through a small space between two reverse-rotating rolls. The dimensionless forms of the governing equations are simplified with the help of the lubrication approximation theory (LAT). By using the perturbation technique, the analytical solutions for velocity, flow rate and pressure gradient were obtained. From an engineering point of view, some significant results such as thickness of the coated web, pressure distribution, separation points, separation force and power input were computed numerically. The effect of velocities ratio $k$ and Weissenberg number $We$ on these physical quantities is presented graphically; others are shown in tabular form. It is noted that the involved material parameters provide a mechanism to control the flow rate, pressure distribution, the thickness of coating, separation force and power input. Moreover, the separation point is shifted toward the nip region by increasing velocities ratio $k$. View Full-Text
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MDPI and ACS Style

Ali, F.; Hou, Y.; Zahid, M.; Rana, M.A. Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating. Polymers 2020, 12, 2285.

AMA Style

Ali F, Hou Y, Zahid M, Rana MA. Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating. Polymers. 2020; 12(10):2285.

Chicago/Turabian Style

Ali, Fateh; Hou, Yanren; Zahid, Muhammad; Rana, Muhammad A. 2020. "Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating" Polymers 12, no. 10: 2285.

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