Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating
1
School of Mathematics & Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan
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 belongs to the Section Polymer Theory and Simulation)
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 and Weissenberg number 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 .
View Full-Text
Keywords:
non-Newtonian fluid; roll-coating analysis; lubrication approximation theory (LAT); perturbation technique; approximate solution; numeric methods
▼
Show Figures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleAli, Fateh; Hou, Yanren; Zahid, Muhammad; Rana, Muhammad A. 2020. "Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating" Polymers 12, no. 10: 2285.
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Search more from Scilit