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Licensed Unlicensed Requires Authentication Published by De Gruyter February 19, 2021

Roll-over-web coating analysis of micropolar-Casson fluid: a theoretical investigation

  • Zaheer Abbas and Sabeeh Khaliq ORCID logo EMAIL logo

Abstract

The theoretical model of micropolar-Casson fluid is studied in roll-coating over a moving substrate based on the lubrication theory. Closed-form solutions for the velocity, pressure gradient, and microrotation are attained, while a numerical technique employed to compute interesting engineering variables such as pressure, roll-separating force, separating point, and power input. The influence of involved parameters on the physical and engineering quantities are displayed via graphs and table. The coupling number (N) and viscoplastic parameter (β) provide the controlling mechanism for the exit sheet thickness, separating force, and power input. Also, the pressure gradient and pressure profile in the nip region enhances for large values of coupling number (N) whereas the viscoplastic parameter (β) gives the opposite behavior.


Corresponding author: Sabeeh Khaliq, Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur63100, Pakistan, E-mail:

Acknowledgments

The constructive criticism of anonymous reviewers is greatly appreciated.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

1. Greener, Y., Middleman, S. A theory of roll coating of viscous and viscoelastic fluid. Polym. Eng. Sci. 1975, 15, 1–10. https://doi.org/10.1002/pen.760150102.Search in Google Scholar

2. Middleman, S. Fundamentals of Polymer Processing; McGraw-Hill: New York, 1977; pp 202–212.Search in Google Scholar

3. Kistler, S. F., Schweiz, P. M. Liquid Film Coating – Scientific Principles and Their Technological Implications; Springer Science + Business Media, B.V.: Netherlands, 1997.10.1007/978-94-011-5342-3Search in Google Scholar

4. Greener, Y., Middleman, S. Theoretical and experimental studies of the fluid dynamics of a two-roll coater. Ind. Eng. Chem. Fundam. 1979, 18, 35–41. https://doi.org/10.1021/i160069a009.Search in Google Scholar

5. Benkreira, H., Edwards, M. F., Wilkinson, W. L. Roll coating of purely viscous liquids. Chem. Eng. Sci. 1981, 36, 429–434. https://doi.org/10.1016/0009-2509(81)85025-7.Search in Google Scholar

6. Benkreira, H., Edwards, M. F., Wilkinson, W. L. A semi-empirical model of the forward roll coating flow of Newtonian fluids. Chem. Eng. Sci. 1981, 423–427. https://doi.org/10.1016/0009-2509(81)85024-5.Search in Google Scholar

7. Benkreira, H., Edwards, M. F., Wilkinson, W. L. Roll coating operations. J. Non-Newton. Fluid Mech. 1984, 14, 377–389. https://doi.org/10.1016/0377-0257(84)80055-5.Search in Google Scholar

8. Benkreira, H., Patel, R., Edwards, M. F., Wilkinson, W. L. Classification and analysis of coating flows. J. Non-Newton. Fluid Mech. 1994, 54, 437–447. https://doi.org/10.1016/0377-0257(94)80035-9.Search in Google Scholar

9. Coyle, D. E., Macosko, C. W., Scriven, L. E. Film-splitting flows in forward roll coating. J. Fluid Mech. 1986, 171, 183–207. https://doi.org/10.1017/s0022112086001416.Search in Google Scholar

10. Gaskell, P. H., Innes, G. E., Savage, M. D. An experimental investigation of meniscus roll coating. J. Fluid Mech. 1998, 355, 17–44. https://doi.org/10.1017/s0022112097007398.Search in Google Scholar

11. Zevallos, G. A., Carvalho, M. S., Pasquali, M. Forward roll coating flows of viscoelastic liquids. J. Non-Newton. Fluid Mech. 2005, 130, 96–109. https://doi.org/10.1016/j.jnnfm.2005.08.005.Search in Google Scholar

12. Sofou, S., Mitsoulis, E. Roll-over-web coating of pseudoplastic and viscoplastic sheets using the lubrication approximation. J. Plast. Film Sheeting, 2, 307–333.10.1177/8756087905059963Search in Google Scholar

13. Hewson, R. W., Kapur, N. Effects of shear thinning on forward roll coating. Chem. Eng. Res. Design 2013, 91, 2427–2436. https://doi.org/10.1016/j.cherd.2013.04.001.Search in Google Scholar

14. Zahid, M., Haroon, T., Rana, M. A. Roll coating analysis of a third grade fluid. J. Plast. Film Sheeting 2016, 33, 1–20. https://doi.org/10.1177/8756087916628326.Search in Google Scholar

15. Zahid, M., Rana, M. A., Siddiqui, A. M. Roll coating analysis of a second-grade material. J. Plast. Film Sheeting 2018, 34, 232–255. https://doi.org/10.1177/8756087917707558.Search in Google Scholar

16. Ali, N., Atif, H. M., Javed, M. A., Sajid, M. A theoretical analysis of roll-over-web coating of couple stress fluid. J. Plast. Film Sheeting 2017, 34, 43–59. https://doi.org/10.1177/8756087917694934.Search in Google Scholar

17. Atif, H. M., Ali, N., Javed, M. A., Abbas, F. Theoretical analysis of roll-over-web coating of a micropolar fluid under lubrication approximation theory. J. Plast. Film Sheeting 2018, 34, 418–438. https://doi.org/10.1177/8756087918769345.Search in Google Scholar

18. Mughees, M., Sajid, M., Ali, N., Shahzad, H. Nonisothermal analysis of a couple stress fluid in blade coating process. Polym. Eng. Sci. 2020, 60, 1129–1137. https://doi.org/10.1002/pen.25366.Search in Google Scholar

19. Sajid, M., Siddique, H., Ali, N., Javed, M. A. Calendering of non-isothermal Rabinowitsch fluid. J. Polym. Eng. 2018, 38, 83–92. https://doi.org/10.1515/polyeng-2016-0294.Search in Google Scholar

20. Atif, H. M., Ali, N., Javed, M. A., Sajid, M. A numerical analysis of calendering of Oldroyd 4-constant fluid. J. Polym. Eng. 2018, 38, 1007–1016. https://doi.org/10.1515/polyeng-2018-0083.Search in Google Scholar

21. Zahid, M., Zafar, M., Rana, M. A., Lodhi, M. S., Awan, A. S., Ahmad, B. Mathematical analysis of a non-Newtonian polymer in the forward roll coating process. J. Polym. Eng. 2020, 40, 703–712. https://doi.org/10.1515/polyeng-2019-0297.Search in Google Scholar

22. Ali, N., Atif, H. M., Javed, M. A., Sajid, M. A mathematical model of the calendered exiting thickness of micropolar sheet. Polym. Eng. Sci. 2018, 58, 327–334. https://doi.org/10.1002/pen.24578.Search in Google Scholar

23. Shahzad, H., Wang, X., Mughees, M., Sajid, M., Ali, N. A mathematical analysis for the blade coating process of Oldroyd 4-constant fluid. J. Polym. Eng. 2019, 39, 852–860. https://doi.org/10.1515/polyeng-2019-0195.Search in Google Scholar

24. Khaliq, S., Abbas, Z. A theoretical analysis of roll-over-web coating assessment of viscous nanofluid containing Cu-water nanoparticles. J. Plast. Film Sheeting 2020, 36, 55–75. https://doi.org/10.1177/8756087919866485.Search in Google Scholar

25. Abbas, Z., Khaliq, S. Calendering analysis of non-isothermal viscous nanofluid containing Cu-water nanoparticles using two co-rotating rolls. J. Plast. Film Sheeting 2020, published ahead of print; https://doi.org/10.1177/8756087920951614.Search in Google Scholar

26. Khaliq, S., Abbas, Z. Theoretical analysis of blade coating process using Simplified Phan-Thien-Tanner (SPTT) fluid model: an analytical study. Polym. Eng. Sci. 2020, published ahead of print; https://doi.org/10.1002/pen.25576.Search in Google Scholar

27. Eringen, A. C. Theory of micropolar fluid. Indiana Univ. Math. J. 1966, 16, 1. https://doi.org/10.1512/iumj.1967.16.16001.Search in Google Scholar

28. Ariman, T., Turk, M. A., Sylvester, N. D. Applications of microcontinuum fluid mechanics. Int. J. Eng. Sci. 1974, 12, 273–293. https://doi.org/10.1016/0020-7225(74)90059-7.Search in Google Scholar

29. Khonsari, M. M., Brewe, D. E. Effect of viscous dissipation on the lubrication characteristics of micropolar fluids. Acta Mech. 1994, 105, 57–68. https://doi.org/10.1007/bf01183942.Search in Google Scholar

30. Iqbal, Z., Mehmood, R., Azhar, E., Mehmood, Z. Impact of inclined magnetic field on micropolar Casson fluid using Keller box algorithm. Eur. Phys. J. Plus 2017, 132, 175. https://doi.org/10.1140/epjp/i2017-11443-7.Search in Google Scholar

31. Mehmood, Z., Mehmood, R., Iqbal, Z. Numerical investigation of micropolar Casson fluid over a stretching sheet with internal heating. Commun. Theor. Phys. 2017, 67, 443. https://doi.org/10.1088/0253-6102/67/4/443.Search in Google Scholar

32. Alkasasbeh, H. Numerical solution on heat transfer magnetohydrodynamic flow of micropolar Casson fluid over a horizontal circular cylinder with thermal radiation. Front. Heat Mass Transf. (FHMT) 2018, 10, 32. https://doi.org/10.5098/hmt.10.32.Search in Google Scholar

33. Qadan, H., Alkasasbeh, H., Yaseen, N., Sawalmeh, M. Z., ALKhalafat, S. A theoretical study of steady MHD mixed convection heat transfer flow for a horizontal circular cylinder embedded in a micropolar Casson fluid with thermal radiation. J. Comput. Appl. Mech. 2019, 50, 165–173.Search in Google Scholar

34. Amjad, M., Zehra, I., Nadeem, S., Abbas, N. Thermal analysis of Casson micropolar nanofluid flow over a permeable curved stretching surface under the stagnation region. J. Therm. Anal. Calorim. 2020. published ahead of print; https://doi.org/10.1007/s10973-020-10127-w.Search in Google Scholar

35. Abbas, Z., Rafiq, S., Sheikh, M., Aly, S. Oscillatory Darcy flow of non-Newtonian Casson fluid with temperature-dependent viscosity in a porous channel. Arab. J. Sci. Eng. 2020. published ahead of print; https://doi.org/10.1007/s13369-020-04408-7.Search in Google Scholar

36. Abbas, Z., Rafiq, M. Y., Hasnain, J., Javed, T. Peristaltic transport of a Casson fluid in a non-uniform inclined tube with Rosseland approximation and wall properties. Arab. J. Sci. Eng. 2020. published ahead of print; https://doi.org/10.1007/s13369-020-04969-7.Search in Google Scholar

37. Turkyilmazoglu, M. Eyring–Powell fluid flow through a circular pipe and heat transfer: full solutions. Int. J. Numer. Method. Heat Fluid Flow 2020, 30, 4765–4774. https://doi.org/10.1108/hff-11-2019-0801.Search in Google Scholar

38. Azam, M., Mabood, F., Xu, T., Waly, M., Tlili, I. Entropy optimized radiative heat transportation in axisymmetric flow of Williamson nanofluid with activation energy. Res. Phys. 2020, 19, 103576. https://doi.org/10.1016/j.rinp.2020.103576.Search in Google Scholar

39. Turkyilmazoglu, M. Velocity slip and entropy generation phenomena in thermal transport through metallic porous channel. J. Non-Equilib. Thermodyn. 2020, 45, 247–256. https://doi.org/10.1515/jnet-2019-0097.Search in Google Scholar

40. Turkyilmazoglu, M. Nanoliquid film flow due to a moving substrate and heat transfer. Eur. Phys. J. Plus 2020, 135, 781. https://doi.org/10.1140/epjp/s13360-020-00812-y.Search in Google Scholar

41. Azam, M., Xu, T., Khan, M. Numerical simulation for variable thermal properties and heat source/sink in flow of Cross nanofluid over a moving cylinder. Int. Commun. Heat Mass Transf. 2020, 118, 104832. https://doi.org/10.1016/j.icheatmasstransfer.2020.104832.Search in Google Scholar

42. Azam, M., Xu, T., Shakoor, A., Khan, M. Effects of Arrhenius activation energy in development of covalent bonding in axisymmetric flow of radiative-Cross nanofluid. Int. Commun. Heat Mass Transf. 2020, 113, 104547. https://doi.org/10.1016/j.icheatmasstransfer.2020.104547.Search in Google Scholar

Received: 2020-12-19
Accepted: 2021-01-28
Published Online: 2021-02-19
Published in Print: 2021-04-27

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