Non-isothermal blade coating analysis of viscous fluid with temperature-dependent viscosity using lubrication approximation theory

Sabeeh Khaliq; Zaheer Abbas

doi:10.1515/polyeng-2021-0087

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Non-isothermal blade coating analysis of viscous fluid with temperature-dependent viscosity using lubrication approximation theory

Sabeeh Khaliq und Zaheer Abbas

Veröffentlicht/Copyright: 14. Juni 2021

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Aus der Zeitschrift Journal of Polymer Engineering Band 41 Heft 8

Abstract

Blade coating process is studied in a nonisothermal analysis of viscous fluid with temperature-dependent viscosity by employing both plane and exponential coaters. The governing expressions are nondimensionalized and simplified under the assumption of lubrication approximation theory. Then, perturbative technique is used to find the solution for velocity, pressure, temperature distribution, and coating thickness. The influence of dimensionless parameter ε, Graetz number Gz, and normalized coating thickness γ on the velocity, maximum pressure, temperature distribution, and pressure gradient is portrayed through graphs, whereas load and coating thickness variations reported in a tabular manner. It is found that maximum pressure, coating thickness, and blade load decreases for temperature variations in viscosity, which leads to improved efficiency of blade coating process and life of the moving substrate.

Keywords: blade coating process; coating thickness; lubrication theory; perturbation technique; temperature-dependent viscosity

Corresponding author: Zaheer Abbas, Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan, E-mail: za_qau@yahoo.com

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

A 1 = ( − 73 − 152 Y − 108 Y 2 − 18 Y 3 + 36 Y 4 ) ,

A 2 = ( − 159 − 31 Y + 411 Y 2 + 351 Y 3 − 2775 Y 4 + 3945 Y 5 − 2475 Y 6 + 630 Y 7 ) ,

A 3 = ( 337 − 3634 Y + 34822 Y 2 − 177984 Y 3 − 529800 Y 4 − 993876 Y 5 + 1225968 Y 6 − 1004304 Y 7 + 531846 Y 8 − 166698 Y 9 + 23814 Y 10 ) ,

A 4 = ( 238 − 2567 Y + 27738 Y 2 − 161242 Y 3 − 559940 Y 4 − 1263420 Y 5 + 1931200 Y 6 − 2009000 Y 7 + 1374920 Y 8 − 564480 Y 9 + 105840 Y 10 ) ,

A 5 = ( 3 − 30 Y + 322 Y 2 − 1856 Y 3 − 6460 Y 4 − 14792 Y 5 + 23224 Y 6 − 25088 Y 7 + 18032 Y 8 − 7840 Y 9 + 1568 Y 10 ) ,

A 6 = ( − 17 + 13 Y + 3 Y 2 + 128 Y 3 − 580 Y 4 − 960 Y 5 − 800 Y 6 + 280 Y 7 )

A 7 = ( 4603 − 50947 Y + 550313 Y 2 − 3190292 Y 3 − 10948756 Y 4 − 24159240 Y 5 + 35738400 Y 6 − 35644560 Y 7 + 23214240 Y 8 − 8996400 Y 9 + 1587600 Y 10 ) ,

A 8 = ( − 127 + 88 Y + 168 Y 2 − 778 Y 3 − 4142 Y 4 + 6750 Y 5 − 5250 Y 6 + 1680 Y 7 ) ,

A 9 = ( 6329 − 70396 Y + 752624 Y 2 − 4304296 Y 3 + 14463068 Y 4 − 30974170 Y 5 + 44089610 Y 6 − 42005740 Y 7 + 25983720 Y 8 − 9525600 Y 9 + 1587600 Y 10 ) ,

A 10 = ( 1 − 254 Y + 1311 Y 2 − 3129 Y 3 − 3990 Y 4 − 2730 Y 5 + 810 Y 6 ) ,

A 11 = ( − 16 + 39 Y − 31 Y 2 − 6 Y 3 + 12 Y 4 ) ,

A 12 = ( − 397 + 153 Y + 973 Y 2 + 1293 Y 3 − 9111 Y 4 + 13695 Y 5 − 9225 Y 6 + 2520 Y 7 ) ,

A 13 = ( 2087 − 22993 Y + 232207 Y 2 − 1248283 Y 3 + 2906405 Y 4 − 7709045 Y 5 + 10011735 Y 6 − 8637720 Y 7 + 4814720 Y 8 − 1587600 Y 9 + 238140 Y 10 ) ,

A 14 = ( − 2 + 13 Y − 27 Y 2 + 18 Y 3 ) ,

A 15 = ( 1 − 56 Y + 258 Y 2 − 543 Y 3 + 591 Y 4 − 333 Y 5 + 81 Y 6 ) ,

A 16 = ( − 11 + 29 Y − 26 Y 2 − 6 Y 3 + 12 Y 4 ) ,

A 17 = ( − 133 + 72 Y + 272 Y 2 + 607 Y 3 − 3748 Y 4 + 5905 Y 5 − 4275 Y 6 + 1260 Y 7 ) ,

A 18 = ( 6869 − 76181 Y + 797109 Y 2 − 4447031 Y 3 + 14491273 Y 4 − 29896455 Y 5 + 40737405 Y 6 − 36970500 Y 7 + 21710430 Y 8 − 7541100 Y 9 + 1190700 Y 10 ) ,

A 19 = ( − 2 + 13 Y − 27 Y 2 + 18 Y 3 ) ,

A 20 = ( 1 − 179 Y + 901 Y 2 − 2054 Y 3 + 2440 Y 4 − 1515 Y 5 + 405 Y 6 ) .

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Received: 2021-03-17

Accepted: 2021-05-15

Published Online: 2021-06-14

Published in Print: 2021-09-27

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Artikel in diesem Heft

https://doi.org/10.1515/polyeng-2021-0087

Schlagwörter für diesen Artikel

blade coating process; coating thickness; lubrication theory; perturbation technique; temperature-dependent viscosity