https://doi.org/10.1140/epjp/s13360-022-02657-z
Regular Article
Mathematical analysis of two-layer calendering of isothermal Newtonian fluids with different viscosities
1
Department of Mathematics, COMSATS University Islamabad, 45550, Islamabad, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, 22060, Abbottabad, Pakistan
Received:
5
January
2022
Accepted:
24
March
2022
Published online:
9
April
2022
Co-extruded multi-layer plastic sheets and polymer structures formed by calendering process or by cold rolling are widely used in the packaging industry and thin-film transistor manufacturing. The different materials are extruded from separate extruders into single sheet die which is capable of delivering a multi-layer sheet with uniform thickness of each layer at die exit. This multi-layer sheet is then stretched between co-rotating rolls to obtain final multi-layer sheet of uniform thickness. In this article, the calendering of single-layered Newtonian or Non-Newtonian material has been extended to analyze a two-layer calendering process for an incompressible Newtonian fluids as upper and lower layer with different viscosity ratios. To simplify the equations of motion, the lubrication approximation theory (LAT) is used. The expressions of non-dimensional pressure gradient, pressure and velocity distribution of both layers are obtained analytically by using proper no slip boundary conditions and dimensionless variables. The dimensionless detachment point is approximated by Regula-Falsi method. The important engineering factors including detachment point, calendered sheet thickness, roll separation force, power input by rolls, torque on each roll, and adiabatic temperature are all computed. In addition, the effect of viscosity ratios on all of these parameters has been investigated and all established results in literature of single layer calendering process of Newtonian fluid have been validated by taking viscosity ratio equal to one.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
