Variable viscosity characteristics of two-layered isothermal calendering phenomena with non-Newtonian fluids

Two-layer calendering using non-Newtonian fluids is used frequently in different industries to improve the working and the quality of the products. In this article, two-layer calendering of incompressible non-Newtonian fluids, that is, couple stress fluid and viscoplastic fluid in the upper and lower layer respectively is investigated. For the simplified governing equations, Lubrication approximation theory is applied. By the use of no-slip condition and non-dimensional variables, the exact solution for pressure gradient, pressure, and velocity profiles for both layers of fluid is calculated. The parameters are important from an engineering point of view like roll separating force, power delivered by rollers, torque acting by each roller, and adiabatic temperature are also calculated analytically. Additionally, the results of a couple stress parameter, viscoplastic Casson parameter, and viscosity ratios on all the parameters are also discussed and investigated in detail. Moreover, all the effects investigated are also verified with the literature results of single-layer calendering of non-Newtonian fluids by using large numeric values for the couple stress parameter and viscoplastic Casson parameter.