Effect of pressure-dependent viscosity on the exiting sheet thickness in the calendering of Newtonian fluids

An analysis of calendering for an incompressible Newtonian fluid flow, with pressure-dependent viscosity is studied theoretically under assumptions of isothermal conditions. We predict the influence of pressure-dependent viscosity on the exiting sheet thickness of the sheet of fluid from the gap. The dimensionless mass and momentum balance equations, which are based on lubrication theory, were solved for the velocity and pressure fields by using perturbation techniques, where the exiting sheet thickness represents an eigenvalue of the mathematical problem. When the above variables were obtained, the dimensionless exiting sheet thickness was determined by considering the influence of the pressure variations in the calendering process. Moreover, quantities of engineering interest are also calculated, which include the cylinder-separating force and power required to drive both cylinders in terms of the geometrical and kinematical parameters of the system. The results show that the inclusion of pressure-dependent viscosity effect increases the leave-off distance and consequently the dimensionless exiting sheet thickness in comparison with the case of pressure-independent viscosity.