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

A theoretical model was developed to describe the calendering process in Newtonian sheets of finite initial thickness taking into account that the viscosity of the fluid is a well-defined function of the pressure. We predict the influence of the pressure effects on the leave-off distance that is related to the exiting sheet thickness in the calendering process. The mass and momentum balance equations, which are based on lubrication theory, were nondimensionalized and solved for the velocity and pressure fields by using perturbation techniques, where the leaveoff distance represents an eigenvalue of the mathematical problem. When the above variables were obtained, the dimensionless leave-off distance in the calendering process was determined. Moreover, quantities of engineering interest were calculated, including the maximum pressure, the roll-separating force and the power transmitted to the fluid by the rolls. The analytical results show that the inclusion of pressure-dependent viscosity effect increases about 3.37 percent the dimensionless exiting sheet thick- ness or 9.4 percent the leave-off distance in comparison with the case of pressure-independent viscosity.