Calendering of Pseudoplastic and Viscoplastic Fluids Using the Lubrication Approximation

Abstract

The Lubrication Approximation Theory (LAT) is used to provide numerical results for calendering a sheet from an infinite reservoir. The Herschel-Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, power-law and Newtonian models. The results give the final sheet thickness as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). Integrated quantities of engineering interest are also calculated. These include the maximum pressure, the roll-separating force, and the power input to the rolls. Decreasing the power-law index n or increasing the Bingham number Bn lead to excess sheet thickness over the thickness at the nip. All engineering quantities calculated in dimensionless form increase substantially with the departure from the Newtonian values.