Calendering Pseudoplastic and Viscoplastic Fluids With Slip at the Roll Surface

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 employed, which reduces with appropriate modifications to the Bingham, power-law, and Newtonian models. A dimensionless slip coefficient is introduced to account for the case of slip at the roll surfaces. The results give the final sheet thickness as a function of the dimensionless power-law index (in the case of pseudoplasticity), the Bingham number or the dimensionless yield stress calculated at the nip (in the case of viscoplasticity), and the dimensionless slip coefficient in both cases. 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 or increasing the dimensionless yield stress 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. The presence of slip decreases pressure and the engineering quantities and increases the domain in all cases.