Roll-over-web Coating of Pseudoplastic and Viscoplastic Sheets Using the Lubrication Approximation

Abstract

The Lubrication Approximation Theory (LAT) is used to provide numerical results in roll coating over a moving flat web. The Herschel–Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, power-law, and Newtonian models. Results are obtained for such quantities as coating thickness, separation point, and the volumetric flow rate required for various values of the power-law index (in the case of pseudoplasticity) and of the Bingham number (in the case of viscoplasticity). All these values increase substantially with the increasing non-Newtonian character of the fluid. Yielded and unyielded areas are quantitatively shown for several cases of viscoplasticity. Pressure gradient and pressure distributions are given for all cases. Integrated quantities of engineering interest are also calculated. These include the maximum pressure, the roll/sheet separating force, and the power input to the roll. These quantities increase substantially and monotonically in a dimensionless form, as the power-law index decreases or the Bingham number increases.