The lubrication approximation theory (LAT) is used to provide numerical results for calendering sheets with a desired final thickness. The Herschel-Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, the power-law and the Newtonian models. For a desired final sheet thickness, the results give the required thickness of the entering sheet as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The corresponding pressure-gradient and pressure distributions are also given. The integrated quantities of engineering interest are calculated. These include the maximum pressure, the roll-separating force, and the power input to the rolls. Both pseudoplasticity and viscoplasticity lead to thicker sheets than the Newtonian model for large entry thickness ratios, while they lead to thinner sheets for small entry thickness ratios. In the case of viscoplastic sheets, the interesting yielded/unyielded regions appear as a function of the dimensionless yield stress. All engineering quantities, given in a dimensionless form, increase substantially with the departure from the Newtonian values. A test case for calendering a plastic sheet with a yield stress is given as an example of implementing the present results.
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.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.