Calendering Pseudoplastic and Viscoplastic Fluids With Slip at the Roll Surface

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 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.

Numerical simulation of calendering viscoplastic fluids

“…Near the nip there are also small unyielded regions around the centreline that remain small and limited as Bn increases. The present results are in contrast with previous ones obtained with LAT [3,[21][22][23][24], which provides erroneous and much bigger yielded/unyielded regions.…”

“…According to LAT, this is resolved by the Swift condition, which requires that P = dP/dx = 0 at . This additional assumption has to be used for the evaluation of (see, e.g., [1] and [22][23][24]). As noted in [13], the Swift condition does not apply to a two-dimensional analysis.…”

“…Chung [21] gave some numerical examples of the analysis and verified Gaskell's presumed unyielded zones. Recently, Sofou and Mitsoulis [22][23][24] undertook an analysis of calendering based on LAT for both pseudoplastic and viscoplastic materials for finite sheets (including the case of an infinite reservoir) and provided results from full parametric studies of the power-law index n and the dimensionless yield stress, * y . They showed the development of the yielded/unyielded zones in the value range for * y from 0 (purely viscous fluid) to 1 (rigid plastic).…”

“…The Bingham number ranges from 0 (purely viscous fluid) to ∞ (unyielded solid). Another definition of a dimensionless yield stress, * y , involves the pressure gradient at the nip and ranges, respectively, from 0 to 1 [21][22][23][24].…”

Calendering and Rolling of Viscoplastic Materials: Theory and Experiments

“…It considers locally a fully developed pressuredriven flow with boundary conditions the roll speeds of each roll. Full parametric results for pseudoplastic and viscoplastic fluids have been recently published for the case of a feed from an infinite reservoir [6], or with a finite sheet [7], while slip effects at the roll surfaces have been also considered [8]. Full parametric results for pseudoplastic and viscoplastic fluids have been recently published for the case of a feed from an infinite reservoir [6], or with a finite sheet [7], while slip effects at the roll surfaces have been also considered [8].…”