Slip Heating in Polymer Processing

Abstract

When one body slips on another, heat is generated at the slipping interface. We call this phenomenon slip heating and apply slip heating theory to cohesive and adhesive slip in extrusion dies. Adhesive slip, which is linked to melt fracture, is a breakdown of the no slip boundary condition at the die wall, where the fluid moves with respect to the wall. Die drool, the accumulation of plastic on the open die face, has been attributed to cohesive melt failure, which results in the formation of a bulk layer that slips on a drool layer. The corresponding isothermal analysis of cohesive slip led to an analytical solution for the drool rate [Schmalzer and Giacomin, J. Pol. Eng., 33, 1 (2013)]. We account for slip heating during adhesive and cohesive slip and develop analytical solutions for temperature rise with and without viscous dissipation. We focus on slit flow, used in film casting, sheet extrusion and curtain coating, and when curvature can be neglected, slit flow is easily extended to pipe extrusion and film blowing. In slit flow, the heat flux from the slipping interface is the product of the shear stress and the slip speed. We present the solutions for the temperature rise in pressure-driven and simple shearing flows, each subject to constant heat generation at the slipping interface. We find expressions for drool rate by modeling viscosity as an Arrhenius function of temperature, and we show how to correct wall slip data for the slip heating temperature rise. We conclude with worked examples showing the importance of slip heating in die drool and wall slip, and we find that slip heating suppresses drool. We also arrive at a necessary dimensionless condition for the accurate use of our results: Pé<<1.