On the channel flow of yield stress fluids with an internal microstructure

Abstract

Thin films consisting of polymer solutions are typically produced through a combination of extrusion and shearing processes, where the anisotropic, non-Newtonian solution is deformed and subjected to thermal treatment. This paper investigates the shearing of polymeric thin films by studying the channel flow rheology of polymer solutions that experience yield stress. The material rheology is described by the transversely isotropic fluid (TIF) model, which contains a yield behavior term related to microstructure distortion. Our results show that this distortional stress is able to resist the pressure gradient, and non-trivial stress distributions can exist in the absence of a flow. This represents a significant improvement over existing viscosity-based yield stress models (e.g., the Heschel–Bulkley model). The unyielded state is achieved as the end result of a transient process, where a pressure gradient produces a short-lived flow that ceases when opposing stresses from microstructure distortion are produced. Predictions of the TIF model are compared with the phenomenological Saramito model. Both models are found to predict yielding when a threshold stress is exceeded. In both cases, the velocity profile is Newtonian near the wall, while plug flows are encountered close to the centerline.