Modeling of Polymer Flow Near Solid Walls

Polymers are known to exhibit various flow instabilities during extrusion in which a molten polymer is forced to flow through a narrow die, in order to form a strand or acquire a desired shape of the final product. Recent developments in experimental techniques revealed that some of the instabilities are interfacial in nature, that is originate from the violation of the no-slip boundary condition at the polymer melt/die wall interface. The ability to control the extrusion instabilities thus lays through the understanding of the boundary conditions at the interface between a polymer melt and a solid wall. The subject of the present work is the modeling of a polymer flow near a solid wall. Its ultimate goal is to develop a consistent mathematical formalism which is able to describe correctly the real mechanics of the melt, such as entanglements between different polymers and chain connectivity. The model should provide an adequate mathematical representation of all the major physical processes inherent to polymer chains in the melt, such as convection, retraction, reptation, and constraint release. Finally, it must be able to reproduce quantitatively available experimental data, provided that the necessary molecular parameters and processing conditions are known. A successful model for polymer melt flow will allow us to understand the mechanics of extrusion instabilities, and perhaps suggest a way to eliminate them. To avoid using adjustable parameters, we start with the consideration of the single polymer dynamics in flow. The derived ”microscopic” equations of motion are then used to find the corresponding constitutive equation for an ensemble of polymer chains. We show that the behavior of the ensemble can successfully be described in terms of the so-called bond vector correlator. All macroscopic quantities of practical interest which represent the state of the ensemble, e.g. local stress, can be readily expressed in terms of this correlator. In a die, the polymer melt comes into contact with the die wall. Due to attractive polymer-wall interaction, some of the polymers become attached to the wall. So there are two ”sorts” of molecules in the melt: adsorbed (i.e., attached to the wall) and bulk (i.e., unattached). As a result, two bond vector correlators must be introduced. We show that these correlators satisfy nonlinear integro-partial differential equations which account for all the major processes for polymers in the melt. Due to entanglements between bulk and adsorbed