Plane Poiseuille Flow of Two Compatible Polymers: Influence of the Interphase on the Flow Stability

Abstract

This paper deals with coextrusion flows of two compatible polymers which are known to be generally more stable than the same flows of incompatible systems. We show that the weak response to disturbance of such flows can be predicted by considering an interphase of nonzero thickness (corresponding to an interdiffusion zone) instead of a purely geometrical interface between the two layers. As a first step we try to explain the weak sensibility to disturbance of compatible systems by the sole presence of this intermediate layer. For that purpose we study the linear stability response to very long waves of a three-layer phase Poiseuille flow with an inner thin layer which represents the interphase. Although this fact is an approximation, it nevertheless takes into account the diffusion phenomena which are generated in the interphase. This first approach (corresponding to a reduction in the effective viscosity ratio) is shown to explain the diminished growth rates but not the reduction in the size of the unstable region. As a second step, we formulate an energetic approach of the problem. We evaluate the energy dissipated during the interdiffusion process and the variation of kinetic energy of the global system. A modified growth rate is then determined by taking into account the energy dissipated by the interdiffusion process. This lower growth rate enables us to explain the increase of the stable domain in the case of compatible polymeric systems.