Longwave stability of three-layer plane Poiseuille flow with an inner thin layer. Application to the coextrusion of polymers

Abstract

This paper deals with the longwave stability of three-layer plane Poiseuille flow of Oldroyd-B fluids. The thickness of the inner layer is assumed to be very thin with respect to the outer layers. The stability is given by two eigenvalues: one corresponds to that obtained for the two-layer flow composed by the two outer layers, whereas the other one expresses the effect of the thin layer. In this way, simple conditions on the rheological properties of the inner layer are given so that the stability is given only by the eigenvalue associated to the two large layers.