Numerical Studies of Axial Instability in Contraction Flow

Abstract

It is known that the instabilities in axisymmetric contraction flows of polymers start with development of axisymmetric, non‐rotational disturbances. Our studies of this instability are based on the extension of previous approximate theory of steady contraction flow. This theory matches at the die entrance a “jet‐like” viscoelastic flow in reservoir with developing viscoelastic shearing flow in the die. A set of PDE's for mass and momentum conservation, along with a viscoelastic constitutive equation and appropriate initial/boundary conditions was numerically analyzed employing finite difference method. The instability which occurs in the reservoir jet‐like flow, reminds a draw resonance in melt spinning. Then unstable fluctuations formed in the reservoir propagate into capillary with their axial decaying. Linear and non‐linear stability analyses have been performed to describe the fluctuations in the whole region of contraction flow up to the die exit. In this problem, a critical Deborah number established for onset of instability strongly depends on contraction ratio.