Numerical Studies of Axial Instability in Contraction Flow

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.