Stability of plane poiseuille flow of a highly elastic liquid

Abstract

The stability of fully developed pressure driven plane laminar flow of a Maxwell fluid has been studied using linear hydrodynamic stability theory. Elasticity is destabilizing in the inertial regime, but the flow is found to be stable to infinitesimal disturbances at low Reynolds numbers. This result contradicts previous calculations, which predicted a low Reynolds number flow instability at a critical recoverable shear of order unity. The previous calculations were carried out using less accurate numerical methods; the eigenvalue problem which must be solved is a delicate one, requiring sophisticated umerical techniques in order to avoid the calculation of spurious unstable modes. This work has direct bearing on the question of the mechanism of a low Reynolds number extrusion instability known as “melt fracture”. It is observed that the intensity of melt fracture increases with increasing die length for high density polyethylene, and it is therfore believed by some experimentalists that fully-developed die flow is unstable for this polymer above a critical recoverable shear. The analysis appears to be at variance with this interpretation of the experimental results.