ELASTIC INSTABILITY AND CURVED STREAMLINES

Hydrodynamic instabilities occur in the motion of non-Newtonian polyme ric-liquids at low flow rates that are entirely absent in the correspo nding motions of Newtonian fluids. We develop a dimensionless criterio n that characterizes the critical conditions for onset of elastic inst abilities in two-dimensional, single-phase isothermal viscoelastic flo ws. The new dimensionless group is analogous to classical Taylor and G ortler numbers characterizing inertial instabilities of Newtonian flui ds and quantifies both the curvature of the streamlines and the dynami cs of the non-Newtonian fluid motion.