THE INSTABILITY MECHANISM FOR 2 ELASTIC LIQUIDS BEING COEXTRUDED

Chen has recently shown (J. Non-Newtonian Fluid Mech., 40 (1991) 155-175) that a jump in the first normal stress difference between two elastic fluids in core-annular flow leads to a longwave varicose instability when the core is more elastic and occupies less than 32% of the cross-section, or when the annulus is more elastic and occupies less than 68% of the cross-section. The purpose of this note is to present a simplified calculation which reveals the physical mechanism, to incorporate the effect of a jump in the second normal stress difference, and to demonstrate the existence of a non-axisymmetric sinuous longwave instability that grows more rapidly than the varicose mode when the annulus is more elastic than the core.