Elastic short wave instability in extrusion flows of viscoelastic liquids

An analysis of the stability to short waves of the flow of concentric coextruded polymeric liquids modeled by upper convected Maxwell models is presented. The flow can be unstable to short waves under various conditions on the elastic parameter. The growth rates for the short wave instability in the elastic case are finite at leading order. The same short wave instability is known to be two orders of magnitude smaller in the purely viscous case with growth rates proportional to α^-2 for large wavenumber α. It is argued that this instability could appear in systems with low surface tension, as in polymer-depleted solutions at the walls of a pipe. Some speculative scenarios concerning the appearance of sharkskin after the loss of adhesion, leading to wet slip, are advanced.