Co-extrusion instabilities modeled with a single fluid

Industrial processes involving co-extrusion of multiple fluids to produce multi-layered products are rife with instabilities. We consider a simple indicative instance of co-extrusion, in which there is only a single fluid involved in the flow, but two different channel branches impose differing flow histories on it. The channels merge and, ideally, a smooth film is extruded with two layers having different stress histories. In experimental studies a wavelike instability is observed with a well defined wavelength in the flow direction and a 'zig-zag' like structure, indicating that the extra flow caused by the instability is three-dimensional. Suggested mechanisms for instabilities in co-extrusion include a jump in viscosity and/or first normal stress difference across a flat interface, and a coupling of normal stresses with streamline curvature in the region where the two streams merge. Using a numerical linear stability tool we investigate this instability (using a single mode fluid model throughout) and explore which of the known mechanisms is the most likely culprit here.