Analogy between the modelling of pullout in solution spinning and the prediction of the vortex size in contraction flows

Solutions of high molecular weight polymers in suitable solvents show a pronounced shear thinning behaviour combined with strong elastic effects and wall slippage. During spinning, these solutions are pulled out of the spinneret at a certain draw ratio. This process is studied. After surveying the equations governing the spinning process, attention is focused on the position of the detachment point and its dependence on the solution properties and the processing conditions. A simple force balance at this point equilibrates the spinning tension (dominated by the elongational viscosity, the draw ratio and the strain rate) and the first normal stress difference (which depends on shear rate and die geometry). This analysis yields the upstream position of the detachment point. Intriguingly, the same analysis applies to the almost classical rheological problem of the entrance flow in a contraction. Following the same procedure, the size of the vortices can be predicted and their dependence on the Deborah number, provided that both the transient elongational viscosity and the first normal stress difference of the solution are known. In fact, the latter problem might be less complicated because the flow occurs under isothermal conditions. However, one has to neglect the two-dimensional character of the flow in order to reach analytical results.