Die-swell effect in draw resonance of polymeric spin-line

Abstract The role of die-swell in the stability of fiber spinning flow of entangled polymer melts is analyzed using the linear as well as finite amplitude stability analyses. The nonlinear extensional rheology of polymer is described by using the eXtended Pom–Pom (XPP) model which captures the strain hardening effect present in the realistic flows. The stability of the slender body fiber profile to axisymmetric disturbances is studied under the isothermal conditions. At the top end of the spinning flow near die-exit, the swelling in fiber cross-section area is introduced whose magnitude is governed both by the flow within the die and the outside spinning force. Introducing die-swell in the analysis significantly influences the stability of the spinning flow. The flexibility in the fiber profile at the upstream end of the flow, a feature absent in the previous analyses ignoring die-swell, plays a stabilizing role. However, for a given flow, die-swell implies stronger effective extension than indicated by the apparent draw ratio, defined based on capillary area. This higher effective extension tends to decrease the critical draw ratio for the onset of draw resonance, suggesting destabilizing role of die-swell. The destabilizing role is found to dominate in the overall stability behavior. The stability diagram is constructed by plotting the critical draw ratio for the onset of draw resonance against the flow Deborah number. The sensitivity of the stability behavior on the rheology parameters and the die-geometry has been studied. The finite amplitude disturbances are also considered using the weakly nonlinear stability analysis in order to understand the nature of flow in the proximity of the transition point. The flow exhibits supercritical Hopf bifurcation for low to moderate Deborah numbers, indicating the presence of an oscillatory steady state in the unstable regime. The amplitude of the oscillations in the fiber cross-section area is estimated. The finite amplitude bifurcation crosses over to the subcritical manifold as Deborah number is increased beyond a certain crossover value. The subcritical state for fast flows manifests in the form of unbounded growth of transient disturbances of amplitude greater than a certain threshold value. The die-swell effect tends to lower the Deborah number for the crossover to the subcritically unstable state.