Investigation of Stationary Solutions of Viscoelastic Melt Spinning Equations and Stability with Respect to Increasing Viscoelasticity

The one-dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take-up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non-stationary equations the effect of viscoelasticity on the stability of the spinning process was studied.