Stability of fiber spinning under filament pull-out conditions

Flow instabilities of wet-spun fibers in the form of draw resonance can result in radius fluctuations which impose limitations on either fiber quality or production rate. Also, at high winding velocities, if the fluid strength is sufficiently high, a filament can be pulled out of the die. The force balance between the integrated normal stress that occurs during flow in the upstream region and the spinning force determines the position of the detachment point when the filament detaches from the spinneret wall. Filament pull-out complicates the stability analysis in the sense that the upstream boundary conditions now depend on the position in the spinneret. In addition, the filament length varies in time. In this work we extend the stability analysis on fiber spinning of a single isothermal filament by including the upstream pull-out condition in a one-dimensional fiber spin model using the eXtended Pom-Pom (XPP) constitutive model. Using a spectral method, our analysis incorporates the detachment point which position is allowed to vary according to the prescribed slope of the upstream integrated normal stress. Changing the slope S for a certain DR (draw ratio) and De (Deborah) number, the growth rate for each S value can be determined. We compare the stability regions of our fiber spin model with pull-out, using different S values, to fiber spinning without pull-out. For low De values a finite value of S is destabilizing the flow whereas for higher De values there is a range of S values that stabilizes the flow. For S = 0 we obtain fiber spinning with a constant force at pull-out, but the critical DR is greatly reduced. This is in contrast to fixed length fiber spinning of a Newtonian fluid at a constant force which is known to be stable for any DR