Linear stability analysis has been applied to a coextrusion fiber spinning flow that consists of a Newtonian fluid as a core layer and a Phan‐Thien/Tanner (PTT) fluid as a skin layer. These two chosen fluids show entirely different rheological behaviors. The stability of this coextrusion system was affected by the choice of three characteristic parameters: the skin layer fraction (f), the extensional parameter (ϵ), and the shear thinning parameter (ξ) in the Phan‐Thien/Tanner model. The linear stability results indicate that the viscoelastic skin layer (PTT fluid) has a stabilizing effect that delays the onset of draw resonance. Under fixed compositions (f is fixed), the stability envelopes changed from upturned curves to flattened ones as extensional force dominated the system. The neutral stable curves closed to the horizontal line at a critical draw ratio of around 20, showing similar behavior to a Newtonian fluid where the system has a very high Deborah number or it is dominated by shear thinning effects.

The steady flow of isothermal bicomponent coextrusion fiber spinning has been investigated. A model has been chosen in which a Newtonian fluid and a Phan‐Thien/Tanner (PTT) fluid were considered to be the core and the skin layer, respectively. This model was adopted to study the effect on spinline velocity of an interaction between two fluids with quite different extensional rheology. The effects of the hoop stress, gravity, inertia, and surface and interfacial tensions were disregarded. Only viscous and viscoelastic forces were considered. A uniaxial extension was also assumed as the radius variation in the axial direction is small. The Newtonian fluid has been considered prone to fluctuate during melt processing while the viscoelastic skin layer has a stabilizing effect. The velocity profile was affected by the choice of two characteristic parameters: extensional and shear‐thinning parameters, as well as the viscoelastic skin flow rate ratio. Both shear‐thinning and extensional parameters play important roles in melt flow. The results show that as the draw ratio increases, the system is dominated by the extensional parameters, whereas slow drawing is dominated by shearing, in spite of the thin viscoelastic skin.