On the role of extensional rheology and Deborah number on the neck-in phenomenon during flat film casting

Effect of die exit stress state, Deborah number, uniaxial and planar extensional rheology on the neck-in phenomenon in polymeric flat film production

“…9, 10, 12, 13, 14 and 17 represent the final set of equations for isothermal viscoelastic 1D membrane model utilized in this work. More detailed derivation of the model is provided in our previous work [55]. Note that due to a geometrical symmetry of the film, only 1/4 th of the film cross-section can be used in the calculation as showed in [68].…”

“…If the level of planar pre-stretching decreases, its effect on the maximum attainable neck-in starts to occur at lower Deborah numbers. [55], it has been found that numerical solution for NI * can be approximated by Eq. 30, if the role of −N2/N1 on the neck-in phenomenon is neglected.…”

“…Third, two extra stress components are adjusted manually without more reasoning [37,38,40]. Fourth, the die exit stress state is given by axial upstream extra stress component [8], thickness to axial extra stress component ratio for upstream/downstream side [9,54] or by second to first normal stress difference ratio, −N2/N1, calculated from upstream side [55] by using viscoelastic constitutive equation. It has been found that if Deborah number is low (0.00161 [49]; 0.07 [20,21]; 0.1 [9,56]), the choice of the initial stress conditions at the die have only a little influence on the steady-state calculations.…”

Non-Newtonian effects on draw resonance in film casting

“…In particular, it is identical to the free boundary condition presented by Papanastasiou et al [24]. Another possibility would be to follow Barborik et al [26], who used the fully developed flow profile in a rectangular channel to obtain the initial stress condition. This approach, however, increases the computational complexity significantly and introduces additional parameters for the channel.…”

Steady-state modeling of extrusion cast film process, neck-in phenomenon, and related experimental research: A review

“…It is important to mention that a different definition of relaxation time can be found in the reviewed literature. In the studies based on single-mode constitutive equations, the utilized Maxwell relaxation time 27 and the shortest 35 or characteristic relaxation time (determined by the reciprocal frequency at the intersection of the storage modulus G ′ and the loss modulus G ′′ curves 36 or by fitting the strain rate dependent steady uniaxial extensional viscosity data 37,38 ) are typically used to calculate De. In the case of multi-mode constitutive equations, the relaxation time for each mode [39][40][41][42][43][44] or an average relaxation time, λ, is calculated to determine De by using the following expression: [45][46][47]…”