Non-Newtonian effects on draw resonance in film casting

Abstract

In this paper, the influence of non-Newtonian material properties on the draw resonance instability in film casting is investigated. Viscoelastic models of infinite width film casting are derived systematically following an asymptotic expansion and using two well-known constitutive equations: the Giesekus model and the simplified Phan-Thien/Tanner (PTT) model. Based on a steady state analysis, a numerical boundary condition for the inlet stresses is formulated, which suppresses the unknown deformation history of the die flow. The critical draw ratio in dependence of both the Deborah number and the nonlinear parameters is calculated by means of linear stability analysis. For both models, the most unstable instability mode may switch under variation of the control parameters, leading to a non-continuous change in the oscillation frequency at criticality. The effective elongational viscosity, which depends exclusively on the local Weissenberg number, is analyzed and identified as crucial quantity as long as the Deborah number is not too high. This is demonstrated by using a generalized Newtonian fluid model to approximate the PTT model. Based on such a generalized Newtonian fluid model, the effects of strain hardening and strain thinning are finally explored, revealing two opposing mechanisms underlying the non-Newtonian stability behavior.

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

“…Individual research groups focused on experimental works 30,48,52,55,[65][66][67][68][69][70][71][72][73][74] dealing with flow visualization, effects of temperature, crystallization, molecular weight distribution, or long chain branching on kinetics of the film casting process (see Table I). Theoretical research has not disappeared, and attention has been drawn to the development and use of numerical models (primarily considering steady-state conditions) of different dimensionalities such as 1D, 22,25,26,45,[75][76][77][78][79][80][81][82][83][84][85] 1.5D, 18,27,29,35,37,38,[41][42][43][44]47,53,[86][87][88][89][90]…”

“…The model was used in the following studies: 1D (1 work), 79 1.5D (0), 2D (1 work), 40 and 3D (0). The above viscosity models use the following parameters: η 0 (zero-shear-rate viscosity), η∞ (infinite-shear-rate viscosity), λ (relaxation time), a (characterizes the sharpness of the transition from the Newtonian to non-Newtonian flow regime), and n (characterizes the slope between the viscosity and deformation rates in a log-log scale) are model parameters.…”

“…The model has been found to provide reasonable predictions for the film neck-in, the centerline velocity profile and the temperature drop in the air-gap, and it also predicts an increase in film neck-in and the temperature drop in the air-gap as the air-gap length is increased. 107 This constitutive equation has been used in the following studies: 1D (1 work), 79 1.5D (0), 2D (3 works), 107,111,113 and 3D (0).…”

“…The discrete relaxation spectrum was determined from frequency-dependent loss and storage moduli, while ξp and εp parameters were identified from steady-state shear viscosity vs shear rate and steady uniaxial extensional viscosity vs extensional strain rate. This constitutive equation was utilized in the following studies within this review: 1.D (1 work), 79 1.5D (2 works), 44,47 2D (7 works), 36,40,46,105,108,109 and 3D (1 work). 116 The linear variant of the PTT model was used only in the following studies: 2D (1 work).…”

Controlling draw resonance during extrusion film casting of nanoclay filled linear low-density polyethylene: An experimental study and numerical linear stability analysis

“…Draw resonance was first reported by Christensen 1 and Miller 2 and further studied both experimentally and numerically by other researchers including Bergonzoni and DiCresce, 3,4 Fisher and Denn; 5 Ishihara and Kase, 6 Roberts et al, 7 Anturkar and Co, 8 Hyun, 9 Burghelea et al 10 and, very recently, by Bechert. 11 One also cannot forget the stalwart work done by the research group of Prof. Agassant [12][13][14][15][16][17][18][19][20][21][22][23] in this area as well. Other researchers, like Sollogoub et al, 14,21 Zheng et al, 24 Zavinska et al 25 and Shiromoto et al, 26 have modelled the EFC process by accounting for the nonisothermal conditions.…”