Effect of Material Parameter of Viscoelastic Giesekus Fluids on Extensional Properties in Spinline and Draw Resonance Instability in Isothermal Melt Spinning Process

The draw resonance instability of viscoelastic Giesekus fluids was studied by correlating the spinline extensional features and transit times of several kinematic waves in an isothermal melt spinning process. The critical drawdown ratios were critically dependent on the Deborah number (De, the ratio of material relaxation time to process time) and a single material parameter (αG) of the Giesekus fluid. In the intermediate range of αG, the stability status changed distinctively with increasing De, i.e., the spinning system was initially stabilized and subsequently destabilized, as De increases. In this αG regime, the level of velocity and extensional-thickening rheological property in the spinline became gradually enhanced at low De and weakened at high De. The draw resonance onsets for different values of αG were determined precisely using a simple indicator composed of several kinematic waves traveling the entire spinline and period of oscillation. The change in transit times of kinematic waves for varying De adequately reflected the effect of αG on the change in stability.

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

Commercially important extrusion film casting (EFC) processes for manufacturing plastic films or sheets are hampered by several instabilities that severely limits their productivity. In this research we focussed on one important instability: the draw resonance that occurs during the EFC process mainly under extensional flow conditions. Draw resonance is the sustained periodic oscillations in the film dimensions, notably film width and thickness, when the process operates beyond a critical draw ratio (CDR). In this research our goal was to reduce this draw resonance instability by incorporating well dispersed nanoclay fillers in a base polymeric resin (such as a linear low density polyethylene – LLDPE) to determine how these nanocomposite (NC) formulations can prevent or reduce the draw resonance defect. EFC experiments were conducted on the base resin and on the NC formulations under non-isothermal conditions to determine the onset of the draw resonance experimentally. Conventional linear stability analysis was performed to determine the onset of the draw resonance defect numerically. Numerical predictions for the onset of draw resonance were in qualitative agreement with our experimental data. Our results showed that incorporating appropriate nanoclay concentrations in a base polymeric resin indeed enhanced the EFC process stability for those polymer formulations and thus can have important economic implications for processors.

Stability analysis of non-isothermal fibre spinning of polymeric solutions

The stability of fibre spinning flow of a polymeric fluid is analysed in the presence of thermal effects. The spinline is modelled as a one-dimensional slender-body filament of the entangled polymer solution. The previous study (Gupta & Chokshi,J. Fluid Mech., vol. 776, 2015, pp. 268–289) analysed linear and nonlinear stability behaviour of an isothermal extensional flow in the air gap during the fibre spinning process. The present study extends the analysis to take in to account the non-isothermal spinning flow in which the spinline loses heat by convection to the surrounding air as well as by solvent evaporation. The nonlinear rheology of the polymer solution is described using the eXtended Pom-Pom (XPP) model. The non-isothermal effects influence the rheology of the fluid through viscosity, which is taken to be temperature and concentration dependent. The linear stability analysis is carried out to obtain the draw ratio for the onset of instability, known as the draw resonance, and a stability diagram is constructed in the$DR_{c}{-}De$plane.$DR_{c}$is the critical draw ratio, and$De$is the flow Deborah number. The enhancement in viscosity driven by spinline cooling leads to postponement in the onset of draw resonance, indicating the stabilising role of non-isothermal effects. Weakly nonlinear stability analysis is also performed to reveal the role of nonlinearities in the finite amplitude manifold in the vicinity of the flow transition point. For low to moderate Deborah numbers, the bifurcation is supercritical, and the flow attains an oscillatory state with an equilibrium amplitude post-transition when$DR>DR_{c}$. The equilibrium amplitude of the resonating state is found to be smaller when non-isothermal effects are incorporated in comparison to the isothermal spinning flow. For very fast flows in the regime of high Deborah numbers, the finite amplitude manifold crosses over to a subcritical state. In this limit, the nonlinearities render the flow unstable even in the linearly stable regime of$DR<DR_{c}$.

Weakly nonlinear stability analysis of polymer fibre spinning

The extensional flow of a polymeric fluid during the fibre spinning process is studied for finite-amplitude stability behaviour. The spinning flow is assumed to be inertialess and isothermal. The nonlinear extensional rheology of the polymer is described with the help of the eXtended Pom-Pom (XXP) model, which is known to exhibit a significant strain hardening effect necessary for fibre spinning applications. The linear stability analysis predicts an instability known as draw resonance when the draw ratio, $\mathit{DR}$, defined as the ratio of the velocities at the two ends of the fibre in the air gap, exceeds a certain critical value, $\mathit{DR}_{c}$. The critical draw ratio $\mathit{DR}_{c}$ depends on the fluid elasticity represented by the Deborah number, $\mathit{De}={\it\lambda}v_{0}/L$, the ratio of the polymer relaxation time to the flow time scale, thus constructing a stability diagram in the $\mathit{DR}_{c}$–$\mathit{De}$ plane. Here, ${\it\lambda}$ is the characteristic relaxation time of the polymer, $v_{0}$ is the extrudate velocity through the die exit and $L$ is the length of the air gap for the spinning flow. In the present study, we carry out a weakly nonlinear stability analysis to examine the dynamics of the disturbance amplitude in the vicinity of the transition point. The analysis reveals the nature of the bifurcation at the transition point and constructs a finite-amplitude manifold providing insight into the draw resonance phenomena. The effect of the fluid elasticity on the nature of the bifurcation and the finite-amplitude branch is examined, and the findings are correlated to the extensional rheological behaviour of the polymer fluid. For flows at small Deborah number, the Landau constant, which captures the role of nonlinearities, is found to be negative, indicating supercritical Hopf bifurcation at the transition point. In the linearly unstable region, the equilibrium amplitude of the disturbance is estimated and shows a limit cycle behaviour. As the fluid elasticity is increased, initially the equilibrium amplitude is found to decrease below its Newtonian value, reaching the lowest value for $\mathit{De}$ when the strain hardening effect is maximum. With further increase in elasticity, the material undergoes strain softening behaviour which leads to an increase in the equilibrium amplitude of the oscillations in the fibre cross-section area, indicating a destabilizing effect of elasticity in this regime. Interestingly, at a certain high Deborah number, the bifurcation crosses over from supercritical to subcritical nature. In the subcritical regime, a threshold amplitude branch is constructed from the amplitude equation.

Three Dimensional Film Stability and Draw Resonance

In order to understand the effects of inertia and gravity on draw resonance and on the physical mechanism of draw resonance in three-dimensional Newtonian film casting, a linear stability analysis has been conducted. An eigenvalue problem resulting from the linear stability analysis is formulated and solved as a nonlinear two-point boundary value problem to determine the critical draw ratios. Neutral stability curves are plotted to separate the stable/unstable domain in different appropriate parameter spaces. Both inertia and gravity stabilize the process and the process is more unstable to two- than to three-dimensional disturbances. The effects of inertia and gravity on the physical mechanism of draw resonance have been investigated using the eigenfunctions from the eigenvalue problem. A new approach is introduced in order to evaluate the traveling times of kinematic waves from the perturbed thickness at the take-up, which satisfies the same stability criterion illustrating the general stability of the system.