Stability analysis of non-isothermal fibre spinning of polymeric solutions

2018 ◽  
Vol 851 ◽  
pp. 573-605 ◽  
Author(s):  
Karan Gupta ◽  
Paresh Chokshi
Keyword(s):  
Stability Analysis ◽  
Polymer Solution ◽  
Nonlinear Stability ◽  
Draw Ratio ◽  
Extensional Flow ◽  
Finite Amplitude ◽  
Subcritical State ◽  
Draw Resonance ◽  
Fibre Spinning

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

2015 ◽  
Vol 776 ◽  
pp. 268-289 ◽  
Author(s):  
Karan Gupta ◽  
Paresh Chokshi
Keyword(s):  
Stability Analysis ◽  
Draw Ratio ◽  
Transition Point ◽  
Finite Amplitude ◽  
Deborah Number ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
Fluid Elasticity ◽  
Draw Resonance ◽  
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.

The role of the matrix-filler affinity on morphology and properties of polyethylene/clay and polyethylene/ compatibilizer/clay nanocomposites drawn fibers

e-Polymers ◽  
2009 ◽  
Vol 9 (1) ◽  
Author(s):  
Nadka Tzankova Dintcheva ◽  
Rosamaria Marino ◽  
Francesco Paolo La Mantia
Keyword(s):  
Draw Ratio ◽  
Mechanical Performance ◽  
Extensional Flow ◽  
Cold Drawing ◽  
Clay Nanocomposites ◽  
Structural Variations ◽  
Calorimetric Analysis ◽  
Elongation At Break ◽  
The Matrix

AbstractIn this work the structural variations and mechanical performance of polyethylene/clay nanocomposite drawn fibres, also in the presence of compatibilizer, such as a commercial maleic anhydride grafted polyethylene, PEgMA, was studied. In the isotropic state both systems show intercalated morphology.After spinning and cold drawing, by adding the nanoparticles, the tensile strength as a function of the draw ratio increases and this rise is more pronounced for the filled compatibilized system. The reduction of the elongation at break, on the contrary, is about the same for all the examined samples. The orientation of the macromolecules, evaluated by measurements of the birefringence and calorimetric analysis, is similar for all the samples, but the filled, drawn fibres show a higher level of intercalation and, in particular, some exfoliation, more and more pronounced with the draw ratio and in presence of compatibilizer, as a consequence of the application of the extensional (at low and high temperature) flow. For the three components system with greater affinity between the polymer matrix and clay, the extensional flow is more efficient. The initial intercalated morphology changes to some more intercalation and finally, at the highest anisotropic condition in the presence of the PEgMA, evolves to delaminated clay structure.

scholarly journals Nonlinear stability analysis of rotor-bearing systems

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 279-280 ◽  
Author(s):  
Aydin Boyaci ◽  
Wolfgang Seemann ◽  
Carsten Proppe
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Rotor Bearing
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