Non-Isothermal Rheological Response During Elongational Flow

A pseudo-time integral scheme based on a finite streamline element method is developed to combine variable temperature with viscoelasticity. A specific KBKZ integral model for isothermal flow is transformed to its non-isothermal version by introducing a pseudo-time and applying the Morland-Lee hypothesis. The coupling between momentum and energy equations is through the time-temperature shifting factor by which the pseudo-time is defined. The observer time and the pseudo-time are simultaneously calculated when tracing the strain history for the stress calculation in a non-homogeneous temperature field. Using this scheme, a full non-isothermal numerical simulation of some IUPAC extrusion experiments is carried out. Results show that while the temperature distribution near the die exit plane is an important factor controlling extrudate swell, either self-heating inside the die tube or external cooling on the free surface dominantly determines the temperature distribution near the die exit when the wall temperature is kept constant, depending on whether the Ptclet number is large or small. The hot layer effect predicted by the inelastic swell mechanism is confirmed and well illustrated by the computation. Calculations with reasonable thermal boundary conditions further convince us that the isothermal assumption in our earlier numerical simulation is a good approximation in this particular case.

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“…As a final remark, we need to be cautious over the too-enthusiastic use of the timetemperature shifting idea [1,[14][15][16].…”

Section: Discussionmentioning

confidence: 99%

A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation

Luo

Tanner

1987

Rheol Acta

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“…For other materials, e.g. polypropylene at 200 °C [33], polystyrene at 160°C [34] and polyisobutylene at 22°C [33], polystyrene at 160 °C [34] and polyisobutylene at 22 °C [35] are reported in [2]. The effects of r on the response of these materials are generally the same.…”

Section: I0 2 T [Sec]mentioning

confidence: 91%

“…Since the previous section has shown the importance of the effective relaxation time, 2ei, nondimensionalized quantities are introduced as, similar to those in eqs. (34),…”

Section: Transient and Steady-state Simple Shear Flow Of Finite Amplimentioning

confidence: 97%

“…The following dimensionless quantities are next introduced to rewrite the evolution equations (7) and (8): (34) where the effective relaxation time )~ei is chosen as reference time since the results of previous sections have indicated that 2e~ is an important time scale in the regime of small deformation. From now on, the subscript i (representing i-th mode) will be dropped for convenience, so for each mode the same equations hold.…”

Section: G71mentioning

confidence: 99%

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A unified constitutive theory for polymeric liquids II. Applications to basic problems

Kwon

Shen

1985

Rheol Acta

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A unified constitutive theory for polymeric liquids has been recently proposed. Its derivation is based on a combination of continuum mechanical approach, transient-network concept and thermodynamics of irreversible processes. In the resulting model, many modes may be present for each of which there are two time scales, associated with the loss rate and the nonaffine motion of transient network junctions, respectively. A single effective relaxation time, constructed from the two time scales, governs the behavior in the linear regime of deformation. Two new parameters for each mode, in comparison with other models, are introduced: (i) the ratio "r" of the two time scales, and (ii) the index "a" distinguishing the rates of loss and creation of junctions. Both are important only for the nonlinear regime of deformation. In this paper, the theory is applied to predict the following cases: (i) stress growth at constant shear strain rate, (ii) steady shear-rate-dependent viscosity and first normal-stress difference and (iii) transient elongational viscosity at constant elongational strain rate. Determination of the model parameters based on usual characterization experiments is described. Comparison of calculated and observed behavior of low-density polyethylene at 150 °C available in the literature are presented. In general, the agreement of the predictions with experiment appear gratifying even with the simplest version of the new model.

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“…McGuirt and Lianis [43], Matsui and Bogue [44] and Matsumoto and Bogue [45] considered non-isothermal large strain flow of polymer melts. Matsumoto and Bogue concluded that during rapid temperature changes the above extended Morland and Lee hypothesis fails.…”

Section: Introductionmentioning

confidence: 98%

Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

Marín¹,

Rasmussen²

2009

Journal of Non-Newtonian Fluid Mechanics

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Non-Isothermal Rheological Response During Elongational Flow

Cited by 26 publications

References 4 publications

A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation

A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation

A unified constitutive theory for polymeric liquids II. Applications to basic problems

Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

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