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![Force as a function of the Hencky strain of a sample extended with a strain rate of ˙ ε = 2.0 s −1 using a four mode Oldroyd-B model. The solvent viscosity, polymer viscosities and relaxation times of the PIB used are η s = 12.4 Pa s, η = [1.69 2.56 2.53 1.85] Pa s and λ = [4.20 1.12 0.167 0.0149] s. The surface tension is neglected and the sample dimensions are L c = L 0 = 1.5 mm and R c = R 0 = 1.5 mm](publication/354553163/figure/fig2/AS:1067652638334976@1631559633591/Force-as-a-function-of-the-Hencky-strain-of-a-sample-extended-with-a-strain-rate-of-e.png)
Force as a function of the Hencky strain of a sample extended with a strain rate of ˙ ε = 2.0 s −1 using a four mode Oldroyd-B model. The solvent viscosity, polymer viscosities and relaxation times of the PIB used are η s = 12.4 Pa s, η = [1.69 2.56 2.53 1.85] Pa s and λ = [4.20 1.12 0.167 0.0149] s. The surface tension is neglected and the sample dimensions are L c = L 0 = 1.5 mm and R c = R 0 = 1.5 mm
Source publication
Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in t...
Contexts in source publication
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... the flow of polyisobutylene (PIB) in a FiSER is simulated using a multi-mode viscoelastic Oldroyd-B constitutive equation. Tirtaatmadja and Sridhar (1993) performed FiSER measurements with an exponential decreasing mid-radius and measured the force at the plate. A comparison of all simulated and experimentally determined forces is given in Fig. 4. For the setup used by Tirtaatmadja and Sridhar (1993) the early response of the fluids is not only masked by the shear correction factors but also by the dynamics of the drive train. The drive has to accelerate from zero velocity to a large velocity instantaneously (L 0 ˙ ε), which takes approximately 0.1 seconds in this experiment. ...
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... the effects of acceleration are not studied in this paper. In Fig. 4, it can also be seen that our simulated force matches the simulated force of Kolte et al. (1997). For the used Oldroyd-B model an analytical solution for the purely uniaxial extensional viscosity can be found as ( Kolte et al. 1997): with De i = ˙ ελ i the Deborah number for the i'th mode and N the number of modes. ...
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... extensional viscosity can be found as ( Kolte et al. 1997): with De i = ˙ ελ i the Deborah number for the i'th mode and N the number of modes. With this extensional viscosity, the analytical (pure uniaxial) force is found by using Eq. 28, whereby that gravity and surface tension are not contributing. This pure uniaxial solution is also shown in Fig. 4. By comparing the simulations and the pure uniaxial solution, it can be concluded that at the start of the simulations, the flow is not purely uniaxial, since the force overshoot is larger in the simulation of an actual filament stretching experiment. This difference between the pure uniaxial force and the experimental force is a ...
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... the rheological behaviour of these materials is different, the similar effective strain rate distributions still result in different stress distributions, as shown in Fig. 14. Herein, the trace of the average conformation tensor is used as an indicator for stress. This stress value is normalized by dividing it by its mean value to compare the shape of the stress distributions. For increasing strain, the stress difference between the middle of the sample and the free surface increases. This is due to the ...
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... different stress distributions over the midfilament radius for the various materials, Fig. 13 shows that the actual strain rate corresponds to the applied strain rate at a radial position r/R around 0.72. Similarly, at this location, the stress corresponds to the average stress of the relevant profile. Therefore, using the extensional viscosity Fig. 14 Stress distributions for the iPPs, LLDPE and the arbitrary nonlinear material at strains of ε = 0.5, ε = 1, ε = 2 and ε = 3. Here, the normalized trace of the average conformation tensor is given, which gives an indication of the relative stress distributions. The compressed aspect ratio is Λ c = 0.5 and the extension is performed at a ...
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Citations
... 14 Pendant drop filament dynamic and droplet pinch-off are intensively studied due to their meaningful information regarding the fluid material properties. Theoretical viewpoints are still under researchers' attention, focusing on transitions through various regimes, [15][16][17] even for more simple systems such as Newtonian fluids. ...
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Graphical Abstract
... where η is the shear viscosity and D is the deformation-rate tensor. The material, rheological and experimental parameters used for the simulation are given in Table 2. Here, the viscosity is obtained by taking the shear viscosity at an effective shear rate of √ 3ε for the iPP 1 13 material used in the work of Roozemond et al., at a temperature of 160 • C. 51 The obtained value is then shifted to a temperature of 133 • C using the Arrhenius equation. 52 Van Berlo et al. 50,51 is followed for applying the mesh movement and remeshing and projection procedure in the numerical simulation. ...
... The material, rheological and experimental parameters used for the simulation are given in Table 2. Here, the viscosity is obtained by taking the shear viscosity at an effective shear rate of √ 3ε for the iPP 1 13 material used in the work of Roozemond et al., at a temperature of 160 • C. 51 The obtained value is then shifted to a temperature of 133 • C using the Arrhenius equation. 52 Van Berlo et al. 50,51 is followed for applying the mesh movement and remeshing and projection procedure in the numerical simulation. [53][54][55] Here, a detailed explanation of the finite element model can be found. ...
... (27)). The thinning of the filament is driven by the competition between capillarity and elasticity (Erik Miller et al. 2009;Anna and McKinley 2001;van Berlo et al. 2021). ...
Interfacial rheology has become a powerful tool to study the viscoelastic properties of interfaces in several multiphase polymer-based systems such as multilayer liquids containing surfactants, proteins or solid particles, and also in polymer blends, 3D printed multimaterials and coextruded multilayer films. During all these manufacturing processes, the elongational flow at interface is predominant. Nevertheless, direct interfacial rheological measurements in extension devoted to such polymer systems are not plentiful and are often based on indirect modelling methods. In the present work, interfacial dilational rheology testing based on the rising oscillating drop method was used to probe surface (and interfacial) properties of model Newtonian polymer melts: polydimethylsiloxane (PDMS)/polyisobutylene (PIB) systems. The interfacial properties in both oscillatory and static drop experiments were carefully corrected, considering the inertia and the contribution of the coexisting phase viscosities during the processing of the numerical data. The influence of molecular weight and temperature on the interfacial rheological responses was particularly examined. A new approach was developed to determine the dilational relaxation times (τ) of the studied polymer systems using a square pulse relaxation test. It was found that the evolution of τ with the temperature followed an Arrhenius behaviour. A comparison with capillary breakup extensional rheometry revealed similar overall values to those obtained with the pulse method. Finally, using interfacial shear rheology, we focused on the Trouton correlation between shear and dilational surface rheology, and a direct link between shear surface viscosities and elongational relaxation times was evidenced for the first time and over the entire viscosity range studied.
Graphical abstract
... A combination of a feedback/feedforward control scheme is used in [16] to maintain a constant strain rate of the midfilament diameter in a filament stretching rheometer for polymer melts. This method was incorporated in a finite element method by van Berlo et al. [17]. If the control parameters were chosen properly, it was found that this is an effective approach to maintain the desired strain rate by controlling the radius of the filament. ...
In this paper we propose a novel approach to solve the inverse problem of three-dimensional die design for extrudate swell, using a real-time active control scheme. To this end, we envisioned a feedback connection between the corner-line finite element method, used to predict the positions of the free surfaces of the extrudate, and the controller. The corner-line method allows for local mesh refinement and transient flow to be taken into account (Spanjaards et al., 2019). We show the validity of this method by showing optimization results for 2D axisymmetric extrusion flows of a viscoelastic fluid for different Weissenberg numbers. In 3D we first give a proof of concept by showing the results of a Newtonian fluid exiting dies with increasing complexity in shape. Finally, we show that this method is able to obtain the desired extrudate shape of extrudates of a viscoelastic fluid for different Weissenberg numbers and different amounts of shear-thinning.
