Fig 2 - available from: Rheologica Acta
This content is subject to copyright. Terms and conditions apply.
Shear and extensional viscosity as a function of the shear and extension rate given by the XPP model. Three different materials are used: the iPP 1 of Roozemond et al. (2015), the iPP 2 of Grosso et al. (2019) and the LLDPE of van Drongelen et al. (2015) (T = 160 °C). The linear viscoelastic prediction (LVE) for each material is also provided
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
Context 1
... of T = 160 °C LLDPE Van Drongelen et al. Arbitrary non-linear material because of the shear thinning behaviour, the non-linear extensional behaviour, the difference in viscosities between iPP and LLDPE (but similar shear viscosity of the iPPs) and the qualitative difference of the viscosity as a function of extension and shear rate. From Fig. 2 it can be concluded that the non-linear behavior is completely different within this set of materials. The uniaxial extensional viscosity can be compared with the linear viscoelastic envelope (LVE). For the linear viscoelastic envelope, the extensional viscosity is found as ...
Context 2
... rheological data at selected temperature can be superposed into a master curve at an arbitrary reference temperature by employing a temperature-dependent factor. For the rheological data given in Fig. 2, an Arrhenius-type relation is used (Morrison ...
Context 3
... for all types of fluids ( Spiegelberg et al. 1996). However, in case of non-linear viscoelastic materials, this is not necessarily true, because initial flow conditions affect chain conformation at all later times ( Spiegelberg et al. 1996). Therefore, the shear correction factors of the iPP 1 of Roozemond et al. (2015) and the LLDPE are shown in Fig. 12. From this figure, it follows that these materials have approximately the same shear correction factor as the iPP 2 of Grosso et al. (2019). This means that although the materials exhibit completely different nonlinear rheological behaviour, the shear correction factors match. This supports the proposed shear correction factor, Eq. 41, ...
Context 4
... geometries of the iPP and the LLDPE is almost the same. Correspondingly, the effective strain rate distributions over the mid-radius are similar for the three polymer melts, as shown in Fig. 13. The distributions are plotted at Hencky strains of ε = 0.5, ε = 1, ε = 2 and ε = 3, where the shear contributions decrease for increasing strains (see Fig. 12). So, although the polymer melts do not follow the LVE at relatively Fig. 13 Effective strain rate distributions for the iPPs, LLDPE and the arbitrary non-linear material at strains of ε = 0.5, ε = 1, ε = 2 and ε = 3. The filaments have a compressed aspect ratio of Λ c = 0.5 and are extended with a strain rate of ˙ ε = 10 s −1 at T = ...
Context 5
... material is introduced. The relaxation spectrum and non-linear parameters are given in Table 3. In Fig. 8d, it can be seen that a clear strain hardening at small strains is present for this artificial non-linear material. A simulation with this non-linear material at a strain rate of ˙ ε = 10 s −1 results in a shear correction factor as shown in Fig. 12. Herein, the simulated shear correction factor does not match our proposed shear correction factor. Hence, the pronounced strain hardening at small strains affects the geometry and the strain rate and stress distributions over the mid-radius. In other words, the non-linear material's plate velocity needs to be higher to follow the ...
Context 6
... strains larger than 1.5, it can be seen in Fig. 12 that the shear correction factor is slightly larger than one. The reason for this is the conformation history which has not equilibrised yet. The history effects for the used strain rate of 10 s −1 will equilibrise at strains larger than 3. In Fig. 15, it can be seen that for a strain rate of ˙ ε = 1.71 s −1 this equilibration takes ...
Context 7
... will be flattened and converge to the applied strain rate at smaller strains. This implies that a near locally homogeneous flow can be achieved before the start of the strain hardening of the non-linear material. As a result, the simulated shear correction factor converges towards the proposed universal shear correction factor, as shown in Fig. ...
Similar publications
A new slit‐radial die capable of simultaneously obtaining steady state shear viscosity ηγ̇ and the average first normal stress difference coefficient Ψ1γ̇ via capillary rheometry has been developed. The steady state shear viscosity ηγ̇ and average first normal stress difference coefficient Ψ1γ̇ are calculated in the slit part and radial part of the...
![Physical characteristics of MWCNT suspensions [2]](publication/369153399/figure/tbl1/AS:11431281126092647@1678540248161/Physical-characteristics-of-MWCNT-suspensions-2_Q320.jpg)
This study evaluates the effects of three carbon nanotubes with different geometric characteristics on the rheological behaviour and mechanical performance, as well as on the microstructure of mortars and cement pastes. For nanotube content ranging from 0.025 to 0.2 wt%, the yield stress and viscosity were determined by rotational rheometry, and me...
Volcanic activity is characteristic of seismic zones. Consequently, volcanic material form part of the landscape in places where earthquakes are common natural phenomena. As volcanic wastes (VW) show pozzolanic activity, the substitution of manufactured Portland cement (PC) with VW is clearly a desirable option not only from an economical point of...
![a−e Corrected steady shear ηSγ˙\documentclass[12pt]{minimal}...](publication/368388544/figure/fig3/AS:11431281130038873@1679712792942/a-e-Corrected-steady-shear-eSgdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
Extensional rheology of a variety of linear and branched polymer melts is investigated using entry flow measurements and 15:1 axisymmetric contraction flow simulations. Using a Cogswell model analysis, we show that log−log plots of entrance pressure drop versus wall shear stress display three distinct power-law regimes, the intermediate one of whic...
The rheological properties of entangled polymers loaded with very small, strongly attractive polyhedral oligomeric silsesquioxane (POSS) fillers differ from that of nanocomposites with larger fillers by (1) the shorter breadth of the entanglement plateau and (2) the relatively unchanged terminal viscosity with increasing POSS loading. Although such...
Citations
... Normally, the mechanical properties largely reflect its resistance to external stress, such as compressive stress under impacting conditions and tensile stress under stretching conditions. Numerous researchers have studied the mechanical characteristics of STFs at various impact rates in detail, including low-speed impact, high-speed impact by split-Hopkinson pressure bar (SHPB), and ballistic impact with increased strain rate [17][18][19][20]. For instance, Cheng et al. [21] studied the impact of impactor shapes on the mechanical characteristics of STF under low-speed impact. ...
... This comparative analysis has practical implications for tailoring STFs to specific engineering applications, such as protective equipment or energy dissipation systems. Related studies mainly focused on rheological properties and ignored the dynamic responses which are very important for engineering applications [17,19,20,22]. Research related to engineering applications concentrated on the preparation of composite materials [23][24][25]. ...
Shear thickening fluids (STFs) are a type of non-Newtonian fluid that disperses particles at the micrometer or nanometer scale into a liquid medium, forming a particle suspension. The viscosity of STF increases with increasing shear rate when the shear rate is above a critical value. During external load impact, STF can absorb substantial impact energy, effectively mitigating shocks and vibrations. This paper focuses on the dynamic characteristics of STFs with different dispersion systems, including cornstarch-water STFs and silica-polyethylene glycol (SiO2-PEG) STFs under low-speed impact. First, from an energy perspective, this paper established a theoretical model to study the impact properties of STFs considering the viscosity characteristic of STFs. Further, the model is numerically solved using the Runge–Kutta method, and variation of impact displacement, velocity, acceleration, and impact force with time during the impact process can be obtained. Then, the rheological properties of STFs were studied, and viscosity models of different STFs were fitted through experimental results. Finally, impact experiments were carried out with a falling hammer onto STFs to validate the established theoretical model. A good consistency between theoretical model and experiments was achieved. Results in this paper show different impact response mechanisms between cornstarch-water STF and silica-polyethylene glycol STF. The former experiences thickening at the moment of impact, resulting in a quasi-solid state phenomenon that generates a significant reverse impact force to slow down the falling hammer. In the latter, the thickening effect creates viscous resistance on the falling hammer, and a smaller impact force is produced.
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.
