On the origin of extrusion instabilities: Linear stability analysis of the viscoelastic die swell

It is well-known that, increasing the flow rate in polymer extrusion, the flow becomes unstable and the smooth extrudate surface becomes wavy and disordered to an increasing degree. In order to investigate the mechanisms responsible for these instabilities we perform a linear stability analysis of the steady extrusion of a viscoelastic fluid flowing through a planar die under creeping flow conditions. We consider the Phan-Thien-Tanner (PTT) model to account for the viscoelasticity of the material. We employ the mixed finite element method combined with an elliptic grid generator to account for the deformable shape of the interface. The generalized eigenvalue problem is solved using Arnoldi’s algorithm. We perform a thorough parametric study in order to determine the effects of all material properties and rheological parameters. We investigate in detail the effect of the interfacial tension and the presence of a deformable interface. It is found that the presence of a finite surface tension destabilizes the flow as compared to the case of the stick-slip flow. We recognize two modes, which become unstable beyond a critical value of the Weissenberg number and perform an energy analysis to examine the mechanisms responsible for the destabilization of the flow and compare against the mechanisms that have been suggested in the literature

Structure-property relationship of a soft colloidal glass in simple and mixed flows

HypothesisUnder specific conditions, rod-like cellulose nanocrystals (CNC) can assemble into structurally ordered soft glasses (SGs) with anisotropy that can be controlled by applying shear. However, to achieve full structural control of SGs in real industrial processes, their response to mixed shear and extensional kinematics needs to be determined. We hypothesise that by knowing the shear rheology of the CNC-based soft glass and adopting a suitable constitutive model, it is possible to predict the structure-property relationship of the SG under mixed flows.ExperimentsWe use an aqueous suspension with 2 wt% CNC at 25 mM NaCl to form a structurally ordered SG composed of a CNC network containing nematic domains. We combine rheometry and microfluidic experiments with numerical simulations to study the flow properties of the SG in shear, extension, and mixed flow conditions. Extensional flow is investigated in the Optimised Shape Cross-slot Extensional Rheometer (OSCER), where the SG is exposed to shear-free planar elongation. Mixed flow kinematics are investigated in a benchmark microfluidic cylinder device (MCD) where the SG flows past a confined cylinder in a microchannel.FindingsThe SG in the MCD displays a velocity overshoot (negative wake) and a pronounced CNC alignment downstream of the cylinder. Simulations using the thixotropic elasto-visco-plastic (TEVP) model yield near quantitative agreement of the velocity profiles in simple and mixed flows and capture the structural fingerprint of the material. Our results provide a comprehensive link between the structural behaviour of a CNC-based SG and its mechanistic properties, laying foundations for the development of functional, built-to-order soft materials

Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation

Three non-Newtonian constitutive models are employed to investigate how fluid rheological properties influence the development of laterally asymmetric flows past confined cylinders. First, simulations with the shear-thinning but inelastic Carreau-Yasuda model are compared against complementary flow velocimetry experiments on a semidilute xanthan gum solution, showing that shear-thinning alone is insufficient to cause flow asymmetry. Next, simulations with an elastic but non-shear-thinning finitely extensible non-linear elastic dumbbell model are compared with experiments on a constant viscosity solution of poly(ethylene oxide) (PEO) in an aqueous glycerol mixture. The simulations and the experiments reveal the development of an extended downstream wake due to elastic stresses generated at the stagnation point but show no significant lateral asymmetries of the flow around the sides of the cylinder. Finally, the elastic and shear-thinning linear Phan-Thien-Tanner (l-PTT) model is compared with experimental velocimetry on a rheologically similar solution of PEO in water. Here, at low flow rates, lateral symmetry is retained, while the growth of a downstream elastic wake is observed, in qualitative similarity to the non-shear-thinning elastic fluids. However, above a critical flow rate, the flow bifurcates to one of the two stable and steady laterally asymmetric states. Further parameter studies with the l-PTT model are performed by varying the degrees of shear-thinning and elasticity and also modifying the confinement of the cylinder. These tests confirm the importance of the coupling between shear-thinning and elasticity for the onset of asymmetric flows and also establish stability and bifurcation diagrams delineating the stable and unstable flow states

Evaluation of constitutive models for shear-banding wormlike micellar solutions in simple and complex flows

Wormlike micellar solutions possess complex rheology: when exposed to a flow field, the wormlike micelles may orientate, stretch, and break into smaller micelles. Entangled wormlike micellar solutions exhibit shear banding characteristics: macroscopic bands with different local viscosities are organized and stacked along the velocity gradient direction, leading to a non-monotonic flow curve in simple shear. We present a systematic analysis of four commonly used constitutive models that can predict a non-monotonic flow curve and potentially describe the rheology of entangled wormlike micellar solutions with shear-banding characteristics: the Johnson–Segalman, the Giesekus, the thixotropic viscoelastic, and the Vasquez–Cook–McKinley (VCM) models. All four constitutive models contain a stress diffusion term, to account for a smooth transition between the shear bands and ensure a uniqueness of the numerical solution. Initially, the models are fitted to shear and extensional experimental data of a shear-banding wormlike micellar solution. Subsequently, they are employed to solve three non-homogeneous flows: the Poiseuille flow in a planar channel, the flow in a cross-slot geometry, and the flow past a cylinder in a straight channel. Each of these flows exposes the wormlike micellar solution to different flow kinematics (shear, extensional, and mixed), revealing different aspects of its rheological response. The predictive capability of each model is evaluated by directly comparing the numerical results to previously published experimental data obtained from microfluidic devices with corresponding flow configurations. While all the models can describe qualitatively the characteristic features observed experimentally in the benchmark flows, such as plug-like velocity profiles and elastic instabilities, none of them yields a quantitative agreement. Based on the overall performance of the models and also accounting for their differing numerical complexity, we conclude that the Giesekus model is at present the most suitable constitutive equation for simulating shear banding wormlike micellar solutions in flows that exhibit both shear and extensional deformations. However, the quantitative mismatch between model predictions and experiments with wormlike micellar solutions demand that improved constitutive models be developed in future works

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields