Viscoelastic Instability Research Articles

Extensional rheology of elastoviscous aqueous PEO/PEG or DMS Boger fluids and weakly elastic alternatives for investigating viscoelastic flows and instabilities

Boger fluids that exhibit a rate-independent shear viscosity (typically ∼ 1 Pa∙s = 1000x water viscosity) and elasticity measurable using torsional rheometers (modulus, relaxation time, or first normal stress difference) are considered as the realization of viscoelastic fluids described by the Oldroyd-B model. However, Boger fluids, conventionally formulated as dilute solutions of high molecular weight (Mw) polymers in relatively high viscosity solvents (or solutions of oligomers or lower Mw polymer), are unsuitable for emulating polymeric fluids used in coating formulations that are lower in viscosity, appear inelastic in torsional shear rheometry, and yet appear prone to viscoelastic instabilities. Therefore, Dontula, Macosko, and Scriven (DMS) (AIChE J, 1998) chose to create an alternative model of elastic fluids by dissolving ultrahigh molecular weight (UHMw) poly(ethylene oxide) (PEO) in an aqueous solution of its lower Mw analog, often referred to as poly(ethylene glycol) or PEG. Even though numerous studies of printing and coating flow instabilities use this aqueous PEO/PEG or DMS Boger fluids as model viscoelastic fluids, only a few explicitly measured elastic properties, especially using relaxation time, and hardly any characterized extensional rheology. In this contribution, we recreate the DMS Boger fluids to examine their elasticity and extensional rheology response using dripping-onto-substrate (DoS) rheometry that relies on an analysis of capillarity-driven pinching dynamics. Though the aqueous PEG solution is often treated as a viscous and Newtonian solvent, we discover that in DoS rheometry, both the PEG solution and the DMS Boger fluid display power law response followed by elastocapillary, in contradiction with the assumptions and the response expected of the Oldroyd-B model. Furthermore, the solution of entangled PEG chains influences specific viscosity, pinching dynamics, and measured extensional rheology response in striking contrast with Newtonian solvents of the same viscosity. Lastly, we describe the possibility of using dilute, aqueous solutions of UHMw PEO as model viscoelastic fluids for coating flows, for both elasticity and extensional viscosity can be determined using DoS rheometry. Due to their water-like viscosity, the aqueous PEO solutions appeal as model fluids that have elasticity, emulate Newtonian fluids in the early stages of pinching, and have a relaxation time tunable by changing polymer Mw or concentration.

Viscoelastic flow instabilities for enhanced heat transfer in battery pack cooling

Effective thermal management plays a critical role in ensuring peak performance for heavy-duty electric vehicle battery packs and high-performance electronics. To address the need for effective heat dissipation, liquid coolants are employed, which exhibit higher heat transfer performance compared to traditional air-cooled systems. However, the associated increased viscosity of such liquid coolants and constricted flow path lead to reduced mixing, thereby deteriorating the thermal performance of the system. Here, we explore the potential of utilizing viscoelastic liquid coolants for enhancing heat transfer from the heated walls of a constricted flow path with obstacles, modeling features of battery coolant channels. At low-Reynolds number regime, viscoelastic fluids exhibit instabilities which can disrupt the thermal boundary layer and enhance fluid mixing in the domain, thereby facilitating wall heat transfer. We employed computational fluid dynamics simulations, validated with experimental observations, to explore the effect of the flow geometry, Weissenberg number, solvent viscosity ratio, polymer extensibility, and Reynolds number on thermal performance. Our study indicates that the heat transfer is enhanced with flow instabilities in viscoelastic fluids, which can be generated exclusively in the flow channel with obstacles by increasing the Weissenberg number, reducing the solvent viscosity ratio, increasing the polymer extensibility, and increasing the Reynolds number. The enhancement in the heat transfer can exclusively be attributed to the elastic properties of the fluid in contrast to the inelastic shear-thinning fluids exhibiting no instability. The insights from the study can play an important role in the development of advanced, high-efficiency battery cooling systems, combining surface engineering and synthesis of optimized heat transfer liquids.

Influence of plasticity on inertialess viscoelastic instabilities in elongational flow regimes

Influence of plasticity on inertialess viscoelastic instabilities in elongational flow regimes

Proceedings of the 2022 Computational Techniques and Applications Conference

CTAC 2022 Queensland University of Technology, Brisbane, Australia 29 November – 2 December, 2022 The 21st Biennial Computational Techniques and Appli- cations Conference (CTAC-2022) was hosted by the School of Mathematical Sciences and Centre for Data Science at Queensland University of Technology in Brisbane. The ANZIAM Special Interest Group in Computational Mathematics is responsible for this series of conferences, the first of which was held in 1981. The meeting provides an interactive forum for researchers interested in the de- velopment and use of computational methods applied to engineering, scientific and other problems. Participants of the conference are able to submit a short article based on their presentation for publication in this special section of the ANZIAM Journal (Electronic Supplement). The ed- itors, Tim Moroney, Qianqian Yang, Vivien Challis and Elliot Carr, thank the referees whose efforts have helped improve the quality of these conference proceedings. This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed conference papers. The eight keynote presentations were as follows. Chris Drovandi, Queensland University of TechnologyLikelihood-Free Bayesian Inference and Model Mis- specification Jennifer Flegg, The University of Melbourne Mathematical Modelling of Avascular Tumour Growth Frances Kuo, The University of New South Wales Lattice Meets Lattice—Application of Lattice Cuba- ture to Models in Lattice Gauge Theory Christian Lubich, University of Tuebingen Convergent evolving surface finite element algo- rithms for geometric evolution equations Marco Palombo, Cardiff University Perspectives on AI-powered brain microstructure imaging Emilie Sauret, Queensland University of TechnologyA hybrid Lattice Boltzmann approach for simulating viscoelastic instabilities and elastic turbulence Karen E Willcox, The University of Texas at Austin Predictive Digital Twins: From Aerospace Engineer- ing to Computational Oncology Andy Wilkins, CSIROThe Importance of Mathematics The presentation by Andy Wilkins was a public lecture. The conference attracted 76 registered participants, and featured a total of 54 contributed talks. CTAC2022 Organising Committee (QUT) • Tim Moroney • Qianqian Yang • Ian Turner• Vivien Challis • Elliot Carr• Sarie Gould CTAC2022 Scientific Committee • Kevin Burrage (QUT)• Vivien Challis (QUT)• Frances Kuo (UNSW)• Bishnu Lamichhane (Newcastle) • Quoc Thong Le Gia (UNSW) • Fawang Liu (QUT)• William Mclean (UNSW) • Tim Moroney (QUT)• Linda Stals (ANU)• Ian Turner (QUT)• Qianqian Yang (QUT) Acknowledgements QUT acknowledges the Turrbal and Yugara, as the First Nations owners of the lands where QUT now stands. We pay respect to their Elders, lores, customs and creation spirits. We recognise that these lands have always been places of teaching, research and learning. QUT acknowledges the important role Aborigi- nal and Torres Strait Islander people play within the QUT community. We gratefully acknowledge support from the following sponsors: School of Mathematical Sciences, QUT Centre for Data Science, QUT Modelling and Simulation Society of Australia and New Zealand Inc Mathematics of Computation and Optimization (MoCaO) special interest group of the Australian Mathematical Society The ANZIAM Student Support Scheme

Viscoelastic jet instabilities studied by direct numerical simulations

Viscoelastic jet instabilities studied by direct numerical simulations

An experimental study on the role and contribution of the first normal stress difference and elongational viscosity in immiscible viscoelastic Saffman-Taylor instability

This study experimentally examined the immiscible viscoelastic Saffman-Taylor instability (STI) in porous media. The viscoelastic displacing fluids are solutions of glycerin, water, and polyacrylamide with concentrations of 100, 200, and 400 ppm, and the immiscible displaced fluids are silicone oils with different viscosities. The viscosity of viscoelastic liquids is rather constant, so they could be considered Boger liquids The main innovative aspect of the present study is the analysis of the role and contribution of the first normal stress difference and elongational viscosity in the immiscible viscoelastic displacement. In this study, instead of using the simple geometry of the Hele-Shaw cell, some more applied results for viscoelastic STI in the low permeability transparent packed bed porous media have been presented. Another novel aspect of the current study is the analysis of the effect of different parameters, such as elasticity, flow rate, and viscosity ratio, on the viscoelastic STI for the case of immiscible displacement, experimentally. The results of the injection of Boger liquids were compared with the injection of equivalent Newtonian fluids to investigate the effect of fluid elasticity. Furthermore, the effects of flow rate and viscosity ratio on the flow instability were studied in detail by analyzing images of the propagation of finger-like patterns and the results of mixing length and sweep efficiency. The results indicate that the contribution of the first normal stress difference to the stabilizing effect of polymeric additives is less than 18% for the different scenarios of Boger liquid injection. Thus, the elongational viscosity of displacing fluid has the main role in enhancing the sweeping of the displaced phase. When decreasing the polymer concentration and increasing the flow rate, the contribution of the elongational viscosity on STI can become more important compared to the first normal stress difference.

Perspective on edge fracture

Edge fracture is a viscoelastic instability characterized by the sudden indentation of a fluid’s free surface when the fluid is subjected to a high enough shear rate. During shear rheometry, the fracture can invade the fluid sample, decreasing its contact area with the rheometer fixture and rendering the measurement of viscosity and normal stresses at high-shear rates invalid. Edge fracture can also induce apparent shear banding in the fluid, complicating the interpretation of experimental results. Over the past several decades, empirical and theoretical research has unraveled the physics underlying edge fracture. The knowledge obtained has allowed rheologists to develop techniques to minimize the adverse effect of fracture in their experiments. In recent years, edge fracture has also been used to break up viscoelastic liquid bridges quickly and cleanly, showing its potential to be adapted to the design of functional dispensing nozzles. This Perspective article aims to give a historical overview of edge fracture and suggests research directions to develop methods for suppressing or harnessing the phenomenon to benefit applications of both fundamental and technological importance.

Numerical study of viscoelastic upstream instability

In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a cylinder in a confined narrow channel. Two-dimensional direct numerical simulations based on the FENE-P model (the finite-extensible nonlinear elastic model with the Peterlin closure) are conducted with numerical stabilization techniques. Our results show that the macroscopic viscoelastic constitutive relation can capture the viscoelastic upstream instability reported in previous experiments for low-Reynolds-number flows. The numerical simulations reveal that the non-dimensional recirculation length (LD) is affected by the cylinder blockage ratio (BR), the Weissenberg number (Wi), the viscosity ratio (β) and the maximum polymer extension (L). Close to the onset of upstream recirculation, LD with Wi satisfy Landau-type quartic potential under certain parameter space. The bifurcation may exhibit subcritical behaviour depending on the values of L2 and β. The parameters β and L2 have nonlinear influence on the upstream recirculation length. This work contributes to our theoretical understanding of this new instability mechanism in viscoelastic wake flows.

Viscoelastic instabilities of Taylor-Couette flows with different rotation regimes.

The critical modes of the instabilities of viscoelastic Taylor-Couette flow are investigated using both experiments and linear stability analysis when only one cylinder rotates and the other is fixed. A viscoelastic Rayleigh circulation criterion highlights that the elasticity of the polymer solution can induce a flow instability even if the Newtonian counterpart is stable. When the inner cylinder solely rotates, experimental results show three critical modes: stationary axisymmetric vortices or Taylor vortices for small elasticity, standing waves, also called ribbons for intermediate values of elasticity, and disordered vortices (DV) for large elasticity values. When the outer cylinder rotates and the inner cylinder is fixed and for large values of elasticity, the critical modes appear in the form of DV. There is a good agreement between experimental and theoretical results provided that the elasticity of the polymer solution is accurately determined. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Geometry dependence of viscoelastic instabilities through porous media

Viscoelastic instabilities are notoriously sensitive to their geometrical environment. Consequently, understanding the onset and general behavior of viscoelastic instabilities in geometrically complex applications where viscoelastic fluids naturally occur, such as porous media, is far from a trivial task. To this aim, this study numerically investigates the geometrical dependence of viscoelastic instabilities through confined one-dimensional channel arrays of circular pore contractions of ideal (i.e., symmetrical) and non-ideal (i.e., asymmetrical) pore configurations. At low elasticity, we demonstrate that the viscoelastic instability behavior in all geometries is the same as it was previously reported in ideal pore geometries, which can be characterized by a gradual loss of the well-defined symmetry in the velocity streamline plots, as well as the buildup of secondary vortices. However, at higher elasticity, we observe the transition into strong transient behavior, whereby the flow in all pore geometries experiences the multistability phenomenon reported by Kumar et al. [“Numerical investigation of multistability in the unstable flow of a polymer solution through porous media,” Phys. Rev. Fluids 6, 033304 (2021)]. Interestingly, it is shown that the viscoelastic instability response is the strongest for the most non-ideal pore geometry, which not only has the fastest transition time but also produces the most chaotic flow fluctuations, characterized by a broadband spectrum. Ultimately, we demonstrate that the viscoelastic instability response in each pore geometry adheres to the Pakdel–McKinley criterion for elastic instability, specifically the streamline curvature and elastic stress anisotropy.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers.

The viscous fingering in the Hele-Shaw cell can be suppressed by replacing the upper-bounding rigid plate with an elastic membrane. Recently, graphene multilayers while polymer-curing-induced blistering showed the dynamical evolution of viscous fingering patterns on a viscoelastic substrate due to their thickness-dependent elasticity. Under certain conditions, the elastic solid-based instability couples with the viscoelastic substrate-based instability. The mechanisms underlying such a coupling in the blisters of 2D materials and the dynamical evolution of the viscous fingering patterns underneath the blisters are yet to be addressed. Herein, we investigate the viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers, and provide thorough analytical and experimental insights for the elucidation of the dynamical evolution of the viscous fingering patterns and the coupled instabilities in the blisters. We also estimate the interfacial adhesion energy of the MoS2 flakes over a (poly)vinyl alcohol (PVA) substrate and the confinement pressure inside the MoS2 blisters using a conventional blister-test model. It is observed that the presence of instability gives rise to anomalies in the modeling of the blister test. The adhesion mechanical insights would be beneficial for fundamental research as well as practical applications of 2D material blisters in flexible optoelectronics.

Volumetric evolution of elastic turbulence in porous media

Viscoelastic flow instability, which is compelled by elastic effects rather than inertia, can be driven to a chaotic state termed elastic turbulence (ET) manifested as strong velocity fluctuations with an algebraic decay in the frequency spectrum and increased mixing. We report the first spatiotemporally complete description of ET by considering a broad volume within a novel three-dimensional ordered porous medium, reconstructing flow at a micrometre characteristic length scale ( $\text {Reynolds numbers} \ll 1$ ) via time-resolved microtomographic particle image velocimetry. Beyond a critical Weissenberg number of 2, we observe an elastic flow instability accompanied by an enhanced pressure drop with spectral characteristics typical of ET. Polymer chains in the ET flow state are advected along increasingly curved streamlines between pores such that they accumulate strain and generate a local flow instability evaluated per an established instability criterion based on local evaluation of elastic tensile stress and streamline curvature. The onset of ET leads to increased pore-scale resistance and positive feedback on upstream streamline curvature. ET is thus characterized by a continuous evolution between states of laminar and unstable flow: pores with unstable flow flood their adjacent peers and thus encourage straightened streamlines and flow stability across the array, while positive feedback from flow resistance on streamline curvature results in the instability propagating upstream along the array. By employing a geometrically ordered medium, we permit flow state communication between pores, yielding generalized insights highlighting the significance of spatial correlation and flow history, and thus provide new avenues for explaining the mechanisms of ET.

Hysteresis in viscoelastic flow instability of confined cylinders

Viscoelastic fluids exhibit hysteresis in response to time-dependent stimuli due to a finite relaxation time of the polymeric chains. We have investigated hysteresis in the context of viscoelastic flow instability, which has applications in industrial, geophysical, and biological processes. The topology of the polymeric stress field regulates distinct flow states in viscoelastic flows, requiring a finite time for the transformation of the polymeric stress topology and leading to hysteresis in the flow field.

Viscoelastic instability in an asymmetric geometry

Viscoelastic instability in an asymmetric geometry

Perspectives on viscoelastic flow instabilities and elastic turbulence

Viscoelastic fluids can exhibit striking flow instabilities under conditions where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. This article provides perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

Announcement: PRFluids Publishes Invited Perspective on Viscoelastic flow instabilities and elastic turbulence

Announcement: PRFluids Publishes Invited Perspective on Viscoelastic flow instabilities and elastic turbulence

Viscoelastic potential flow instability theory of Rivlin-Ericksen electrified fluids of cylindrical interface

A linear electrohydrodynamic Kelvin-Helmholtz instability of the interface between two viscoelastic Rivlin-Ericksen fluids enclosed by two concentric horizontal cylinders has been studied via the viscoelastic potential flow theory. The dispersion equation of complex coefficients for asymmetric disturbance has been obtained by using normal mode technique. the stability criteria are analyzed theoretically and illustrated graphically. The imaginary part of growth rate is plotted versus the wave number. The influences of dynamic viscoelastic, uniform velocities, Reynolds number, electric field, dynamic viscosity, density fluids ratio, dielectric constant ratio and inner fluid fraction on the stability of the system are discussed. The study finds its significance in Ocean pipelines to transfer oil or gas such as Eastern Siberia-Pacific Ocean oil pipeline.

A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation

This report summarizes our recent experimental findings [Xie et al., Phys. Rev. Lett., 2022] and pore-scale simulation results [Xie et al., Phys. Rev. Fluids., 2020] on viscoelastic oscillation, which is a new observation of viscoelastic instability in the multiphase flow state. The viscoelastic oscillation causes trapping of droplets in contraction-expansion micro-channels regardless of the injection rate. Based on the force balance analysis on the viscous, capillary and elastic forces, the oscillation amplitude is found to linearly increase with viscoelasticity, and the trapped droplet size is determined by the elasto-capillary number. The oscillation also helps to extract droplets from their originally trapped positions such as dead-ends once a critical Deborah number is reached. These results successfully explain the phenomenon that the alternative injection of viscoelastic and inelastic fluids continually produces additional oil, indicating that the viscoelastic oscillation is a new important mechanism of viscoelastic fluid for enhanced oil recovery. Cited as: Xie, C., Xu, K., Qi, P., Xu, J., Balhoff, M. T. A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation. Advances in Geo-Energy Research, 2022, 6(3): 267-268. https://doi.org/10.46690/ager.2022.03.10

Towards Predicting the Onset of Elastic Turbulence in Complex Geometries

Flow of complex fluids in porous structures is pertinent in many biological and industrial processes. For these applications, elastic turbulence, a viscoelastic instability occurring at low Re—arising from a non-trivial coupling of fluid rheology and flow geometry—is a common and relevant effect because of significant over-proportional increase in pressure drop and spatio-temporal distortion of the flow field. Therefore, significant efforts have been made to predict the onset of elastic turbulence in flow geometries with constrictions. The onset of flow perturbations to fluid streamlines is not adequately captured by Deborah and Weissenberg numbers. The introduction of more complex dimensionless numbers such as the M-criterion, which was meant as a simple and pragmatic method to predict the onset of elastic instabilities as an order-of-magnitude estimate, has been successful for simpler geometries. However, for more complex geometries which are encountered in many relevant applications, sometimes discrepancies between experimental observation and M-criteria prediction have been encountered. So far these discrepancies have been mainly attributed to the emergence from disorder. In this experimental study, we employ a single channel with multiple constrictions at varying distance and aspect ratios. We show that adjacent constrictions can interact via non-laminar flow field instabilities caused by a combination of individual geometry and viscoelastic rheology depending (besides other factors) explicitly on the distance between adjacent constrictions. This provides intuitive insight on a more conceptual level why the M-criteria predictions are not more precise. Our findings suggest that coupling of rheological effects and fluid geometry is more complex and implicit and controlled by more length scales than are currently employed. For translating bulk fluid, rheology determined by classical rheometry into the effective behaviour in complex porous geometries requires consideration of more than only one repeat element. Our findings open the path towards more accurate prediction of the onset of elastic turbulence, which many applications will benefit.Article HighlightsWe demonstrate that adjacent constrictions “interact” via the non-laminar flow fields caused by individual constrictions, implying that the coupling of rheological effects and fluid geometry is more complex and implicit.The concept of characterizing fluid rheology independent of flow geometry and later coupling back to the geometry of interest via dimensionless numbers may fall short of relevant length scales, such as the separation of constrictions which control the overlap of flow fields.By providing direct experimental evidence illustrating the cause of the shortcoming of the status-quo, the expected impact of this work is to challenge and augment existing concepts that will ultimately lead to the correct prediction of the onset of elastic turbulence.