Elastic Instability Research Articles

Evolution of flow reversal and flow heterogeneities in high elasticity wormlike micelles (WLMs) with a yield stress

The formation and evolution of a heterogeneous flow and flow reversal are examined in highly elastic, gel-like wormlike micelles (WLMs) formed from an amphiphilic triblock poloxamer P234 in 2M NaCl. A combination of linear viscoelastic, steady shear, and creep rheology demonstrate that these WLMs have a yield stress and exhibit viscoelastic aging, similar to some soft glassy materials. Nonlinear shear rheology and rheoparticle tracking velocimetry reveal that these poloxamer WLMs undergo a period of strong elastic recoil and flow reversal after the onset of shear startup. As flow reversal subsides, a fluidized high shear rate region and a nearly immobile low shear rate region of fluid form, accompanied by wall slip and elastic instabilities. The features of this flow heterogeneity are reminiscent of those for aging yield stress fluids, where the heterogeneous flow forms during the initial stress overshoot and is sensitive to the inherent stress gradient of the flow geometry. Additionally, macroscopic bands that form transiently above a critical shear rate become “trapped” due to viscoelastic aging in the nearly immobile region. This early onset of the heterogeneous flow during the rapidly decreasing portion of the stress overshoot differs from that typically observed in shear banding WLMs and is proposed to be necessary for observing significant flow reversal. Exploring the early-time, transient behavior of this WLM gel with rheology similar to both WLM solutions and soft glassy materials provides new insights into spatially heterogeneous flows in both of these complex fluids.

Effect of cavity aspect ratio on mixed convective heat transfer phenomenon inside a lid-driven cavity due to elastic turbulence

This study performs extensive numerical simulations to investigate how the aspect ratio (AR) of a lid-driven cavity influences the onset of elastic instability and elastic turbulence and the subsequent mixed convective heat transfer rate inside it. To this end, we utilize the finite volume method based open source code OpenFOAM along with Rheotool to solve the mass, momentum, energy, and viscoelastic constitutive equations. We find that the dependency of the cavity AR on the heat transfer rate is highly complicated depending upon the values of the Richardson (Ri) and Prandtl numbers (Pr). At low values of Ri, the heat transfer rate continuously decreases with AR irrespective of the value of the Prandtl number and the fluid type, i.e., Newtonian or viscoelastic. The same trend is also observed at high values of Ri and low values of Pr. At these combinations of Ri and Pr, the heat transfer rate is always higher in viscoelastic fluids than in Newtonian fluids due to the presence of elastic turbulence in the former fluids. However, a different trend is observed at high values of both Ri and Pr. At this combination of Ri and Pr, the heat transfer rate increases with AR in Newtonian fluids, whereas it decreases in viscoelastic fluids. Therefore, at high values of AR, Ri, and Pr, the heat transfer rate is higher in Newtonian fluids than that in viscoelastic fluids despite the presence of elastic turbulence in the latter fluids. This is in contrast to the assumption that the elastic turbulence phenomenon always increases the rate of transport processes. A possible explanation for this behavior is provided in this study. Along with the heat transfer aspects, we also provide a detailed discussion on how the cavity aspect ratio influences the corresponding flow dynamics inside the cavity. In particular, we find that the onset of the elastic instability (and the subsequent elastic turbulence) phenomenon is delayed to higher values of the Weissenberg number as the cavity aspect ratio increases. This is in line with prior experimental studies reported in the literature.

Edge fracture of thixotropic elastoviscoplastic liquid bridges.

It has recently been shown that torsion can break liquid bridges of viscoelastic fluids, with potential application to their clean and rapid dispensing. However, many commonplace fluids (paints, adhesives, pastes, and foodstuffs like chocolate) have more complex thixotropic elastoviscoplastic (TEVP) properties that depend on the imposed stress and the timescale of deformation. Using a commercial thermal paste, we show that liquid bridges of TEVP fluids can also be broken by torsion, demonstrating the applicability of the technique for improved dispensing of real industrial fluids. The liquid bridge breaking mechanism is an elastic instability known as "edge fracture." Dimensional analysis predicts that the effects of thixotropy and plasticity can be neglected during edge fracture. Simulation using a nonlinear, phenomenological TEVP constitutive model confirms such a prediction. Our work yields new insight into the free-surface flows of TEVP fluids, which may be important to processes such as electronic packaging, additive manufacturing, and food engineering.

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.

Investigations of In-Plane Fluidelastic Instability in a Multispan U-Bend Tube Array—Part II: Tests in Two-Phase Flow

Abstract Tests to study fluidelastic instability (FEI) in an array of U-bend tubes were recently completed in the multispan U-Bend test rig at Canadian Nuclear Laboratories. These tests were sponsored by the Electric Power Research Institute and were designed to study in-plane fluid elastic instability of steam generator tubes in two-phase cross flow. This instability mechanism was first observed in previous experiments by Atomic Energy of Canada Limited. This mechanism was not thought to be a serious practical concern until 2012 when it caused severe damage to tubes in a new replacement steam-generator in a nuclear power plant in the United States. In this study, tests were conducted both with flows of air and two-phase liquid/vapor Refrigerant 134a. The tube bundle consisted of 22 flexible U-bend tubes supported by a configurable flat-bar arrangement. Testing focused on the effects of support geometry and tube-to-support interaction. Data were recorded from 33 dynamic signals from accelerometers, displacement probes, force transducers, and void-fraction probes. Part I of this two-part series presented results of air tests. Part II presents results of tests using two-phase Freon refrigerant (R-134a) as the working fluid.

Effect of viscoelasticity on displacement processes in porous media

Improving the displacement efficiency of capillary entrapments in porous media by adding high molecular weight polymers to the invading phase has various industrial applications, from enhanced oil recovery to soil remediation. Apart from an increased viscosity contrast compared to regular water flooding, the flow of viscoelastic polymer solutions exhibits unstable flow behavior even at small Reynolds numbers, which can lead to an additional displacement mechanism of the capillary entrapments. In this work, we employ a microfluidic approach to unravel the underlying physics and mechanism of this enhanced pore scale displacement. To this end, we show that the major complex topological flow features in a typical porous medium can be mimicked by a flow geometry consisting of a single capillary entrapment connected to two symmetric serpentine channels. This design excludes the effect of viscous stresses and allows direct focus on displacement processes driven solely by elastic stresses. We show that the unique viscoelastic fluid features, such as the significant storage and release of elastic stresses and first normal stress difference, combined with the flow geometry, lead to purely elastic instability and secondary flow, which in turn provide the stresses necessary to overcome the capillary threshold and displace the capillary entrapment.

Why does an elastomer layer confined between two rigid blocks grow numerous cavities?

For a thin layer of elastomer sandwiched between two rigid blocks, when the blocks are pulled, numerous cavities grow in the elastomer like cracks. Why does the elastomer grow numerous small cracks instead of a single large crack? Here we answer this question by analyzing an idealized model, in which the elastomer is an incompressible neoHookean material and contains a penny-shaped crack. To simulate one representative crack among many, the model is axisymmetric with zero radial displacement at the edge. When the rigid blocks are pulled by a pair of forces, a hydrostatic tension develops in the elastomer. At a critical hydrostatic tension, a small crack deforms substantially, as predicted by an elastic instability, resulting in an unbounded energy release rate. Consequently, the small crack initiates its growth, regardless of the toughness of the elastomer. As the crack grows, the energy release rate decreases, so that the crack arrests. Meanwhile, the rigid blocks constrain deformation of the elastomer far away from the crack, where hydrostatic tension remains high, allowing other cracks to grow. For an elastomer of thickness H, shear modulus μ, and toughness Gc, the crack radius and spacing decrease as the normalized toughness Gc/(μH) increases. Therefore, a tough elastomer of small modulus and thickness will grow numerous small cracks when confined by two rigid blocks and pulled beyond a critical force.

Universal properties of non-Hermitian viscoelastic channel flows

An addition of long-chain, flexible polymers strongly affects laminar and turbulent Newtonian flows. In laminar inertia-less viscoelastic channel flow, the supercritical elastic instability of non-normal eigenmodes of non-Hermitian equations at finite-size perturbations leads to chaotic flow. Then three chaotic flow regimes: transition, elastic turbulence (ET), and drag reduction (DR), accompanied by elastic waves, are observed and characterized. Here we show that independently of external perturbation strength and structure, chaotic flows above the instability onset in transition, ET, and DR flow regimes reveal similar scaling of flow properties, universal scaling of elastic wave speed with Weissenberg number, Wi, defined the degree of polymer stretching, and the coherent structure of velocity fluctuations, self-organized into cycling self-sustained process, synchronized by elastic waves. These properties persist over the entire channel length above the instability threshold. It means that only an absolute instability exists in inertia-less viscoelastic channel flow, whereas a convective instability, is absent. This unexpected discovery is in sharp contrast with Newtonian flows, where both convective and absolute instabilities are always present in open flows. It occurs due to differences in nonlinear terms in an elastic stress equation, where except for the advective term, two key terms describing polymer stretching along the channel length are present.

Failure analysis on fully-transparent deep-sea pressure hulls used at 2,500 m depth

Fully-transparent deep-sea pressure hulls have been attracted attention in recent years with the increasing demand for underwater observation. So far, public researches on design rule and failure modes for fully-transparent deep-sea pressure hulls are limited and the relevant experience cannot meet the requirements of new cabin design. In this study, the compression test is carried on, in which the material samples are subjected to quasi-static compressive load until failure in tests at different loading rates, and the hyperelastic finite element model is established in LS-DYNA software to simulate the failure process. Simulation results of material properties in finite element analysis on the cylindrical samples are compared with the experimental data, including the characteristic points of the mechanical properties in elastic stage and hardening stage, the ultimate load and failure mode of the samples. Mesh convergence analysis is conducted, and the appropriate mesh quality is accordingly selected in simulation of fully-transparent deep-sea pressure hulls. An equation for prediction of instability-type failure is described, which is derivation based on the classical analytical expression of elastic instability, thus, when 5 times of safety factor is taken, the wall thickness of the pressure hull is calculated to be t/R0 = 0.0685 at 2,500 m depth. Ultimate strength and failure mode of a typical fully-transparent deep-sea pressure hull are simulated. First, the first-order linear buckling modal analysis is carried out to simulate initial geometric imperfections. Then, simulations for the loading and collapse process of two fully-transparent pressure hulls respectively with one opening and two openings are conducted, and the ultimate load of 126 MPa and 128 MPa for the two kinds of hulls are obtained. Finally, simulation of a scaled pressure hull is carried out and simulation results are compared with the experimental data in reference, which are basically consistent. The calculated failure strength shows that the spherical hulls satisfy the safety factor requirement of 5 times. The provided simulation procedure can be referred for failure analysis of fully-transparent pressure hulls.

Theoretical study of second and third order elastic constants of β-SiC

First principles calculations of the second and third order elastic constants of the cubic silicon carbide β-SiC have been accomplished using the density functional theory within the local density approximationand the pseudopotential plane-wave method with the Hartwigsen Goedecker Hutter scheme. The secondorder elastic constants Cij compared fairly well with those previously measured by one of us using theBrillouin light scattering technique (P. Djemia) [1]. The ab-initio calculations include parameterspressure dependence determinations in relation with the structural transformation from a zinc Blende toa rocksalt structure. The transition pressure at which arises elastic instabilities is found to be Pt = 113GPa. Also, we investigate the effects of anharmonicity by calculating the third order elastic constantsC_ijk . The experimental values are still unknown and comparisons with our calculations are suitable in thefuture.
 

Effect of fin density and fin height on flow-induced vibration behavior of finned tube arrays subjected to water cross flow

PurposeThe prediction of critical velocity at instability threshold for shell and tube heat exchangers is important to avoid failure of tubes as a result of flow-induced vibrations due to water cross flow. The flow-induced vibration in finned tube heat exchangers is affected by various parameters such as fin height, fin pitch, fin material, tube array, pitch ratio, fin type, fluid velocity etc. In this paper, an experimental investigation of fluid elastic instability in shell and tube heat exchangers is carried out by subjecting normal square finned tube arrays of pitch ratio 1.79 to water cross flow.Design/methodology/approachThe five tube arrays, namely plain array, two finned tube arrays with 3 fpi and 9 fpi fin density, and two finned tube arrays with 3 mm and 6 mm fin height are tested in the experimental test setup with water flow loop and vibration measurement system. The research objective is to evaluate the effect of fin density and fin height on the instability threshold. The critical velocity at instability threshold is determined to characterize the fluid elastic instability behavior of different tube arrays. The vortex shedding behavior of the tube arrays is also studied by determining Strouhal number corresponding to the small peaks before fluid elastic instability.FindingsThe fluid elastic instability behavior of the tube arrays was found to be the function of fin tube parameters. The experimental results indicate that an increase in fin density and fin height results in delaying the instability threshold for finned tube arrays. It is also observed that critical velocity at instability is increased for finned tube arrays compared to plain tube arrays of the same pitch ratio. The design modifications in the outer box have resulted in further reduction in the natural frequency. This enabled to reach clear instability for all the five-tube arrays.Originality/valueThe research data add the value to the present body of knowledge by knowing the effect of fin height and fin density on the fluid elastic instability threshold of normal square finned tube arrays subjected to water cross flow.

Elastic interactions of plastic events in strained amorphous solids before yield

It has been widely accepted that the plastic events of amorphous solids after mechanical yield belong to a highly correlated avalanche state. However, whether the plastic events before yield are correlated or not is still unsettled, leaving their interactions largely unexplored. In this paper, by means of atomistic simulations, typical ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ metallic glasses, as the model system, are sheared under athermal quasistatic limit to study these plastic events. The statistical analysis of both stress drops and waiting times reveals that plastic events before yield are in the correlated avalanche state and the interactions among them are mediated by the robust elasticity. The temporal correlation analysis of the nonaffine displacement fields further reveals that the elastic interactions are short-lived strong but long-standing weak, which results in the fractal morphology of potential energy landscape. By introducing vibrational modes to explore plastic events, we clearly exhibit the way how the elastic interactions organize the Eshelby-type shear transformations into avalanched plastic events. The correlation matrix, with its component being the dot product of the vibrational modes at different configurations, is defined to trace the evolution of vibrational modes during elastic deformation and across plastic events. Three reasons accounting for the robust elasticity are identified: (i) the limited destruction of plastic events on global elasticity, (ii) the persistent hard spots embedded in elastic matrix, and (iii) the self-recovery of elastic matrix during elastic deformation. Our results clarify the atomic-scale nature of both elastic deformation and plastic instabilities before yield in amorphous solids, providing fundamental information for the development of elastoplastic constitutive models.

Fluid elastic instability and vortex shedding in finned tube arrays: the effects of tube material and fin density

PurposeThe purpose of this paper is to present investigations on the significant influence of the tube material and fin density on fluid elastic instability and vortex shedding in a parallel triangular finned tube array subjected to water cross flow.Design/methodology/approachThe experiment was conducted on finned tube arrays with a fin height of 6 mm and fin density of 3 fins per inch (fpi) and 9 fpi. A dedicated setup has been developed to examine fluid elastic instability and vortex shedding. Nine parallel triangular tube arrays with a pitch to tube diameter ratio of 1.78 were considered. The plain tube arrays, coarse finned tube arrays and fine finned tube arrays each of steel, copper and aluminium materials were tested. Plain tube arrays were tested to compare the results of the finned tube arrays having an effective tube diameter same as that of the plain tube.FindingsA significant effect of fin density and tube material with a variable mass damping parameter was observed on the instability threshold. In the parallel triangular finned tube array subjected to water cross flow, a delay in the instability threshold was observed with an increase in fin density. For steel and aluminium tube arrays, the natural frequency is 9.77 Hz and 10.38 Hz, which is close to each other, whereas natural frequency of the copper tubes is 7.40 Hz. The Connors’ stability constant K for steel and aluminium tube arrays is 4.78 and 4.87, respectively, whereas it is 5.76 for copper tube arrays, which increases considerably compared to aluminum and steel tube arrays. The existence of vortex shedding is confirmed by comparing experimental results with Owen’s hypothesis and the Strouhal number and Reynolds number relationship.Originality/valueThis paper’s results contribute to understand the effect of tube materials and fin density on fluid elastic instability threshold of finned tube arrays subjected to water cross flow.

Rock-on-a-chip: "Seeing" the association/disassociation of an adaptive polymer in solutions flowing through porous media.

The flow and transport of polymer solutions through porous media are ubiquitous in myriad scientific and engineering applications. With escalating interest in adaptive polymers, understanding the flow dynamics of their solutions is indispensable (yet lacking). Here, the hydrophobic-effect-driven reversible associations in a self-adaptive polymer (SAP) solution and its flow characteristics in a microfluidic-based "rock-on-a-chip" device have been analyzed. The hydrophobic aggregates were fluorescent labeled; this enabled a direct visualization of the in situ association/disassociation of the polymer supramolecular assemblies in pore spaces and throats. Furthermore, the influence of this adaptation on the macroscopic flow behavior of the SAP solution was analyzed by comparing its flow with that of two partially-hydrolyzed polyacrylamide (the molecular weight (MW)-equivalent HPAM-1 and ultrahigh-MW HPAM-2) solutions in the semi-dilute regime with similar initial viscosities. At low flow rates (with shear predominance), the SAP solution showed a low shear viscosity compared to HPAM-1, indicating a higher shear susceptibility for association than chain entanglement. Although the SAP exhibited the same elastic instability as the non-adaptive polymers above a threshold flow rate, the adaptable structure of the former advanced the onset of its viscoelastic-governed flow, providing a stronger flow resistance, possibly through an extension resistance. Furthermore, 3D-media analysis indicated that the reversible association/disassociation of SAP increased the accessible pore space during nonaqueous-liquid displacement, facilitating oil production.

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.

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.

Plastic ridge formation in a compressed thin amorphous film

We demonstrate that surface morphogenesis in compressed thin films may result from spatially correlated plastic activity. A soft glassy film strongly adhering to a smooth and rigid substrate and subjected to uniaxial compression, indeed, does not undergo any global elastic pattern-forming instability, but responds plastically via localized burst events that self-organize, leading to the emergence of a series of parallel ridges transverse to the compression axis. This phenomenon has been completely overlooked, but results from common features of the plastic response of glasses hence should be highly generic for compressed glassy thin films.

Homogeneous nucleation of dislocations as a pattern formation phenomenon

Dislocation nucleation in homogeneous crystals begins as a symmetry-breaking elastic instability. In the absence of explicit nucleation centers, such instability develops simultaneously all over the crystal and due to the dominance of long range elastic interactions it advances into the nonlinear stage as a collective phenomenon through pattern formation. In this paper we use a novel mesoscopic tensorial model (MTM) of crystal plasticity to study the delicate role of crystallographic symmetry in the development of the dislocation nucleation patterns in defect free crystals. The model is formulated in 2D and we systematically compare the unfolding of the pattern formation phenomenon in lattices with square and triangular symmetry. To avoid the dominance of the conventional plastic mechanisms, we consider the loading paths represented by pure shears applied on the boundary of the otherwise unloaded body. These peculiar loading protocols can be qualified as exploiting the ‘softest’ and the ‘hardest’ directions and we show that the associated dislocation patterns are strikingly different.

Role of micellar entanglements on kinetics of shear banding flow formation

We investigate the effects of micellar entanglement number on the kinetics of shear banding flow formation in a Taylor–Couette flow. Three sets of wormlike micellar solutions, each set with a similar fluid elasticity and zero-shear-rate viscosity, but with varying entanglement densities, are studied under the startup of steady shear. Our experiments indicate that in the set with low fluid elasticity, the transient shear banding flow is characterized by the formation of a transient flow reversal in a range of entanglement densities. Outside of this range, the transient flow reversal is not observed. For the sets of medium and high elasticities, the transient flow reversals exist for relatively small entanglement densities and disappear for large entanglement densities. Our analysis shows that wall slip and elastic instabilities do not affect the transient flow feature. We identify a correlation between micellar entanglement number, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement number increases, the width of the stress plateau first increases; then, at a higher micellar entanglement number, the plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement number through the width of the stress plateau.

The bending of thin strips with a non-uniform transverse curvature

The non-linear flexural behaviour of a tape spring — whose cross section has a uniform curvature — is produced by the presence of an elastic instability. However, these are not the only structures that possess non-linear flexural behaviour. Panel-springs and bridged tape springs are examples of structures that can also produce this behaviour. Predicting the flexural behaviour of these structures is more challenging because their cross section is non-uniform. This work presents an analytical model that can predict the opposite-sense flexural behaviour of thin strips that have a non-uniform cross section. The novel attribute of this model is in the utilisation of a univariate polynomial series to describe the initial cross section of the strip. The model is applied to a range of bridged tape springs and panel-springs, with the results compared with solutions obtained from the Finite Element (FE) method. A consistent error of less than 5.5% is achieved between the analytical model and the FE model when the snap-through moment and propagation moment are compared. The analytical model is also compared with independent experimental data of the flexural behaviour of a traditional carpenter’s tape measure. An error of less than 1% and 7% of the snap-through moment and propagation moment, respectively, is achieved.