arXiv subjects

Gareth H. McKinley

Publications and source records attributed to Gareth H. McKinley.

At least 19 recordsLinked to original sources

arXiv2026

Kinematic and rheological equivalence of steady shearing and planar extensional flows

Steady shearing and planar extension are commonly viewed as two distinct types of flow field, especially in the context of probing the rheology of complex fluids. By leveraging the kinematic equivalence between the two flows, we derive an effective extension rate experienced by a material element which removes the rotational component of the shearing flow. This enables reconstruction of the steady planar extensional viscosity of an unknown fluid using only material functions measured in a steady shearing flow, revealing a deep rheological equivalence between the two deformation histories. We demonstrate this equivalency through phenomenological and microscopically motivated frame-invariant constitutive models as well as using experimental data obtained with a viscoelastic polymer solution and a polymer melt.

cond-mat.soft↗

arXiv2026

PocketCaBER and PocketDoS: Low-cost open-source tools for teaching and learning advanced topics in fluid mechanics

We describe two open-source, 3D-printable, flexure-based tools for the quantitative measurement of extensional properties of viscoelastic fluids. These low-cost, portable, and scalable devices (which we have termed ``PocketCaBER'' and ``PocketDoS'') are particularly applicable for use in the field and in graduate-level teaching environments due to their low cost, printability on hobby 3D printers, compatibility with cell phone cameras, portability and user-friendly operation. We characterize and benchmark each device's performance against its lab-equivalent counterpart and provide downloadable STL files for rapid fabrication. We discuss experimental limitations of these devices compared with their bench-top counterparts. Finally, we illustrate the use of such tools in facilitating student engagement in polymer science and complex fluids classes---specifically, how progress in learning goals can be uniquely and effectively accelerated by providing the necessary rheological instruments directly to each individual student (especially for advanced modules such as nonlinear extensional rheology). By giving students personal, indefinite access to laboratory-level instrumentation through these open-source frugal science tools, we discuss our efforts to expand participation and engagement within the field of nonlinear rheology.

physics.ed-ph↗

arXiv2026

Numerical analysis of capillarity-driven thinning rheometry for polydisperse polymer solutions

Liquid bridges of polymer solutions that are self-thinning due to the action of capillarity undergo a transition from Newtonian-like linear thinning to exponential elastocapillary (EC) thinning when the polymer chains are stretched by the elongational flow and the resulting elastic contribution to the stress exceeds the viscous stress. As the Oldroyd-B model predicts that the EC thinning rate is set by the relaxation time ($τ$) of the polymer, the characteristic thinning timescale extracted from the exponential decay ($τ_{EC}$) is commonly interpreted as a direct measure of $τ$. Here we show that for real polydisperse polymer solutions, $τ_{EC}$ reflects only a subset of the molecular weight (MW) distribution -- those chains actively stretched by the flow. We demonstrate this using a multi-mode FENE-PM model that explicitly incorporates the molecular weight distribution, validated against the filament thinning experiments of Calabrese et al. [Phys. Rev. X 15, 021025 (2025)] on bidisperse blends of narrowly-distributed low-MW and high-MW polystyrene solutions. The model predicts that only chains with effective Weissenberg number $Wi = \dot{\varepsilon} τ> 1/2 $ are extended by the flow and contribute elastic stress; this threshold naturally favors high molecular weight species, whose longer relaxation times allow them to remain stretched throughout the elastocapillary regime. The measured $τ_{EC}$ is therefore set by this stress-contributing sub-ensemble rather than the full distribution. Further, our model predicts that $τ_{EC}$ depends on both the molecular weight distribution and total polymer concentration, as well as experimental parameters including pre-stretch and initial filament diameter, confirming that it is best understood as an experiment-specific quantity rather than an intrinsic fluid property.

cond-mat.soft↗

arXiv2025

DoS Dos and Don'ts

Dripping-onto-Substrate (DoS) rheometry is a well-established method for measuring the extensional rheology of low-viscosity liquids. However, clear guidelines on the capabilities and limitations of the technique are lacking. In the present work, we define operational limits for measuring a transient extensional viscosity directly from observation of the rate of filament thinning, as well as model-based bounds on calculating a viscosity $η$ and extensional relaxation time $τ_E$ of a liquid using DoS. Dilute solutions of polyethylene oxide (PEO) and polyacrylamide (PAM) are used to probe the lower limit of measurable $τ_E$, demonstrating that values as low as 0.1 ms can be resolved, provided (a) the intrinsic Deborah number (based on the ratio of the relaxation time and the Rayleigh breakup time scale) is $De \geq \mathcal{O}(0.1)$ and (b) an instrumental constraint related to spatial and temporal resolution is satisfied. This instrumental constraint is quantified through a new metric we define as the \textit{filament capture rate}, a ``figure of merit'' (expressed in Hz) that can be used to quantify the number of data points within the elasto-capillary regime that are available for extraction of $τ_E$. We also investigate the sensitivity to other experimental parameters including variations in nozzle radius and Bond number ($Bo$). Across the tested range ($0.2 < Bo < 0.7$), extensional relaxation times for the same fluid vary by less than $\pm16$ \%; however, experiments with low viscosity fluids at $Bo > 0.5$ exhibit damped gravitational oscillations that affect early-time dynamics. Collectively, these results provide a quantitative roadmap for reliable DoS rheometry and affirm its use for measuring sub-millisecond relaxation times in weakly elastic fluids.

cond-mat.soft↗

arXiv2025

Self-Consistent Fourier-Tschebyshev Representations of the First Normal Stress Difference in Large Amplitude Oscillatory Shear

Large Amplitude Oscillatory Shear (LAOS) is a key technique for characterizing nonlinear viscoelasticity in a wide range of materials. Most research to date has focused on the shear stress response to an oscillatory strain input. However, for highly elastic materials such as polymer melts, the time-varying first normal stress difference $N_1(t;ω,γ_0)$ can become much larger than the shear stress at sufficiently large strains, serving as a sensitive probe of the material's nonlinear characteristics. We present a Fourier-Tschebyshev framework for decomposing the higher-order spectral content of the $N_1$ material functions generated in LAOS. This new decomposition is first illustrated through analysis of the second-order and fourth-order responses of the quasilinear Upper Convected Maxwell model and the fully nonlinear Giesekus model. We then use this new framework to analyze experimental data on a viscoelastic silicone polymer and a thermoplastic polyurethane melt. Furthermore, we couple this decomposition with the recently developed Gaborheometry strain sweep technique to enable rapid and quantitative determination of the $N_1$ material function from experimental normal force data obtained in a single sweep from small to large strain amplitudes. We verify that asymptotic connections between the oscillatory shear stress and $N_1$ in the quasilinear limit are satisfied for the experimental data, ensuring self-consistency. This framework for analyzing the first normal stress difference is complementary to the established framework for analyzing the shear stresses in LAOS, and augments the content of material-specific data sets, hence more fully quantifying the important nonlinear viscoelastic properties of a wide range of soft materials.

cond-mat.soft↗

arXiv2024

High-frequency Optimally Windowed Chirp rheometry for rapidly evolving viscoelastic materials: application to a crosslinking thermoset

Abstract Knowledge of the evolution of mechanical properties of the curing matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint we utilize a combined frequency and amplitude-modulated chirped strain waveform in conjunction with a home-made sliding plate piezo-operated (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to sub-second scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast curing resins. The method is validated via calibration tests in both instruments and the corresponding limitations are discussed. As a proof of concept the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 seconds to monitor the rapid evolution of the time- and frequency-dependence of the complex modulus. Finally, FTIR spectroscopy is utilized to gain insights on the evolution of the chemical network while the gap-dependence of the evolving material properties in these heterogeneous systems is also investigated.

cond-mat.soft↗

arXiv2024

The fluid dynamics of a viscoelastic fluid dripping onto a substrate

Extensional flows of complex fluids are pivotal in industrial applications like spraying, atomisation, and microfluidic drop deposition. The Dripping-on-Substrate (DoS) technique is a conceptually simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. DoS involves capillary-driven thinning of a liquid bridge formed by a slowly dispensed drop onto a partially-wetting solid substrate. By following the filament thinning and pinch-off, the extensional viscosity and relaxation time can be determined. Importantly, DoS enables measurements for lower viscosity solutions than commercially available capillary break-up extensional rheometers. To understand DoS operation, we employ a computational rheology approach via adaptively-refined, time-dependent axisymmetric simulations using the open-source Eulerian code, \textit{Basilisk}. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable viscoelastic solution. We focus on understanding the roles of surface tension, elasticity, and finite chain extensibility in the Elasto-Capillary (EC) regime. Additionally, we explore perturbative effects of gravity and substrate wettability in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model capturing the initial thinning rates, balancing inertia and capillarity. This model also describes the structure of the transition region to the nonlinear EC regime, where elastic stresses counteract capillary pressure in the thread as the filament thins toward breakup. Finally, we propose a fitting methodology based on the analytical solutions for FENE-P fluids to enhance accuracy in determining the effective relaxation time for unknown fluids.

physics.flu-dyn↗

arXiv2024

Strain stiffening universality in composite hydrogels and soft tissues

Soft biological tissues exhibit a remarkable resilience to large mechanical loads, a property which is associated with the strain stiffening capability of the biopolymer networks that structurally support the tissues. Yet, recent studies have shown that composite systems such as tissues and blood clots exhibit mechanical properties that contradict those of the polymer matrix - demonstrating stiffening in compression, but softening in shear and tension. The microscopic basis of this apparent paradox remains poorly understood. We show that composite hydrogels and tissues do indeed exhibit non-linear elastic stiffening in shear - which is governed by the stretching of the polymer chains in the matrix - and that it is driven by the same mechanism that drives compression stiffening. However, we show that the non-linear elastic stiffening in composite hydrogels and tissues is masked by mechanical dissipation arising from filler-polymer interactions known as the Mullins effect, and we introduce a method to characterize the non-linear elasticity of the composites in isolation from this overall strain softening response through large-amplitude oscillatory shear experiments. We present a comprehensive characterization of the non-linear elastic strain stiffening of composite hydrogels and soft tissues, and show that the strain stiffening in shear and compression are both governed by universal strain amplification factors that depend on essential properties of the composite system, such as the filler concentration and the filler-polymer interaction strength. These results elucidate the microscopic mechanisms governing the non-linear mechanics of tissues, which provides design principles for engineering tissue-mimetic soft materials, and have broad implications for cell-matrix mechanotransduction in living tissues under strain.

cond-mat.soft↗

arXiv2024

Elasto-Inertial Instability in Torsional Flows of Shear-Thinning Viscoelastic Fluids

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg (Wi) number. However, the combined effects of fluid elasticity, shear thinning, and finite inertia (as quantified by the Reynolds number Re) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone-plate geometries, we experimentally explore the entire Wi - Re phase space for a series of rate-dependent viscoelastic fluids (quantified using a shear thinning parameter $β_P$). We tune $β_P$ by varying the polymer concentration in solutions. This progressively reduces shear-thinning but leads to finite inertial effects before the onset of elastic instability, thus naturally resulting in elasto-inertial coupling. Transient rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry and document the combined effects of varying Wi, Re, and $β_P$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel and McKinley 1996 for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, thus bridging the gap between purely elastic and elasto-inertial curved streamline instabilities.

physics.flu-dyn↗

arXiv2024

Interplay between wall slip and shear banding in a thixotropic yield stress fluid

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate $\dot γ_c$. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the flow profile of the flowing band is set by the applied shear rate $\gd$ instead of $\dot γ_c$. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

cond-mat.soft↗

arXiv2024

Evanescent Gels: Competition Between Sticker Dynamics and Single Chain Relaxation

Solutions of polymer chains are modelled using non-equilibrium Brownian dynamics simulations, with physically associative beads which form reversible crosslinks to establish a system-spanning physical gel network. Rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. It is shown that a system-spanning network can form regardless of binding energy at sufficiently high concentration. However, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single chain relaxations. If the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes ``evanescent'', decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. In our simulations, the concentration of elastically active chains and the dynamic modulii are computed independently. This makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of binding energy. Further, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines if the gel is in the evanescent regime.

cond-mat.soft↗

arXiv2023

Transition to elasto-capillary thinning dynamics in viscoelastic jets

We perform simulations of an impulsively-started, axisymmetric viscoelastic jet exiting a nozzle and entering a stagnant gas phase using the open-source code Basilisk. This code allows for efficient computations through an adaptively-refined volume-of-fluid technique that can accurately capture the deformation of the liquid-gas interface. We use the FENE-P constitutive equation to describe the viscoelasticity of the liquid and employ the log-conformation transformation, which provides stable solutions for the evolution of the conformation tensor as the jet thins down under the action of interfacial tension. For the first time, the entire jetting and breakup process of a viscoelastic fluid is simulated, including the pre-shearing flow through the nozzle, which results in an inhomogeneous initial radial stress distribution in the fluid thread that affects the subsequent breakup dynamics. The evolution of the velocity field and the elastic stresses in the nozzle are validated against analytical solutions where possible, and the early-stage dynamics of the jet evolution are compared favourably to the predictions of linear stability theory. We study the effect of the flow inside the nozzle on the thinning dynamics of the viscoelastic jet (which develops distinctive "beads-on-a-string" structures) and on the spatio-temporal evolution of the polymeric stresses in order to systematically explore the dependence of the filament thinning and breakup characteristics on the initial axial momentum of the jet and the extensibility of the dissolved polymer chains.

physics.flu-dyn↗

arXiv2023

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Gels made of telechelic polymers connected by reversible crosslinkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low valence crosslinkers, while larger supramolecular crosslinkers bring about much slower dynamics involving a wide distribution of time scales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring crosslinkers all disconnect. Larger crosslinkers allow for a greater average number of bonds connecting them, but also generate more heterogeneity. We characterize the resulting distribution of relaxation time scales analytically, and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of crosslinker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any crosslinker size and could thus be harnessed for the rational design of complex viscoelastic materials.

cond-mat.soft↗

arXiv2023

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a new, single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

cond-mat.soft↗

arXiv2023

Spatio-temporal Signatures of Elasto-inertial Turbulence in Viscoelastic Planar Jets

The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertio-elastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatio-temporal features compared to Newtonian turbulence, termed elasto-inertial turbulence (EIT). We explore EIT by studying the dynamics of a submerged planar jet of a dilute aqueous polymer solution injected into a quiescent tank of water using a combination of schlieren imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a nonmonotonic effect on the jet stability depending on its magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. In agreement with linear stability analyses of viscoelastic jets, an inertio-elastic shear-layer instability emerges near the edge of the jet for small levels of elasticity, independent of bulk undulations in the fluid column. The growth of this disturbance mode destabilizes the flow, resulting in a turbulence transition at lower Reynolds numbers and closer to the nozzle compared to the conditions required for the transition to turbulence in a Newtonian jet. Increasing the fluid elasticity merges the shear-layer instability into a bulk instability of the jet column. In this regime, elastic tensile stresses generated in the shear layer act as an "elastic membrane" that partially stabilizes the flow, retarding the transition to turbulence to higher levels of inertia and greater distances from the nozzle. In the fully turbulent state far from the nozzle, planar viscoelastic jets exhibit unique spatio-temporal features associated with EIT. The time-averaged angle of jet spreading, an Eulerian measure of the degree of entrainment, and the centerline velocity of the jets both evolve self-similarly with distance from the nozzle. The autocovariance of the schlieren images in the fully turbulent region of the jets shows coherent structures that are elongated in the streamwise direction, consistent with the suppression of streamwise vortices by elastic stresses. These coherent structures give a higher spectral energy to small frequency modes in EIT characterized by LDV measurements of the velocity fluctuations at the jet centerline. Finally, our LDV measurements reveal a frequency spectrum characterized by a $-3$ power-law exponent, different from the well-known $-5/3$ power-law exponent characteristic of Newtonian turbulence.

physics.flu-dyn↗

arXiv2023

Master Curves for FENE-P Fluids in Steady Shear Flow

The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number ($\textrm{Wi}$), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter ($L$), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio, commonly denoted $β$. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high $\textrm{Wi}$ as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of $\textrm{Wi}$ , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is $\textrm{Wi}/L$ and it is only in strong shear flows exceeding $\textrm{Wi}/L \gtrsim 1$ that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of $\textrm{Wi}/L$ when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects.

physics.flu-dyn↗

arXiv2023

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, the Maxwell model is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and dis-cuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

cond-mat.soft↗

arXiv2023

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar and biaxial extensional rheology of dilute polymer solutions using numerically-optimized stagnation point microfluidic devices

In Part I of this paper [Haward et al. submitted (2023)], we presented a new three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. In this Part II of the paper, we employ the OUBER device to examine the uniaxial and biaxial extensional rheology of some model dilute polymer solutions. We also compare the results with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [or OSCER, Haward et al. Phys. Rev. Lett. (2012)]. In each case (uniaxial, planar and biaxial extension), we use micro-particle image velocimetry to measure the extension rate as a function of the imposed flow rate, and we measure the excess pressure drop across each device in order to estimate the tensile stress difference generated in the fluid. We present a new analysis, based on solving the macroscopic power balance for flow through each device, to refine the estimate of the tensile stress difference obtained from the measured pressure drop. Based on this analysis, we find that for our most dilute polymer sample, which is "ultradilute", the extensional viscosity is well described by the finitely extensible non-linear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as polymers unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, limiting the utility of this flow type for extensional viscosity measurement.

physics.flu-dyn↗