Gareth H. McKinley

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 experiments with a viscoelastic polymer solution.

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 experiments with a viscoelastic polymer solution.

The operational efficiency of fire suppression systems, municipal sewage networks, marine vehicles, and various other technologies are constrained by the large viscous frictional drag associated with fluid turbulence. This provides a strong incentive to develop engineering strategies that attenuate turbulence, ultimately mitigating the carbon footprint of large-scale hydrodynamic applications. We demonstrate the effective use of natural salivary mucins as a cost-effective, widely accessible drag-reducing additive. Diluted samples of human saliva are shown to substantially reduce frictional drag (up to 30%), with similar efficacy as synthetic drag-reducing polymers. Saliva contains long glycoproteins that can physically associate to form a supramolecular network with a large extensional viscosity. The non-Newtonian rheology of dilute solutions of glycoproteins makes them well-suited for turbulent drag reduction (DR). Under sustained turbulent flow conditions, the supramolecular associations of the mucin network slow the effects of mechanical degradation, resulting in more persistent DR compared to synthetic hydrocarbon polymers.

HYPOTHESIS Volume partitioning during liquid-bridge stretching and pinch-off between solid surfaces is controlled by dynamic wetting competing with hydrodynamic forcing arising from viscous extensional stresses and inertia generated during plate separation. Previous studies have focused on liquid transfer between parallel surfaces and suggest three distinct regimes: quasi-static, transitional, and dynamic. Here we test whether these regimes remain valid for slightly tilted (non-parallel) geometries relevant to roll-based processes, and whether tilting modifies transfer primarily through contact-line physics. EXPERIMENTS AND SIMULATIONS Liquid bridges of glycerol-water mixtures were stretched between parallel and slightly tilted 0°-10° plates while varying separation velocity, viscosity, and surface wettability. High-speed imaging quantified the transfer ratio ϕ (fraction of volume transferred from donor to acceptor surface). Complementary phase-field simulations incorporating contact-angle hysteresis were performed to resolve realistic contact-line motion during bridge stretching and breakup. FINDINGS The same three regimes are observed for both parallel and tilted plates. In the quasi-static regime, ϕ is primarily determined by the differences in receding contact angles between two surfaces; in the dynamic regime, contact lines become effectively pinned, yielding an approximately constant ϕ≈43%. In the transitional regime, liquid transfer dynamics is governed by a dimensionless withdrawal number Πw=μV3/ρg2ℓc3. Transfer ratios reveal the scaling ϕ∼Πw1/6and collapse onto a single master curve ϕΠw. Notably, the alteration to the lateral contact-line slip resulting from a tilt between the two surfaces affects the transfer ratio only when both surfaces have comparable wettability; surfaces with highly disparate wettability exhibit negligible sensitivity to such tilting.

High Resolution Image Download MS PowerPoint Slide Man-made cellulose fibers from well-managed forestry provide an eco-friendly alternative to polyester and cotton. The Ioncell process converts cellulose-based raw materials into high-quality textiles and offers strong potential for upcycling cellulose-based textile waste. Recycling discarded textiles is challenging because washing and abrasion degrade synthetic and natural fibers, reducing molecular weight and processability. Here, we demonstrate that adding a very small fraction of ultrahigh molecular weight bacterial cellulose enhances the spinnability of textile waste streams dominated by short-chain cellulose. This high molecular weight dopant systematically increases solution extensibility, stabilizing the extension-dominated fiber-spinning process. Viscoelastic stresses in a stable spinline scale with steady extensional viscosity at high strain rates and depend sensitively on chain extensibility. We quantify the enhanced tensile stress differences using capillarity-driven extensional rheometry combined with transient exponential shear rheometry to develop a spinnability metric for cellulose/ionic liquid solutions. These findings advance strategies for efficient recycling of postconsumer cellulose textiles.

The failure resistance of polymer networks dictates their utility as material candidates across industries. However, relating the key length scales driving crack growth to molecular mechanisms remains a key bottleneck in predicting and designing against fracture. The fractocohesive length—defined in terms of the ratio of fracture energy to the specific work to rupture—of a material correlates with the length scale of energy dissipation and controls fracture resistance. Although the Lake–Thomas model predicts the fractocohesive length of a perfect polymer network to match the undeformed mesh size, real soft materials exhibit values that far exceed this prediction. Here, we report extraordinarily high fractocohesive lengths in polymer-like networks with and without defects. We find that even perfect networks can have fractocohesive lengths orders of magnitude higher than the undeformed mesh size due to highly nonlinear chain behavior giving rise to nonlocal effects during fracture. Introducing defects further increases the fractocohesive length. We identify quantitative relations between nonlinear chain mechanics, defect length, defect density, and fractocohesive length. Overall, strain-stiffening chain behavior, defect density, and defect size independently correlate with larger fractocohesive lengths in polymer-like networks, and their individual effects can be collapsed into a single power law scaling. These outcomes point the way towards improved physics-informed design of soft yet tough polymers and metamaterials.

Optimally windowed chirp rheometry—a technique employing both frequency and amplitude-modulated exponential chirps—is gaining popularity for its ability to precisely capture the linear viscoelastic spectrum of complex materials while dramatically reducing the experimental time required to acquire data. To date, the chirp signals used for characterizing the linear viscoelasticity of such materials have featured a high time-bandwidth product (TB>50), calculated as the product of chirp duration or experiment time (Towc) and frequency bandwidth (Δω). However, for time-evolving materials, it is essential to also adjust the chirp duration (Towc) according to the characteristic mutation timescale, τmu(t) of the material to ensure time-translation invariance (Towc≪τmu(t)) during experiments. For rapidly mutating materials, the values of the time-bandwidth product TB thus systematically decrease as the chirp duration is progressively reduced during the mutation process. However, the signal must also be sufficiently long, relative to the material’s inherent relaxation timescale (τ), to ensure that a steady-state periodic viscoelastic response is obtained. To explore the trade-offs between these two competing conditions, we perform exploratory numerical simulations using canonical constitutive models: the classical Maxwell model, characterized by a single dominant relaxation time and the fractional Maxwell model, which compactly and accurately captures the broad relaxation spectra typical of many viscoelastic materials. For highly viscoelastic systems and/or rapidly mutating samples, we show that when employing short exponential chirp sequences, substantially improved accuracy can be obtained by shifting the initial phase of the chirp waveform through a single new phase offset parameter, φ0. Experimental validation tests performed on wormlike micellar solutions, a pressure-sensitive adhesive, and a UV-curable acrylate system—each having relaxation times comparable to the signal duration—further demonstrate that adjusting the initial phase significantly enhances the data quality of linear viscoelastic measurements made with optimally windowed chirp protocols.

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 N1(t;ω,γ0) 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 N1 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 N1 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 N1 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.

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.

Understanding the coupling between the dynamics of microstructural deformation and the bulk flow behavior of colloidal suspensions is crucial for both fundamental studies and practical applications of this important class of soft matter systems. In this study, we investigated the flow behavior of cellulose nanofibril (CNF) suspensions─renewable, sustainable materials with low environmental impact─using the "Rheo-Iris," a rheo-polarized imaging system we developed to visualize two-dimensional microstructural changes in fluid under applied stress. Creep tests under constant shear stress revealed an initial elastic material response, a yield transition, followed by viscoplastic flow at long times. Simultaneous polarized imaging identified three distinct retardation patterns, depending on the applied shear stress. At low stresses (≤10 Pa), or small strain immediately after stress application, the phase retardation remained uniformly low, and the orientation axis of the microstructure was randomly distributed, indicating that the homogeneously dispersed CNFs form an isotropic, entangled network structure. At a stress near the yield point (40 Pa), a spiral-shaped region of high retardation appeared, and the orientation axis shifted to 60-85° away from the flow direction. This corresponds to the formation of rosary-like structures aligned in the vorticity direction, exhibiting spatially nonuniform birefringence and an oriented microstructure. At higher stresses far above the yield point (200 Pa), this "log-rolling" mesostructure collapsed, and smaller CNF aggregates became aligned in the flow direction, leading to spatially uniform oriented birefringence across the entire field. Both cases represent distinct fiber orientation phenomena, and our noninvasive rheo-polarization method clearly distinguishes how the spatial orientation distribution in the field changes with applied stress. The Rheo-Iris system enables real-time, quantitative analysis of internal microstructural evolution under imposed shear strain or stress and offers a powerful tool for exploring the orientation dynamics in soft matter systems, opening a new eye on complex fluid rheology in colloidal dispersions.

In this work, we investigate the transient rheological behavior of two soft glassy materials: a clay dispersion and a silica gel, emphasizing their unconventional shear stress buildup behavior under conditions of constant imposed strain. For both materials, the elastic modulus and static yield stress undergo time-dependent evolution or aging. In addition, following an intense period of preshearing (i.e., shear rejuvenation or destructuration), the material relaxation time is observed to show a stronger than linear dependence on the sample age, indicative of hyperaging dynamics. We show that these features are consistent with nonmonotonic steady-state flow curves characterized by a local stress minimum. When a steady shearing flow is suddenly ceased, and the total imposed sample strain is held constant, both materials show an initial relaxation of the shear stress, followed by a period of shear stress buildup, resulting in a local minimum in the evolution of shear stress with time. For the clay dispersion, the intensity of these effects increases at higher preshear rates, whereas for the silica gel, the effects are largely independent of the preshear rate. We also propose a simple time-dependent linear Maxwell model that qualitatively predicts the experimentally observed trends in which the shear stress buildup is directly related to a monotonic increase in the elastic modulus with time, giving keen insight into this peculiar phenomenon.

Abstract The mechanobiology of single cells plays a crucial role in various biological processes, including embryonic development, cancer treatment, and wound healing. This study highlights the use of the fractional Kelvin-Voigt model (FKVM)—a viscoelastic model consisting of two Scott Blair elements in parallel—to compactly and accurately characterize single-cell rheology. Unlike traditional power law models, which primarily capture the key features of the mechanical response at long timescales, the FKVM effectively captures both short- and long-timescale mechanical responses with a minimal number of constitutive parameters. Experimental small-amplitude oscillatory shear (SAOS) data for dividing canine kidney cells, creep data of human K562 erythroleukemic cells, and creep recovery data of blastomere cytoplasm are all analyzed to showcase the accuracy and versatility of the FKVM. Additionally, for the first time, the continuous relaxation and retardation spectra corresponding to the fractional differential formulation of the FKVM are derived. These results establish a comprehensive framework for predictive analysis of single-cell rheology in both the time and frequency domains. Graphical abstract

We analyze the capillarity-driven thinning dynamics of entangled polymer solutions described by the Doi–Edwards–Marrucci–Grizzuti (DEMG) model and the Rolie-Poly (RP) model. Both models can capture the physics of polymer reptation, finite rates of chain retraction, and finite extensibility of single polymer molecules, while differing slightly in their final form depending on how they capture convective constraint release. We calculate numerically the filament thinning profiles predicted by the two models with realistic entanglement densities, assuming slender cylindrical filament profiles and no fluid inertia effects. Simulations with both models reveal an early tube reorientation regime, followed by a brief intermediate elasto-capillary regime, and finally a finite extensibility regime close to the pinch-off singularity. The results presented in this work reveal two critical features in the transient extensional rheology of entangled polymer solutions that have been observed in previous experimental studies but which are poorly described by the FENE-P model that is widely used to interpret capillarity-driven thinning experiments. First, the effective relaxation time obtained from capillary breakup extensional rheometry is notably smaller than the longest (reptation) time obtained from steady shear rheometry. The ratio of these relaxation times can be expressed as a universal function of the entanglement state and the polymer concentration, which agrees well with published experimental data for a range of entangled polymer solutions. Second, the filament thinning dynamics at sufficiently high polymer concentrations are governed by the tube reorientation process, and the apparent extensional viscosity shows a noticeably rate-thinning response. To support these conclusions, we evaluate the filament thinning dynamics expected for aqueous poly(ethylene oxide) solutions (1 MDa) in the dilute, semidilute, and entangled regimes. As the concentration increases beyond the entangled threshold, the temporal evolution of the filament radius deviates from the well-studied exponential-thinning form and becomes increasingly power-law in character.

In this work, we investigate the transient rheological behavior of two soft glassy materials: a clay dispersion and a silica gel, emphasizing their unconventional shear stress build-up behavior under conditions of constant imposed strain. For both materials, the elastic modulus and static yield stress undergo time-dependent evolution or aging. In addition, following an intense period of pre-shearing (i.e. shear-melting or destructuration), the material relaxation time is observed to show a stronger than linear dependence on the sample age, suggestive of hyper-aging dynamics. We show that these features are consistent with non-monotonic steady-state shear stress/shear rate flow curves characterized by a local stress minimum. When a steady shear flow is suddenly ceased, and the total imposed sample strain is held constant, both materials show an initial relaxation of the shear stress followed by a period of shear stress buildup, resulting in a local minimum in the evolution of shear stress with time. For the clay dispersion, the intensity of these effects increases with higher pre-shear rates, whereas for the silica gel, the effects are largely independent of the pre-shear rate. We also propose a simple time-dependent linear Maxwell model, which qualitatively predicts the experimentally observed trends in which the shear stress build-up is directly related to a monotonic increase in the elastic modulus, giving keen insight into this peculiar phenomenon.

While it is widely acknowledged that system-spanning particulate structures contribute to the observed yield stress and shear-thinning in attractive colloidal gels, a comprehensive understanding of the underlying microscopic mechanisms remains elusive. In this study, we present findings from coarse-grained simulations focusing on model depletion gels to shed light on this intriguing phenomenon. Contrary to conventional belief, our simulations reveal that the mere presence of attractive interactions and aggregate formation does not sufficiently explain the observed yield stress. Instead, we identify a crucial physics element in the form of microscopic constraints on the relative rotational motion between bonded particles. Through a detailed analysis of microstructure and particle dynamics, we elucidate how these constraints lead to the emergence of yield stress in soft particulate gels. This research provides essential insights into the micromechanical origins of yield stress in soft particulate gels, paving the way for improved understanding and engineering of these versatile materials for various real-world applications.

Mucus supports human health by hydrating, lubricating, and preventing infection of wet epithelial surfaces. The beneficial material properties and bioactivity of mucus stem from glycoproteins called mucins, motivating the development of mucin-derived hydrogels for wound dressings and antifouling coatings. However, these applications require robust gelation and adhesion to a wide range of substrates. Inspired by the chemical cross-linking and water-tolerant adhesion of marine mussel adhesive structures, we use catechol-thiol bonding to drive gelation of native mucin proteins and synthetic mucin-inspired polymers, forming soft, adhesive hydrogels that can be coated onto diverse surfaces. The gelation dynamics and adhesive properties can be systematically tuned by varying the hydrogel composition, polymer architecture, and thiol availability, with gelation timescales adjustable from seconds to hours, and values of elastic modulus, failure stress, and debonding work spanning orders of magnitude. We demonstrate the functionality of these gels in two applications: as tissue adhesives, using porcine skin as a proxy for human skin, and as bioactive surface coatings to prevent bacterial colonization. The results highlight the potential of catechol-thiol cross-linking as a versatile platform for engineering multifunctional glycoprotein hydrogels with applications in wound repair and antimicrobial surface engineering.

We derive an operating limit line for the non-ideal artifacts caused by machine stiffness (instrument compliance) which causes measured apparent viscoelastic moduli to be systematically lower than the true values. The limit is represented as a maximum measurable apparent shear modulus Gmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\max }$$\end{document}, or tensile modulus Emax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{\max }$$\end{document}, which can be shown explicitly on plots of viscoelastic moduli independent of the applied displacement, load, or frequency. Uncorrected data should be much lower than these limits. Corrected data can be above these limits and credible. These interpretations are supported by studying how correction equations can be re-written in terms of Gmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\max }$$\end{document} or Emax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{\max }$$\end{document} and how error propagates in the corrections. We also show how the dynamic compliance representation leads to simpler corrections and how machine stiffness can be calibrated from apparent dynamic compliance measurements of a single sample at two different geometry conditions. Equations are provided for rotational rheometers as well as linear displacement dynamic mechanical analyzers. Used as an operational limit line, Gmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\max }$$\end{document} or Emax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{\max }$$\end{document}, the method can assess the credibility of data from others—even without access to their primary data of displacement, force, torque, or amount of correction, which are rarely reported. The method can also anticipate future issues before data are taken, e.g., to understand operational limits when selecting instruments and test geometries.

due to the higher frequency of particle-particle collisions during shear within the network of smaller and more intrinsically conductive GO sheets to store charge. Therefore, the results of this study have implications for future studies in flowable carbon nanomaterials in flow battery and flow capacitor technologies.

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.

Semi-flexible polyelectrolytes are a group of biopolymers with a wide range of applications from drag reducing agents in turbulent flows to thickening agents in food and cosmetics. In this study, we investigate the rheology of aqueous solutions of xanthan gum as a canonical semi-flexible polyelectrolyte in steady shear and transient extensional flows via torsional rheometry and dripping-onto-substrate (DoS), respectively. The high molecular weight of the xanthan gum and the numerous charged groups on the side branches attached to the backbone allow the shear and extensional rheology of the xanthan gum solutions to be tuned over a wide range by changing the ionic strength of the solvent. In steady shear flow, increasing the xanthan gum concentration increases both the zero shear viscosity and the extent of shear-thinning of the solution. Conversely, increasing the ionic strength of the solvent by addition of sodium chloride (NaCl) decreases both the zero shear viscosity and the level of shear-thinning. In transient extensional flow, increasing the xanthan gum concentration changes the dynamics of the capillary thinning from an inelastic power-law (IP) response to an elastocapillary (EC) balance, from which an extensional relaxation time can be measured based on the rate of filament thinning. Increasing the NaCl concentration decreases the extensional relaxation time and the transient extensional viscosity of the viscoelastic solution. Based on the dynamics of capillary thinning observed in the DoS experiments, we provide a relationship for the smallest extensional relaxation time that can be measured using DoS. We suggest that the change in the dynamics of capillary thinning from an IP response to an EC response can be used as an easy and robust experimental method for identifying the rheologically effective overlap concentration of a semi-flexible polyelectrolyte solution, i.e., the critical concentration at which polymer molecules start to interact with each other to produce a viscoelastic strain-stiffening response (often perceived as "stringiness") in transient extensional flows such as those involved in dripping, dispensing and filling operations.

Recent advances in rheometry exploiting frequency-modulated (chirp) waveforms have dramatically reduced the time required to perform linear viscoelastic characterisation of complex materials. However, the technique was optimised for ‘separate motor transducer’ instruments, in which the drive motor imposing the strain deformation is decoupled from the torque transducer. Whilst the use of optimised windowed chirps (OWCh) using other rheometers has been recently reported in the literature, no systematic study concerning the use of ‘combined motor transducer’ instruments (in which the motor and transducer subsystems are integrated into a single ‘head’) has been undertaken. In the present study, we demonstrate the use of OWCh rheometry using combined motor transducer/single-head rheometers using a stress-controlled operating principle, thus avoiding the reliance on complicated and instrument-specific feedback control systems that would be required to perform strain-controlled experiments. The use of stress-controlled chirps requires a modification to the established OWCh analysis protocol such that the complex viscosity η ∗ ( ω ) is used as an intermediate proxy function for ultimately computing the complex modulus G ∗ ( ω ) . This approach negates the effect of the strain offset that is inherent to stress-controlled oscillatory rheometry. Secondly, a correction algorithm and operational criteria for identifying inertial artefacts is established before we consider the impact of chirp digitisation on data acquisition. The use of stress-controlled OWCh rheometry (which we term Stress-OWCh, i.e. σ OWCh) is demonstrated for a diverse range of material classes including, Newtonian calibration fluids (silicone oil), polymer solutions (polyethylene oxide in water), an entangled polymer melt (polydimethylsiloxane), worm-like micellar systems (cetylpyridinium chloride/sodium salicylate), time-evolving critical gels (gelatin) and aging elastoviscoplastic materials (Laponite®). This novel implementation of chirp waveforms using a single-head rheometer will facilitate the wider adoption of OWCh rheometry and allow the benefits of frequency-modulation techniques to be exploited where separate motor transducer instruments are unavailable/unsuitable. • Stress-Controlled Optimally Windowed Chirp ( σOWCh ) rheometry is developed. • A novel data analysis protocol is presented which accounts for strain offset. • Corrections for the effects of instrument inertia are validated. • Guidelines for the design of σOWCh experiments are developed. • σOWCh is demonstrated using a wide range of viscoelastic and mutating fluids.

A number of commercial fluids, including synthetic automotive oils, food and consumer products containing polymer additives exhibit weakly rate-thickening responses in the final stages of capillarity-driven thinning, where a large accumulated strain and high extensional strain rate alter the thinning dynamics of the slender liquid filament. Consequently, the capillarity-driven thinning dynamics typically feature two distinct regions at the early and late stages of the filament breakup process, each dominated by distinct mechanisms. These features have been incorporated in a simple Inelastic Rate-Thickening (IRT) model with linear and quadratic contributions to the constitutive stress-strain rate relationship, where the apparent extensional viscosity slowly thickens at high strain rates. We numerically compute the thinning dynamics of the IRT model assuming an axially-slender axisymmetric filament and no fluid inertia. The computational results motivate a new self-similar solution dominated by the second-order stress obtained through a similarity transformation. The new asymptotic solution leads to a self-similar filament shape that is more slender than the Newtonian counterpart and results in a quadratic thinning of the mid-point radius of the filament with time to breakup close to singularity. A new and distinct asymptotic geometric correction factor, $X\approx 0.5778$ is obtained, from which a more accurate true extensional viscosity can be recovered from an interpolated time-varying geometric correction factor based on the magnitudes of different stress components. Finally, we propose a statistics-based protocol to select the best-fit constitutive model using a parameter-free criterion, enabling us to quantify the extensional rheological behavior through capillarity-driven thinning dynamics more systematically on complex rate-thickening viscoelastic fluids.

Gels made of telechelic polymers connected by reversible cross-linkers 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 cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales 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 cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.

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 nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved 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 $\beta _P(\dot {\gamma })$ 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 & McKinley ( Phys. Rev. Lett. , vol. 77, no. 12, 1996, p. 2459) 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, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

Knowledge of the evolution in the mechanical properties of a curing polymer 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 homemade sliding plate piezo-operated rheometer (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 subsecond 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 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated.

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.

The gelation behaviour of two different pea protein isolates and one soy protein isolate were investigated with a focus on the role of the protein properties. Protein solubility was the lowest in pH 3 citrate-phosphate buffer (<10% w/w), increased in pH 7.4 phosphate-buffered saline (12–21% w/w), and was the highest in pH 7.6 MilliQ water (~20–40% w/w). Heat-induced gelation conditions for the protein sources were sensitive to both the soluble and the insoluble fractions as obtained during extraction. At low protein concentrations (≤5% w/v), the proteins started to lose their viscoelastic behaviour and exhibited predominantly viscous properties. Fitting of the fractional Kelvin-Voigt model to the frequency sweeps showed an increase in the fractal gel strength with increasing protein concentration. Secondary structures of the soluble species showed mostly unordered proteins, suggesting that the proteins were denatured during the commercial extraction process although gelation has to date been suggested to be highly dependent on the denaturation of soluble proteins. Synchrotron Radiation Circular Dichroism measurements of the insoluble proteins showed a significant amount of ordered protein structures. SEM imaging of the gels also suggested a new gelation pathway in which insoluble proteins act as dispersed fillers within a continuous matrix of soluble proteins. The goal of this research is to elucidate the the role of different protein fractions, globulins and albumins, and their secondary structure in the formation of a gel network and how this affects their viscoelastic behaviour.

High Resolution Image Download MS PowerPoint Slide Solutions of polymer chains are modeled using nonequilibrium Brownian dynamics simulations, with physically associative beads which form reversible cross-links 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 the binding energy at a 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 moduli 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 the binding energy. Furthermore, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines whether the gel is in the evanescent regime.

. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable and accurate solution of the viscoelastic constitutive equation. Here, we focus on understanding the roles of surface tension, elasticity and finite chain extensibility in controlling the elasto-capillary (EC) regime, as well as the perturbative effects that gravity and substrate wettability play 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 that captures the initial rate of thinning when the dynamics are dominated by a balance between inertia and capillarity. This model also captures the structure of the transition region to the nonlinear EC regime in which the rapidly growing elastic stresses in the thread balance the capillary pressure as the filament thins towards breakup. Finally, we propose a fitting methodology based on the analytical solution for FENE-P fluids to improve the accuracy in determining the effective relaxation time of an unknown fluid.

Aluminosilicate hydrogels are often considered to be precursors for the crystallisation of zeolites carried out under hydrothermal conditions. The preparation of mechanically homogeneous aluminosilicate gels enables the study of these materials through bulk rheology and observation of the aging dynamics until the precipitation of crystalline zeolites. The first part of this study deals with the establishment of ternary state diagrams, in order to identify the range of chemical formulations that enable preparation of single-phase homogeneous gels. Then, by studying the viscoelastic moduli during the gelation reaction, and by yielding the gel under large deformation, we propose an empirical law considering the partial order of reaction on each chemical element, to predict the gelation time according to the chemical formulation. The scaling behavior of the elastic properties of this colloidal gel shows a transition from a strong link behavior to a weak link regime. Long term aging results in the shrinkage of the gel, accompanied by syneresis of interstitial liquid at the surface. Zeolites precipitate through crystallisation by a particle attachment mechanism, when thermodynamic equilibrium is reached. The stoichiometry of the precipitated zeolites is not only consistent with the concentration of the remaining species in the supernatant but, surprisingly, it is also very close to the partial order of the reaction of the chemical elements involved in the determination of the critical gel point. This indicates a strong correlation between the morphology of the soft amorphous gel network that is formed at an early age and those of the final solid precipitated crystals.