Nonlinear Rheology Research Articles

Rational mutual interactions in starch-lipid-chlorogenic acid ternary systems enable formation of ordered starch structure for anti-digestibility during hot-extrusion 3D printing: Based on the nonlinear rheology and molecular simulation

Rational mutual interactions in starch-lipid-chlorogenic acid ternary systems enable formation of ordered starch structure for anti-digestibility during hot-extrusion 3D printing: Based on the nonlinear rheology and molecular simulation

Co-vulcanization of natural rubber and Eucommia ulmoides gum for mediation of the nonlinear rheology behaviors

Co-vulcanization of natural rubber (NR) and high-moduli Eucommia ulmoides gum (EUG) is promising while the reduction in crystallinity of crosslinked EUG is adverse for developing high-performance materials. Proposed herein is a novel method to prepare high-strength and high-stretchability NR/EUG vulcanizates with rapid vulcanization of EUG into slightly crosslinked particles, followed by further vulcanization of NR to form crosslinked matrix network. Deep eutectic solvents (DESs) are employed to facilitate the vulcanization of EUG during its blending with NR. The two-step vulcanization results in vulcanizates exhibiting superior mechanical properties under shear, tensile, and compressive conditions, significantly exceeding those of vulcanizates prepared by traditional processing methods. The reinforcement mechanism is elucidated by controlling thermomechanical coupling conditions and is supported by comprehensive structural characterizations. It is suggested that the EUG crystalline regions, maintained through the special processing method, work in conjunction with the stress-induced crystallization of the matrix to enhance the vulcanizates, nearly doubling the deformation stress at 800% strain. The crystalline regions can mediate the deformation stress during shear and compression and weaken nonlinear rheological behavior. The established structure-performance relationship is guidable for preparing high-performance NR/EUG blend vulcanizates.

Two-species model for nonlinear flow of wormlike micelle solutions. Part II: Experiment

Applications often expose wormlike micelle solutions to a very wide range of shear and temperature conditions. The two-species model presented in Part I [Salipante et al., J. Rheol. 68 (2024)] describes the nonlinear rheology over a wide range of shear rates. Here, we compare the model predictions to measurements using a combination of microcapillary and rotational rheology to measure the viscosity of surfactant solutions across seven decades of shear rate and five decades of viscosity. The effect of temperature is studied between 20 and 60 °C for different surfactant concentrations. Model parameters are determined from both small-amplitude shear measurements and fitting to the nonlinear data. Under shear stress, the model predicts due to hindered combination kinetics that the average micelle length decreases from several micrometers to a few hundred nanometers. At sufficiently high stress, the micelle shear rheology exhibits a transition from entangled wormlike behavior to a dilute rod rheology in agreement with the model. Transient stress-growth measurements exhibit a large overshoot, which is rather well predicted by the model with hindered combination rate. Microcapillary flow birefringence also is adequately predicted by the model, confirming the accuracy of its predicted micelle lengths and exhibiting a marked change in stress-optic response at the transition between entangled polymers and dilute rods. The relaxation of retardance after flow cessation follows model predictions that include micelle-micelle interactions, which are sensitive to the rotational diffusivity and length. These methods can be applied broadly to explore relationships between composition and performance.

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

On the Relation between the Viscoelastic Properties of Granular Hydrogels and Their Performance as Support Materials in Embedded Bioprinting.

Granular hydrogels, formed by jamming microgels suspension, are promising materials for three-dimensional bioprinting applications. Despite their extensive use as support materials for embedded bioprinting, the influence of the particle's physical properties on the macroscale viscoelasticity on one hand and on the printing performance on the other hand remains unclear. Herein, we investigate the linear and nonlinear rheology of κ-carrageenan granular hydrogel through small- and large-amplitude oscillatory shear measurements. We tuned the granular hydrogel's properties by changing the stiffness (soft, medium, stiff) and the packing density of the individual microgels. Characterizations in the linear viscoelasticity regime revealed that the storage modulus of granular hydrogels is not a simple function of microgel stiffness and depends on the microgel packing density. At larger strains, increasing the microgel stiffness reduced the energy dissipation of the granular beds and increased the solid-fluid transition point. To understand how the different rheological properties of granular support materials influence embedded bioprinting, we examined the printing fidelity and cellular filament shrinkage within the granular beds. We found that microgels with low packing density diminished the printing quality, while stiff microgels promoted filament roughness. In addition, we found that highly packed stiff microgels significantly reduced the postprinting contraction of cellular filaments. Overall, this work provides a comprehensive knowledge of the rheology of granular hydrogels that can be used to rationally design support beds for bioprinting applications with specific characteristics.

Universality and nonuniversality in nonlinear shear rheology of entangled polystyrene solutions and melts with the same number of entanglements

The linear and nonlinear shear rheology of entangled polystyrene (PS) solutions diluted by styrene oligomers with various lengths was compared with the shear rheology of a pure melt having the same number of entanglements (Z) during startup shear and step-shear strain experiments using a cone partitioned-plate geometry. By fixing the same Z, the shear rheology of the PS solutions and the melt shows some universal features in the linear and nonlinear regimes. Undershoot of the shear stress growth coefficient is observed during the startup flow of the PS solutions and depends strongly on the length of the oligomers. The Rotation Zero Stretch model captures the stress overshoot and the steady shear viscosity quantitatively, except at the high shear rates when undershoot is observed. Stress relaxation after step-shear strain experiments reveals that the PS solutions show a transition from type A damping (close to the Doi–Edwards prediction) to type B (weaker than the Doi–Edwards prediction), while the pure melt having the same Z shows a type A response, which suggests that the length of the oligomers influences the nonlinear damping response. The nonuniversality of the nonlinear damping response of the solutions and the melt is possibly due to the changes in flow-induced friction reduction during step-shear strain deformation.

Modeling Subduction With Extremely Fast Trench Retreat

AbstractThe Tonga‐Kermadec subduction zone exhibits the fastest observed trench retreat and convergence near its northern end. However, a paradox exists: despite the rapid trench retreat, the Tonga slab maintains a relatively steep dip angle above 400 km depth. The slab turns flat around 400 km, then steepening again until encountering a stagnant segment near 670 km. Despite its significance for understanding slab dynamics, no existing numerical model has successfully demonstrated how such a distinct slab morphology can be generated under the fast convergence. Here we run subduction models that successfully reproduce the slab geometries while incorporating the observed subduction rate. We use a hybrid velocity boundary condition, imposing velocities on the arc and subducting plate while allowing the overriding plate to respond freely. This approach is crucial for achieving a good match between the modeled and observed Tonga slab. The results explain how the detailed slab structure is highly sensitive to physical parameters including the seafloor age and the mantle viscosity. Notably, a nonlinear rheology, where dislocation creep reduces upper mantle viscosity under strong mantle flow, is essential. The weakened upper mantle allows for a faster slab sinking rate, which explains the large dip angle. Our findings highlight the utilizing rheological parameters that lead to extreme viscosity variations within numerical models to achieve an accurate representation of complex subduction systems like the Tonga‐Kermadec zone. Our study opens new avenues for further study of ocean‐ocean subduction systems, advancing our understanding of their role in shaping regional and global tectonics.

Applying the SPP nonlinear rheology framework to characterize the effect of fermentation time and the gluten-to-chickpea flour ratio in yeasted bread

In this work, doughs made with gluten add chickpea composite flour were mixed to reach the 500BU standard and baked into bread products. Chickpea flour was substituted at the level of 20%, 30%, and 40% by wheat gluten to provide structural support for the dough. Higher gluten concentrations improved gas bubble retention as determined by crumb image analysis, resulting in higher final loaf volume. Dough samples were taken out of the fermentation chamber at 0, 30, 60, and 90 min to study the effect of fermentation on rheology. Utilizing SPP deltoids (Gt′ vs Gt″ plot), the intracycle and intercycle network rearrangement of dough were studied in details. Obtaining deltoids as a function of fermentation time offers an insight into the impact of fermentation on dough structure. It is found that longer fermentation time makes gluten-chickpea composite dough more elastic in the linear region (<1% strain) and less elastic in the nonlinear region. This work helps to demonstrate an application of SPP analysis in facilitating the development of innovative bread products made with a mixture of pulse flour and wheat gluten.

Linear and nonlinear interfacial rheology of responsive microgels at the oil-water interface

Microgelation can significantly enhance the interfacial activity of polysaccharide and the ability to stabilize emulsion, but the interfacial behaviour of microgels and the intrinsic mechanism of stabilizing emulsion is not fully understood. In this study, chitosan microgels (h-CSMs) with uniform size were successfully prepared by electrostatic crosslinking hydrophobically modified chitosan (h-CS) with sodium phytate (SP) using microfluidic technique. The microfluidic conditions for fabricating of h-CSM were optimized: the mass ratio of h-CS: SP = 5: 1 with h-CS concentration of 0.5 mg/ml, and the pressure ratio of Ph-CS (Pa):PSP (Pa) = 1600:1000. The prepared h-CSMs were pH-responsive, with a swollen state at pH 5 and a shrunken state at pH 3 and 7. Further, the interfacial adsorption kinetics, and the interfacial rheology particularly the nonlinear interfacial rheology were systematically studied. The instantaneous Si-factor was proposed to describe the nonlinear responses of the microgel interface during an individual dilatational oscillation cycle. The results showed that microgelation significantly improved the interfacial ability of chitosan molecules at the oil-water interface. The h-CSM interface exhibited strain-softening response during extension and strain-hardening response during compression. The interface formed by h-CSMs under the swollen state had higher viscoelastic modulus, lower degree of nonlinearity and higher emulsifying capacity compared to that formed under the shrinking state. Low ionic strength significantly increased the viscoelastic modulus and reduced the nonlinearity and enhanced emulsifying capacity of the h-CSM interface, whereas high ionic strength disrupted the interaction between the h-CSMs and increased the nonlinear of the h-CSM interface due to too strong electrostatic screening effect.

Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks

Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.

Freeze-thaw stability of high-internal-phase emulsion stabilized by chickpea protein microgel particles and its application in surimi.

Future applications of high-internal-phase emulsions (HIPEs) are highly regarded, but poor freeze-thaw stability limits their utilization in frozen products. This study aimed to characterize the structure of chickpea protein microgel particles (HCPI) induced by NaCl and to assess its impact on the freeze-thaw stability of HIPEs. The results showed that NaCl induction (0-400 mmol L-1) increased the surface hydrophobicity (175.9-278.9) and interfacial adsorbed protein content (84.9%-91.3%) of HCPI. HIPEs prepared with HCPI induced by high concentration of NaCl exhibited superior flocculation index and centrifugal stability, and their freeze-thaw stability was better than that of natural chickpea protein. The increase in NaCl concentration reduced the droplet aggregation and coalescence index of the freeze-thaw emulsions, diminishing the precipitation of oil from the emulsion. Linear and nonlinear rheology showed that the strengthened gel structure (higher G' values) restricted water flow and counteracted the damage to the interfacial film by ice crystals at 100-400 mmol L-1 NaCl, thus improving the viscoelasticity of the freeze-thaw emulsions. Finally, the thawing loss of surimi gel with HCPI-200 HIPE was reduced by 2.04% compared to directly adding oil. This study provided a promising strategy to improve the freeze-thaw stability of HIPEs and reduce the thawing loss of frozen products. © 2024 Society of Chemical Industry.

Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time

Abstract. Reconstructing the thermo-chemical evolution of Earth's mantle and its diverse surface manifestations is a widely recognised grand challenge for the geosciences. It requires the creation of a digital twin: a digital representation of Earth's mantle across space and time that is compatible with available observational constraints on the mantle's structure, dynamics and evolution. This has led geodynamicists to explore adjoint-based approaches that reformulate mantle convection modelling as an inverse problem, in which unknown model parameters can be optimised to fit available observational data. Whilst there has been a notable increase in the use of adjoint-based methods in geodynamics, the theoretical and practical challenges of deriving, implementing and validating adjoint systems for large-scale, non-linear, time-dependent problems, such as global mantle flow, has hindered their broader use. Here, we present the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), an advanced computational modelling framework that overcomes these challenges for coupled, non-linear, time-dependent systems by integrating three main components: (i) Firedrake, an automated system for the solution of partial differential equations using the finite-element method; (ii) Dolfin-Adjoint, which automatically generates discrete adjoint models in a form compatible with Firedrake; and (iii) the Rapid Optimisation Library, ROL, an efficient large-scale optimisation toolkit; G-ADOPT enables the application of adjoint methods across geophysical continua, showcased herein for geodynamics. Through two sets of synthetic experiments, we demonstrate the application of this framework to the initial condition problem of mantle convection, in both square and annular geometries, for both isoviscous and non-linear rheologies. We confirm the validity of the gradient computations underpinning the adjoint approach, for all cases, through second-order Taylor remainder convergence tests and subsequently demonstrate excellent recovery of the unknown initial conditions. Moreover, we show that the framework achieves theoretical computational efficiency. Taken together, this confirms the suitability of G-ADOPT for reconstructing the evolution of Earth's mantle in space and time. The framework overcomes the significant theoretical and practical challenges of generating adjoint models and will allow the community to move from idealised forward models to data-driven simulations that rigorously account for observational constraints and their uncertainties using an inverse approach.

Yielding behaviour of chemically treated Pseudomonas fluorescens biofilms

The mechanics of biofilms are intrinsically shaped by their physicochemical environment. By understanding the influence of the extracellular matrix composition, pH and elevated levels of cationic species on the biofilm rheology, novel living materials with tuned properties can be formulated. In this study, we examine the role of a chaotropic agent (urea), two divalent cations and distilled deionized water on the nonlinear viscoelasticity of a model biofilm Pseudomonas fluorescens. The structural breakdown of each biofilm is quantified using tools of non-linear rheology. Our findings reveal that urea induced a softening response, and displayed strain overshoots comparable to distilled deionized water, without altering the microstructural packing fraction and macroscale morphology. The absorption of divalent ferrous and calcium cations into the biofilm matrix resulted in stiffening and a reduction in normalized elastic energy dissipation, accompanied by macroscale morphological wrinkling and moderate increases in the packing fraction. Notably, ferrous ions induced a predominance of rate dependent yielding, whereas the calcium ions resulted in equal contribution from both rate and strain dependent yielding and structural breakdown of the biofilms. Together, these results indicate that strain rate increasingly becomes an important factor controlling biofilm fluidity with cation-induced biofilm stiffening. The finding can help inform effective biofilm removal protocols and in development of bio-inks for additive manufacturing of biofilm derived materials.

Unified Understanding of Nonlinear Rheology near the Jamming Transition Point.

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear γ. We find the universal scaling behavior for the ratio of the shear stress σ and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening σ/P∼γ^{1/2} over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.

Scaling Properties of Gelling Systems in Nonlinear Shear Experiments.

We study model near-critical polymer gelling systems made of gluten protein dispersions stabilized at different distances from the gel point. We impose different shear rates and follow the time evolution of the stress. For sufficiently large shear rates, an intermediate stress overshoot is measured before reaching the steady state. We evidence self-similarity of the stress overshoot as a function of the applied shear rate for samples with various distances from the gel point, which is related to the elastic energy stored by the samples, as for dense systems close to the jamming transition. In concordance with the findings for glassy and jammed systems, we also measure that the stress after flow cessation decreases as a power law with time, with a characteristic relaxation time that depends on the shear rate previously imposed. These features revealed in nonlinear rheology could be the signature of a mesoscopic dynamics, which would depend on the extent of gelation.

Unexpected Stress Overshoot in Extensional Flow of Star Polymer Melts.

Previous studies have shown that the nonlinear rheological behavior of 3-arm star polymer melts in fast extensional flow is identical to that of linear polymers with the same span molecular weight, because the star polymers are highly aligned and have a similar conformation as the corresponding linear polymers. However, with more arms, it would be more difficult for the stars to be aligned like linear chains, and the nonlinear extensional rheology of star polymers with more arms under large deformations has not been investigated yet. Here we show that the star polystyrene (8-10 arms) melts behave differently from the linear polystyrenes. A transient stress overshoot is observed in the fast extensional flow, probably due to the difference in entanglement density near and far away from the branch point.

Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice

Abstract The flow of glacial ice is typically approximated as a nonNewtonian viscous fluid, with the momentum balance described by (an approximation to) the Stokes equations, and the nonlinear rheology described by a flow law. The most commonly used rheological law for glacial ice, Glen's flow law, yields infinite viscosity in the case of zero deformation, which can be the case at the ice surface. This poses a problem when solving the momentum balance numerically. We show that two commonly-used discretisation schemes for the boundary conditions at the ice surface and base, which yield proper numerical convergence when applied to simpler problems, produce poor numerical convergence and large errors, when used to solve the momentum balance with Glen's flow law. We show that a discretisation scheme based on the concept of ghost nodes, which substitutes the boundary conditions directly into the momentum balance equations, yields second-order numerical convergence and errors that can be up to four orders of magnitude smaller. These results are robust across different momentum balance approximations. We show that the improved boundary conditions are particularly useful for solving the 3-D higher-order Blatter-Pattyn Approximation (BPA). In general, this work underlines the importance of thoroughly verifying the numerical solvers used in ice-sheet models, before applying them to future projections of ice-sheet mass loss.

Influence of cellulose nanofibers on the behavior of Pickering emulsions. Part II: Thixotropy and dynamic-mechanical tests

Nonlinear rheology of Pickering emulsions is used to further investigate the nonlinear and unrecoverable transformation of inner structures, which is beyond the linear viscoelastic regime of tiny structural disturbances. Exploring various rheological methods plays a vital role in emulsion applications, such as simulating the macroscopic structural transformation between static and liquidlike flow states, strain overshoot, and regeneration for broken structures. According to our previous studies, cellulose nanofibers (CNFs) Pickering emulsions are a typical system for investigating polymer-based emulsions with the auxiliary surfactant [didodecyldimethylammonium bromide (DDAB)] for enhancing CNF absorption. To further study different rheological properties by varying CNF or DDAB contents, multiple interval thixotropic test, large amplitude oscillatory shear, and concentration-time-dependent superposition are employed to study the linear viscoelasticity and structural transformation of nonlinear range. This research was conducted based on the previous published works [Cui et al., Materials 15, 8285 (2022)] as a further characterization for the same sample series.

A comprehensive model for viscoplastic flows in channels with a patterned wall: longitudinal, transverse and oblique flows

We develop a comprehensive model for the creeping Poiseuille Bingham flow in channels equipped with a patterned wall, i.e. decorated with grooves or stripes that may represent a superhydrophobic (SH) or a chemically patterned (CP) surface, respectively, with longitudinal, transverse and oblique groove (stripe) orientations with respect to the applied pressure gradient. We rely on the Navier slip law to model the boundary condition on the slippery grooves. We develop semi-analytical, explicit-form and complementary computational fluid dynamics models, with solutions that have reasonable agreement. In contrast to its Newtonian analogue, a distinct solution for the oblique configuration, with an a priori unknown transform matrix, must be developed due to the viscoplastic nonlinear rheology. Our focus is to systematically analyse the effects of the Bingham number ( $B$ ), slip number ( $b$ ), groove periodicity length ( $\ell$ ), slip area fraction ( $\varphi$ ) and groove orientation angle ( $\theta$ ), on the slip velocities, effective slip length ( $\chi$ ), slip angle difference ( $\theta -s$ ), mixing index ( $I_M$ ), flow anisotropy and flow regimes. In particular, we demonstrate that, as $B$ increases, the maximum values of the shear component of $\chi$ , $\theta -s$ and $I_M$ occur progressively at smaller values of $\theta$ , compared with their Newtonian counterparts.

Exploring induced microstructural changes in magnetically modified crude oils through nonlinear rheology and magnetometry

Adsorptive phenomena involving dispersed iron oxide superparamagnetic nanoparticles and asphaltenes in crude oil have been profiled as promising technological alternatives, particularly since these interactions can induce significant structural changes within the oil matrices, effectively inhibiting the formation of complex long-range viscoelastic structures. Furthermore, the effect of adsorbed asphaltenes on magnetic dipolar interactions among particles has been proven, showing the formation of multiple asphaltene layers that stimulate a steric repulsive barrier. Despite the discussed hindering phenomena, this research demonstrated the effectiveness of the sequence of physical processes framework to provide intra-cycle structure-rheological interpretations in large amplitude oscillatory shear of a ferrofluid-modified heavy oil, upon the application of an external magnetic field. The analysis proved that disordered nanoparticle/asphaltene aggregates are highly extended and naturally formed in the absence of magnetic forces. In contrast, in the presence of a perpendicular field applied by a controlled rate magneto-rheometer, the formation of interacting structural aggregates of several hundred nanometers was observed, analogous to magnetorheological fluids. These results were validated by adjusting a phenomenological model that effectively represented the intricate processes involved in the formation and reorientation of aggregates, based on the experimental data acquired from zero-field-cooled and field-cooled magnetization curves. This revealed a distinct blocking temperature distribution at around 274 K, which was linked to Brownian relaxation phenomena exhibited by nanoparticle aggregates. In this regard, this research provided a precise extended description of the effect of magnetic fields on the microstructural organization of complex fluids using nonlinear rheology and magnetometry.