Rheological hysteresis in soft glassy materials

Internal Microstructure Dictates Yielding and Flow of Jammed Suspensions and Emulsions

We propose a microstructural classification of jammed suspensions made of soft, deformable colloids with purely repulsive interactions. Three distinct classes of particles are identified, depending on their ability to accommodate topological constraints upon increasing concentration: emulsions with constant particle volume, noninterpenetrating microgels (without dangling ends), which deswell osmotically, and star polymers, which deswell and interpenetrate. Each class has a specific rheological response in transient and steady-state flows. The transient behavior of emulsion-like systems and noninterpenetrating microgel suspensions is characterized by a single colloidal yielding process, whereas dispersions of star-like particles exhibit both colloidal and polymeric yielding due to their fuzzy microstructure with dangling arms. The flow of emulsions and microgels or stars at relatively low concentrations is characterized by a single process that controls cooperative rearrangements. Deswelling and interpenetration mark a departure from this universality and lead to more complex flow mechanisms. This simple generic description of yielding and flow demonstrates the importance of the microstructure and at the same time serves as a powerful indicator of the internal microstructure of particles.

Formulation and Characterization of Carbopol-Based Porphyrin Gels for Targeted Dermato-Oncological Therapy: Physicochemical and Pharmacotechnical Insights

Malignant skin conditions are classified as the most common forms of cancer, with an evolution of one million new cases reported every year. Research efforts in the medical field are focused on developing innovative strategies for the dissemination of measures for preventing cancer and providing new antitumor compounds. The present research examines the development and evaluation of 1% Carbopol-based hydrogels incorporating two porphyrin derivatives-5,10,15,20-tetrakis-(4-acetoxy-3-methoxyphenyl) porphyrin (P2.1) and 5-(4-hydroxy-3-methoxyphenyl)-10,15,20-tris-(4-acetoxy-3-methoxyphenyl) porphyrin (P2.2)-to create formulations suitable for topical photodynamic therapy (PDT) applications. The physicochemical properties of the obtained hydrogels were carefully evaluated, revealing the successful integration of the porphyrins into the 1% Carbopol hydrogel matrix. Rheological analysis demonstrated pseudoplastic behavior, with an increase in viscosity properties for P2.1 and P2.2, suggesting interactions with the Carbopol polymer structure. UV-visible and fluorescence spectroscopy confirmed the maintenance of the porphyrins' photodynamic properties, essential for therapeutic efficacy. Pharmacotechnical studies highlighted the hydrogels' suitability for topical applications. The formulations maintained an optimal pH range, ensuring skin compatibility and minimizing the potential for skin irritation. Their mechanical properties, including elasticity and rigidity, provided stability during handling and application. The high swelling capacity indicated effective moisture retention, enhancing skin hydration and drug release potential. Furthermore, the hydrogels demonstrated excellent spreadability, enabling uniform application and coverage, crucial for efficient light activation of the photosensitizers. The combination of robust physicochemical and pharmacotechnical properties highlights the potential of these porphyrin-loaded 1% Carbopol hydrogels as promising carriers for topical PDT. These results permit further biological and therapeutic investigations to optimize the formulation for clinical use, advancing the development of effective localized photodynamic therapies.

Elucidating the role of physicochemical interactions on gel rheology

Soft materials are characterized by their intricate interplay of structure, dynamics, and rheological properties. This complexity makes it challenging to accurately predict their response to shear stress. Here, we investigate how the nature of bonds - electrostatic attractions, physical entanglements, physical repulsion, and covalent bonds - affects the linear and nonlinear rheology of gels. Specifically, we determine the critical roles these bonds play in the yield transition and thixotropic recovery of gel properties through a combination of linear oscillatory deformations, serial creep divergence measurements, and time-resolved flow sweeps. Different classes of gels are prepared with nearly identical linear rheology but significantly different yield transitions and nonlinear properties post-yielding. These differences are directly related to the kinetics by which the underlying elastic networks rebuild after flow. Gels which exhibit thixotropic hysteresis are able to fully recover their yield stress over time while non-thixotropic gels possess time-independent yielding metrics. This direct comparison between thixotropy and yielding reveals the intimate relationship between these phenomena and their controlling physical mechanisms within soft, amorphous materials.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Thermo-rheological properties of xanthan solutions: from shear thinning to elasto-viscoplastic behavior

The thermo-rheological behavior of xanthan solutions with concentrations spanning a wide range is investigated experimentally. After carefully identifying four distinct regimes of concentration we focused on highly concentrated xanthan solutions. By combining several rheological techniques, it is shown for the first time that such solutions belong to the broad class of elasto-viscoplastic materials by exhibiting both a yield stress and elasticity that manifests around the solid-fluid transition. The soft and weakly entangled structure responsible for the elasto-viscoplastic rheological behavior is controlled by two factors:imposed stress, temperature. Consequently, concentrated solutions of xanthan may yield to either imposed stress or temperature. The systematic analysis of the elasticity mediate solid-fluid transition at various operating temperatures revealed the presence of a novel state termed as "molten solid". A clear relationship between the rheological states and the molecular states (native, denaturated, re-naturated) is established.

Shear layers and plugs in the capillary flow of wormlike micellar gels

Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex and interesting rheological features. We study the dynamics of these wormlike micellar gels in a pipe-flow scenario using particle imaging and tracking velocimetry and report the existence of plug flows with strong wall slip and non-parabolic velocity profiles for different surfactant concentrations and imposed flow rates. We rationalize these results as features of a developing transient flow of a viscoelastic solution in space and time. We show that evolution of shear layers is governed by intermittent flows, asymmetric velocity profiles and flow induced heterogeneity. Our experiments shed light on the transient fluid dynamics of wormlike micelles in simple geometries and highlight the complexity of flows involving wormlike micellar gels and similar soft matter systems in canonical flows.

Design of gum Arabic/gelatin composite microcapsules and their cosmetic applications in encapsulating tea tree essential oil

Microencapsulation has been widely used to protect essential oils, facilitating their application in cosmetics. In this study, gelatin, gum arabic and n-butyl cyanoacrylate were used as wall materials, and composite microcapsules of tea tree essential oil (TTO) were prepared using a combination of composite coagulation and in situ polymerization methods. When the ratio of gelatin to gum arabic is 1 : 1, the ratio of TTO to n-butyl cyanoacrylate is 4 : 1, the curing time is 10 h, and the encapsulation efficiency (EE) under these conditions is 73.61%. Morphological observation showed that the composite capsule was a micron-sized spherical particle with an average particle size of 10.51 μm, and Fourier transform infrared spectroscopy (FT-IR) confirmed a complex coagulation reaction between gelatin and gum arabic, and the disappearance of the n-butyl cyanoacrylate peak indicated that the film was formed in a condensation layer. The thermogravimetric analysis (TGA) results showed that the composite capsule greatly improved the thermal stability of TTO. Rheological testing showed that the viscosity and viscoelasticity of the surface composite capsules have been improved. In addition, the composite capsule showed good stability in the osmotic environment and has good sustained-release performance and antioxidant capacity in the average human skin environment.

Investigating Fundamental Principles of Nonequilibrium Assembly Using Temperature-Sensitive Copolymers

Both natural biomaterials and synthetic materials benefit from complex energy landscapes that provide the foundation for structure-function relationships and environmental sensitivity. Understanding these nonequilibrium dynamics is important for the development of design principles to harness this behavior. Using a model system of poly(ethylene glycol) methacrylate-based thermoresponsive lower critical solution temperature (LCST) copolymers, we explored the impact of composition and stimulus path on nonequilibrium thermal hysteretic behavior. Through turbidimetry analysis of nonsuperimposable heat-cool cycles, we observe that LCST copolymers show clear hysteresis that varies as a function of pendent side chain length and hydrophobicity. Hysteresis is further impacted by the temperature ramp rate, as insoluble states can be kinetically trapped under optimized temperature protocols. This systematic study brings to light fundamental principles that can enable the harnessing of out-of-equilibrium effects in synthetic soft materials.

Shear induced tuning and memory effects in colloidal gels of rods and spheres

Shear history plays an important role in determining the linear and nonlinear rheological response of colloidal gels and can be used for tuning their structure and flow properties. Increasing the colloidal particle aspect ratio lowers the critical volume fraction for gelation due to an increase in the particle excluded volume. Using a combination of rheology and confocal microscopy, we investigate the effect of steady and oscillatory preshear history on the structure and rheology of colloidal gels formed by silica spheres and rods of length L and diameter D (L/D = 10) dispersed in 11 M CsCl solution. We use a non-dimensional Mason number, Mn (=F_visc./F_attr.), to compare the effect of steady and oscillatory preshear on gel viscoelasticity. We show that after preshearing at intermediate Mn, attractive sphere gel exhibits strengthening, whereas attractive rod gel exhibits weakening. Rheo-imaging of gels of attractive rods shows that at intermediate Mn, oscillatory preshear induces large compact rod clusters in the gel microstructure, compared to steady preshear. Our study highlights the impact of particle shape on gel structuring under flow and viscoelasticity after shear cessation.

Stress overshoot, hysteresis, and the Bauschinger effect in sheared dense colloidal suspensions

The mechanical nonlinear response of dense Brownian suspensions of polymer gel particles is studied experimentally and by means of numerical simulations. It is shown that the response to the application of a constant shear rate depends on the previous history of the suspension. When the flow starts from a suspension at rest, it exhibits an elastic response followed by a stress overshoot and then a plastic flow regime. Conversely, after flow reversal, the stress overshoot does not occur, and the apparent elastic modulus is reduced while numerical simulations reveal that the anisotropy of the local microstructure is delayed relative to the macroscopic stress.

Modulation of soft glassy dynamics in aqueous suspensions of an anisotropic charged swelling clay through pH adjustment

HYPOTHESIS

Sodium-montmorillonite (Na-Mt) particles are geometrically anisometric that carry a pH dependent anisotropic surface charge. Therefore, it should be possible to manipulate the particle-particle interaction of colloidal range Na-Mt suspensions through pH changes which in turn should alter the soft glassy dynamics of Na-Mt suspensions.

EXPERIMENTS

Rheological experiments were used to probe the impact of pH mediated colloidal particle-particle interaction on the physical aging, linear viscoelastic response, and yield stress behavior of Na-Mt suspension.

FINDINGS

The temporal evolution of the storage modulus (G') was stronger in the acid regime (pH < 9.5) than the base (pH ≥ 9.5) pH regime. Horizontal shifting of the aging curves in the acid and base regimes led to aging time-H⁺ concentration and aging time-OH^- concentration superposition. An aging time-Na-Mt concentration superposition was also observed in both pH regimes. The critical stress associated with the viscosity bifurcation behavior increased linearly with G' but with different slopes for acid and base regime. We propose that positively charged patches on the Na-Mt particle edge merge with the characteristic surface as a function of H⁺ ions in the system. This leads to a strongly associated microstructure at low pH and a relatively weak but associated microstructure at natural pH, hence confirming the hypothesis.

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. In this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

Physical aging in aqueous nematic gels of a swelling nanoclay: sol (phase) to gel (state) transition

Aqueous dispersions of geometrically anisometric, nano-sized sodium-montmorillonite (Na-Mt) display a sol-gel transition at very low solids concentrations. The microstructure of the gel formed at very low ionic strengths is considered electrostatically repulsive with a nematic character, and the gel state at ionic strengths where Debye length is of the order of particle size is conjectured to be free of physical aging. We investigated the nature of osmotically prepared Na-Mt dispersions at low ionic strength (∼10^-5 M), below and above the gel point. The sol phase exhibited very low yield stress compared to the gel state, without any sign of physical aging, thus behaving as an equilibrium state. In contrast, the gel exhibited signatures of physical aging, that is, an evolving microstructure that consolidated with time when left undisturbed thus behaving as out of equilibrium state. The physical aging behaviour became more pronounced at Na-Mt concentrations far above the gel point. A critical shear rate existed, below which no stable flows were possible in the gel state representing the microstructural reorganization timescale. Overall, Na-Mt dispersions in the gel state behave like systems that were out of equilibrium with an ever-evolving microstructure, in opposition to the assumption that low ionic strength Na-Mt gels are in an equilibrium phase. The possible origin of physical aging, such as the reversible orientation of Brownian anisotropic particles, stiffening of an existing microstructure, or reorganization of microstructure towards minimal energy configuration is discussed in detail.

Shear thickening behavior in dense repulsive and attractive suspensions of hard spheres

Shear thickening in stable dense colloidal suspensions is a reversible phenomenon and no hysteresis is observed in the flow curve measurements. However, a reduction in the stability of colloids promotes particle aggregation and introduces a time dependent rheological response. In this work, by using a model colloidal system of hard spherical silica particles (average diameter of 415 nm) with varying particle volume fractions 0.2 ≤ ϕ ≤ 0.56, we study the effect of particle stability on the hysteresis of the shear thickening behavior of these suspensions. The particle stability is manipulated by adding a simple monovalent salt (sodium chloride) in the silica suspension with varying concentrations α ∈ [0,0.5] M. For repulsive and weakly attractive suspensions, the flow behavior is history independent and the shear thickening behavior does not exhibit hysteresis. However, significant hysteresis is observed in rheological measurements for strongly attractive suspensions, with shear history playing a critical role due to the dynamic nature of particle clusters, resulting in time dependent hysteresis behavior. By performing numerical simulations, we find that this hysteresis behavior arises due to the competition among shear, electrostatic repulsive, van der Waals attractive, and frictional contact forces. The critical shear stress (i.e., the onset of shear thickening) decreases with increasing salt concentrations, which can be captured by a scaling relationship based on the force balance between particle-particle contact force and electrostatic repulsive force. Our combined experimental and simulation results imply the formation of particle contacts in our sheared suspensions.

Molecular and micro-scale heterogeneities in Raman modes of a relaxing polymer glass

We have used Raman spectroscopy to study relaxation dynamics at two different length scales, molecular level and micro-scale in order to probe the presence of cooperative rearranging regions in a polymer glass. Response to slow thermal cycles and fast quench through the glass transition temperature (T_g) is analyzed for film and unprocessed forms of polyvinyl acetate (PVAc). In PVAc film, enhanced disorder and molecular mobility lead to peak broadening by about a factor of 10 compared to unprocessed PVAc. Thermal cycles (10 K min^-1) produce hysteresis in integrated Raman peak intensity (loop areaAINTI).AINTIvalues of film are two orders of magnitude more than unprocessed, indicating more configurational mosaics with higher interfacial energy dissipations. Ageing after 60 K min^-1quench manifests as heterogeneous molecular dynamics of film Raman modes with significant peak-width variations, differentiating high mobility and low mobility modes. Two-dimensional mapping of film Raman modes after quench reveal micro-scale clusters of average size ≈250 molecules having fractal boundaries with fractal dimensiond_f= 1.5, resemblingd_fof percolation clusters below percolation threshold. During thermal cycling and relaxation after a quench, cooperative segmental dynamics with large correlations between skeletal C-C stretch and side branch modes is observed. The observations are analyzed in the context of the random first order transition theory of glasses, which attributes heterogeneous relaxations in glasses to the presence of clusters of variable configurational states.

Rheology-Informed Neural Networks (RhINNs) for forward and inverse metamodelling of complex fluids

Reliable and accurate prediction of complex fluids’ response under flow is of great interest across many disciplines, from biological systems to virtually all soft materials. The challenge is to solve non-trivial time and rate dependent constitutive equations to describe these structured fluids under various flow protocols. We present Rheology-Informed Neural Networks (RhINNs) for solving systems of Ordinary Differential Equations (ODEs) adopted for complex fluids. The proposed RhINNs are employed to solve the constitutive models with multiple ODEs by benefiting from Automatic Differentiation in neural networks. In a direct solution, the RhINNs platform accurately predicts the fully resolved solution of constitutive equations for a Thixotropic-Elasto-Visco-Plastic (TEVP) complex fluid for a series of flow protocols. From a practical perspective, an exhaustive list of experiments are required to identify model parameters for a multi-variant constitutive TEVP model. RhINNs are found to learn these non-trivial model parameters for a complex material using a single flow protocol, enabling accurate modeling with limited number of experiments and at an unprecedented rate. We also show the RhINNs are not limited to a specific model and can be extended to include various models and recover complex manifestations of kinematic heterogeneities and transient shear banding of thixotropic fluids.

Simple production of cellulose nanofibril microcapsules and the rheology of their suspensions

Microcapsules are commonly used in applications ranging from therapeutics to personal care products due to their ability to deliver encapsulated species through their porous shells. Here, we demonstrate a simple and scalable approach to fabricate microcapsules with porous shells by interfacial complexation of cellulose nanofibrils and oleylamine, and investigate the rheological properties of suspensions of the resulting microcapsules. The suspensions of neat capsules are viscous liquids whose viscosity increases with volume fraction according to a modified Kreiger-Dougherty relation with a maximum packing fraction of 0.74 and an intrinsic viscosity of 4.1. When polyacrylic acid (PAA) is added to the internal phase of the microcapsules, however, the suspensions become elastic and display yield stresses with power-law dependencies on capsule volume fraction and PAA concentration. The elasticity appears to originate from associative microcapsule interactions induced by PAA that is contained within and incorporated into the microcapsule shell. These results demonstrate that it is possible to tune the rheological properties of microcapsule suspensions by changing only the composition of the internal phase, thereby providing a novel method to tailor complex fluid rheology.

Simultaneous memory effects in the stress and in the dielectric susceptibility of a stretched polymer glass

We report experimental evidence that a polymer stretched at constant strain rate λ[over ̇] presents complex memory effects after λ[over ̇] is set to zero at a specific strain λ_{w} for a duration t_{w}, ranging from 100s to 2.2×10^{5}s. When the strain rate is resumed, both the stress and the dielectric constant relax to the unperturbed state nonmonotonically. The relaxations depend on the observable, on λ_{w} and on t_{w}. Relaxation master curves are obtained by scaling the time and the amplitudes by ln(t_{w}). The dielectric evolution also captures the distribution of the relaxation times, so the results impose strong constraints on the relaxation models of polymers under stress and they can be useful for a better understanding of memory effects in other disorder materials.

Rheological characterization of CNC-CTAB network below and above critical micelle concentration (CMC)

The network of Cellulose Nanocrystal (CNC) suspension is explored below and above the critical micelle concentration (CMC), in the presence of cetyltrimethylammonium bromide (CTAB) with a positively charged head using TEM imaging and rheological characterization. CNC-CTAB gels show shear thinning behavior, complex relationship between strain amplitudes and CTAB concentration, diminishing thixotropic behavior as a function of CTAB and single and two yielding stress maxima as a function of CTAB, resulting from different microstructure below and above the critical Micelle Concentration (CMC) of CTAB. Comparing the flow curves of CNC-CTAB suspension/gel revealed the role played by CTAB content, CNC concentration and sonication energy in strengthening of the network. We analyzed and obtained yield stress from steady shear, creep testing and oscillatory experiments and compared them.

Signatures of Overaging in an Aqueous Dispersion of Carbopol

In this work, we study the effect of the deformation field on the physical aging behavior of an aqueous Carbopol dispersion. It is composed of soft swollen particles of gel that get deformed and acquire a polygonal shape, with flat interfaces rendering the dispersion a soft solid-like consistency as filled volume fraction approaches unity. It has been proposed that owing to release of stored elastic energy in the deformed particles, Carbopol dispersion undergoes microstructural evolution that is reminiscent of physical aging in soft glassy materials. We observe that application of moderate magnitude of oscillatory strain to Carbopol dispersion slows down its relaxation dynamics, thereby showing characteristics of overaging. On the other hand, the sufficiently high magnitude of strain makes the relaxation dynamics faster, causing rejuvenation. We also solve the soft glassy rheology model, which, when subjected to the same flow field, corroborates with experimental observations on the Carbopol dispersion. This behavior, therefore, suggests that in a system of jammed soft particles of Carbopol, the particles occupying shallow energy wells upon application of moderate strain field adjust themselves in such a manner that they predominantly occupy the deeper energy wells leading to observe the overaging dynamics.

Investigation of the swollen state of Carbopol molecules in non-aqueous solvents through rheological characterization

We explore how different types of solvent influence the rheological properties of non-aqueous Carbopol dispersions from the dilute to the jammed state. In novel non-aqueous formulations, polar solvents are used more and more frequently, because they can form Carbopol microgels without the need of any neutralizing agents. However, the swelling behaviour of Carbopol molecules in the absence of water, when ionic forces are weak, is still poorly understood. To this end, we study the swelling behaviour of Carbopol 974P NF in different polar solvents, i.e. glycerol, PEG400 and mixtures of the two solvents, by mapping the rheological behaviour of Carbopol suspensions from very dilute to highly concentrated conditions. The rheological study reveals that the onset of the jamming transition occurs at different critical polymer concentrations depending on the solvents used. Nevertheless, once the jammed state is reached, both elastic and yielding behaviours are scalable with the particle volume fraction. These results suggest that the type of solvent influences the final volume of the single Carbopol particles but does not alter the interactions between the particles. The final radius of the swollen particles is estimated from shear rheology measurements in dilute conditions, showing a decrease of the final swelling ratio of Carbopol molecules of almost 50% for PEG400 solutions, a result that confirms the shift to higher values of the critical jamming concentration obtained from linear viscoelasticity for the same solutions.

Interparticle attraction controls flow heterogeneity in calcite gels

We couple rheometry and ultrasonic velocimetry to study experimentally the flow behavior of gels of colloidal calcite particles dispersed in water, while tuning the strength of the interparticle attraction through physico-chemistry. We unveil, for the first time in a colloidal gel, a direct connection between attractive interactions and the occurrence of shear bands, as well as stress fluctuations.

How clay particulates affect flow cessation and the coiling stability of yield stress-matched cementing suspensions

The remarkable increase in the flow resistance of dense suspensions can hinder 3D-printing processes on account of flow cessation in the extruder, and filament fragility/rupture following deposition. Understanding the nature of rheological changes that occur is critical to manipulate flow conditions or to dose flow modifiers for 3D-printing. Therefore, this paper elucidates the influences of clay particulates on controlling flow cessation and the shape stability of dense cementing suspensions that typically feature poor printability. A rope coiling method was implemented with varying stand-off distances to probe the buckling stability and tendency to fracture of dense suspensions that undergo stretching and bending during deposition. The contributions of flocculation and short-term percolation due to the kinetics of structure formation to deformation rate were deconvoluted using a stepped isostress method. It is shown that the shear stress indicates a divergence with a power-law scaling when the particle volume fraction approaches the jamming limit; φ → φj ≈ φmax. Such a power-law divergence of the shear stress decreases by a factor of 10 with increasing clay dosage. Such behavior in clay-containing suspensions arises from a decrease in the relative packing fraction (φ/φmax) and the formation of fractally-architected aggregates with stronger interparticle interactions, whose uniform arrangement controls flow cessation in the extruder and suspension homogeneity, thereby imparting greater buckling stability. The outcomes offer new insights for assessing/improving the extrudability and printability behavior during slurry-based 3D-printing process.

Multiscale Nature of Thixotropy and Rheological Hysteresis in Attractive Colloidal Suspensions under Shear

Colloids with short range attractions self-assemble into sample-spanning structures, whose dynamic nature results in a thermokinematic memory of the deformation history, also referred to as "thixotropy." Here, we study the origins of the thixotropic effect in these time- and rate-dependent materials by investigating hysteresis across different length scales: from particle-level local measurements of coordination number (microscale), to the appearance of density and velocity fluctuations (mesoscale), and up to the shear stress response to an imposed deformation (macroscale). The characteristic time constants at each scale become progressively shorter, and hysteretic effects become more significant as we increase the strength of the interparticle attraction. There are also strong correlations between the thixotropic effects we observe at each scale.

Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear

We study the rheological responses and shear-rate inhomogeneities and shear banding behaviors of a thixotropic fumed silica suspension in shear startup tests and flow reversal tests. We find that this suspension under transient shear exhibits not only viscoelasticity, yielding, kinematic hardening, and thixotropy, but also time-dependent shear inhomogeneities including bands when the apparent shear rate is below a critical value between 0.1 and 0.25 s-1. Through multiple shear startup tests and flow reversal tests, we find that thixotropy promotes flow heterogeneity while kinematic hardening suppresses it. We propose a simple thixo-plastic constitutive equation that can qualitatively predict the important features of the rheological response and banding dynamics in shear startup tests and flow reversal tests.

Multi-block analysis for the correlation of physico-chemical and rheological data of 42 fruit pulps

The common dimension (ComDim) chemometric method for multi-block analysis and hierarchical cluster analysis (HCA) were used to evaluate the data obtained from the physico-chemical and rheological characterization of 42 commercial fruit pulps. The physico-chemical characteristics and the rheological behavior of the pulps were found to be considerably different. The Herschel-Bulkley equation was fit to the steady-state flow curves of the fruit pulps, and it was found to appropriately describe the materials, which showed a wide range of yield stresses. The soluble solids content and the yield stress were the main factors responsible for the sample discrimination in the multivariate statistical analysis. The ComDim model indicates that these parameters may have a direct correlation. Namely, the soluble solids amount can influence the viscosity, as demonstrated by the similar scores of the samples in both common components, and this corroborated with the HCA analysis. PRACTICAL APPLICATIONS: Fruit pulps can be used as raw materials in the food industry to obtain several products, such as nectars, jellies, ice creams, and juices, which can also be sold directly to consumers. To evaluate the technical and economic feasibility of those industrial processes, it is important to know the physico-chemical properties of the products. Therefore, in this study we attempt to correlate the physical-chemical and rheological data using a new statistical approach.

Dynamic Behavior of Dilute Bentonite Suspensions under Different Chemical Conditions Studied via Magnetic Resonance Imaging Velocimetry

This study investigates dilute aqueous suspensions of bentonite particles using magnetic resonance imaging (MRI) velocimetry. Four different chemical conditions are tested to investigate the influence of pH and type of monovalent electrolyte on the local rheological behavior of bentonite suspensions. The results indicate the shear banding in a dilute suspension of 0.1 vol.% solid due to the formation of a continuous three-dimensional particle network under a certain chemical environment (i.e., pH 4 in 1 × 10−2 M KNO3). This network is responsible for the existence of the yield stress in that dilute suspension. Structural changes induced by modification of suspensions’ chemistry are examined via scanning electron microscopy. A previously established method based on processing the torques acquired via conventional rheometric measurement is also applied as an alternative way to recover local flow information. Within the shear rate range covered by our MRI velocimetry, the results of both methods show good agreement. This study suggests that the existence of a master curve (or global flow curve) for dilute suspensions is dependent on the bentonite particle organization, which is influenced by the suspension chemistry and the previous flow history.

Stable small bubble clusters in two-dimensional foams

Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio σ_L/σ_S ≃ 1.4. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

Understanding rheological hysteresis in soft glassy materials

Motivated by recent experimental studies of rheological hysteresis in soft glassy materials, we study numerically strain rate sweeps in simple yield stress fluids and viscosity bifurcating yield stress fluids. Our simulations of downward followed by upward strain rate sweeps, performed within fluidity models and the soft glassy rheology model, successfully capture the experimentally observed monotonic decrease of the area of the rheological hysteresis loop with sweep time in simple yield stress fluids, and the bell shaped dependence of hysteresis loop area on sweep time in viscosity bifurcating fluids. We provide arguments explaining these two different functional forms in terms of differing tendencies of simple and viscosity bifurcating fluids to form shear bands during the sweeps, and show that the banding behaviour captured by our simulations indeed agrees with that reported experimentally. We also discuss the difference in hysteresis behaviour between inelastic and viscoelastic fluids. Our simulations qualitatively agree with the experimental data discussed here for four different soft glassy materials.

Morphology of viscoplastic drop impact on viscoplastic surfaces

The impact of viscoplastic drops onto viscoplastic substrates characterized by different magnitudes of the yield stress is investigated experimentally. The interaction between viscoplastic drops and surfaces has an important application in additive manufacturing, where a fresh layer of material is deposited on a partially cured or dried layer of the same material. So far, no systematic studies on this subject have been reported in literature. The impact morphology of different drop/substrate combinations, with yield stresses ranging from 1.13 Pa to 11.7 Pa, was studied by high speed imaging for impact Weber numbers between 15 and 85. Experimental data were compared with one of the existing models for Newtonian drop impact onto liquid surfaces. Results show the magnitude of the yield stress of drop/substrate strongly affects the final shape of the impacting drop, permanently deformed at the end of impact. The comparison between experimental data and model predictions suggests the crater evolution model is only valid when predicting the evolution of the crater at sufficiently high Weber numbers.

Structural fingerprints of yielding mechanisms in attractive colloidal gels

Core-Modified Dissipative Particle Dynamics (CM-DPD) with a modified depletion potential and full hydrodynamics description is used to study non-equilibrium properties of colloidal gels with short range attraction potentials at an intermediate volume fraction (ϕ = 0.2) under start-up shear deformation. Full structural and rheological analysis using the stress fabric tensor complemented by bond number and bond distribution evolution under flow reveals that similarly to dilute colloidal gels, flow-induced anisotropy and strain-induced stretching of bonds are present during the first yielding transition. Unlike in low volume fraction depletion gels however, a small fraction of bond dissociation is required to facilitate bond rotation at intermediate volume fractions. The strain at which structural stretching and anisotropy in bond distribution emerge coincides with the first maximum in the shear stress (first yielding transition). At higher strains, depending on flow strength, a second peak in stress signal appears which is attributed to the compaction and melting of clusters. In this work, for the first time we provide evidence that multibody hydrodynamic interactions are essential to predict the correct dynamics of depletion gels under flow, namely two-step yielding process.

Athermal rheology of weakly attractive soft particles

We study the rheology of a soft particulate system where the interparticle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions (ϕ), attraction strengths (u), and imposed shear rates (γ[over ̇]). In striking contrast to repulsive systems, we find that at small shear rates generically a fragile isostatic solid is formed even if we go to ϕ≪ϕ_{J}. Further, with increasing shear rates, even at these low ϕ, nonmonotonic flow curves occur which lead to the formation of persistent shear bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough ϕ, we also observe structural changes via the interplay of low shear rates and attraction with the formation of microclusters and voids. Finally, we characterize the properties of the emergent shear bands, and thereby, we find surprisingly small mobility of these bands, leading to prohibitively long time scales and extensive history effects in ramping experiments.

Soft hydrated sliding interfaces as complex fluids

Hydrogel surfaces are biomimics for sensing and mobility systems in the body such as the eyes and large joints due to their important characteristics of flexibility, permeability, and integrated aqueous component. Recent studies have shown polymer concentration gradients resulting in a less dense region in the top micrometers of the surface. Under shear, this gradient is hypothesized to drive lubrication behavior due to its rheological similarity to a semi-dilute polymer solution. In this work we map 3 distinct lubricating regimes between a polyacrylamide surface and an aluminum annulus using stepped-velocity tribo-rheometry over 5 decades of sliding speed in increasing and decreasing steps. These regimes, characterized by weakly or strongly time-dependent response and thixotropy-like hysteresis, provide the skeleton of a lubrication curve for hydrogel-against-hard material interfaces and support hypotheses of polymer mechanics-driven lubrication. Tribo-rheometry is particularly suited to uncover the lubrication mechanisms of complex interfaces such as are formed with hydrated hydrogel surfaces and biological surfaces.

Micro-mechanics of electrostatically stabilized suspensions of cellulose nanofibrils under steady state shear flow

In this study, we characterized and modeled the rheology of TEMPO-oxidized cellulose nanofibril (NFC) aqueous suspensions with electrostatically stabilized and unflocculated nanofibrous structures. These colloidal suspensions of slender and wavy nanofibers exhibited a yield stress and a shear thinning behavior at low and high shear rates, respectively. Both the shear yield stress and the consistency of these suspensions were power-law functions of the NFC volume fraction. We developed an original multiscale model for the prediction of the rheology of these suspensions. At the nanoscale, the suspensions were described as concentrated systems where NFCs interacted with the Newtonian suspending fluid through Brownian motion and long range fluid-NFC hydrodynamic interactions, as well as with each other through short range hydrodynamic and repulsive colloidal interaction forces. These forces were estimated using both the experimental results and 3D networks of NFCs that were numerically generated to mimic the nanostructures of NFC suspensions under shear flow. They were in good agreement with theoretical and measured forces for model colloidal systems. The model showed the primary role played by short range hydrodynamic and colloidal interactions on the rheology of NFC suspensions. At low shear rates, the origin of the yield stress of NFC suspensions was attributed to the combined contribution of repulsive colloidal interactions and the topology of the entangled NFC networks in the suspensions. At high shear rates, both concurrent colloidal and short (in some cases long) range hydrodynamic interactions could be at the origin of the shear thinning behavior of NFC suspensions.

Avalanche-like fluidization of a non-Brownian particle gel

We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age for a time tw before being subjected to a constant shear rate [small gamma, Greek, dot above]. We investigate in detail the effects of both tw and [small gamma, Greek, dot above] on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may display either transient shear banding towards complete fluidization or steady-state shear banding. In the former case, we unravel that the progressive fluidization occurs by successive steps that appear as peaks on the global stress relaxation signal. Flow imaging reveals that the shear band grows until complete fluidization of the material by sudden avalanche-like events which are distributed heterogeneously along the vorticity direction and correlated to large peaks in the slip velocity at the moving wall. These features are robust over a wide range of tw and [small gamma, Greek, dot above] values, although the very details of the fluidization scenario vary with [small gamma, Greek, dot above]. Finally, the critical shear rate [small gamma, Greek, dot above]* that separates steady-state shear-banding from steady-state homogeneous flow depends on the width of the shear cell and exhibits a nonlinear dependence with tw. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging whose modeling constitutes a major challenge that has not been met yet.

Hysteresis of inertial cavitation activity induced by fluctuating bubble size distribution

Amongst the variety of complex phenomena encountered in nonlinear physics, a hysteretic effect can be expected on ultrasound cavitation due to the intrinsic nonlinearity of bubble dynamics. When applying successive ultrasound shots for increasing and decreasing acoustic intensities, a hysteretic behaviour is experimentally observed on inertial cavitation activity, with a loop area sensitive to the inertial cavitation threshold. To get a better insight of the phenomena underlying this hysteretic effect, the evolution of the bubble size distribution is studied numerically by implementing rectified diffusion, fragmentation process, rising and dissolution of bubbles from an initial bubble size distribution. When applying increasing and decreasing acoustic intensities, the numerical distribution exhibits asymmetry in bubble number and distribution. The resulting inertial cavitation activity is assessed through the numerical broadband noise of the emitted acoustic radiation of the bubble cloud dynamics. This approach allows obtaining qualitatively the observed hysteretic effect and its interest in terms of control is discussed.

A microscopic Gibbs field model for the macroscopic yielding behaviour of a viscoplastic fluid

We present a Gibbs random field model for the microscopic interactions in a viscoplastic fluid. The model has only two parameters which are sufficient to describe the internal energy of the material in the absence of external stress and a third parameter for a constant externally applied stress. The energy function is derived from the Gibbs potential in terms of the external stress and internal energy. The resulting Gibbs distribution, over a configuration space of microscopic interactions, can mimic experimentally observed macroscopic behavioural phenomena that depend on the externally applied stress. A simulation algorithm that can be used to approximate samples from the Gibbs distribution is given and it is used to gain several insights about the model. Corresponding to weak interactions between the microscopic solid units, our model reveals a smooth solid-fluid transition which is fully reversible upon increasing/decreasing external stresses. If the interaction between neighbouring microscopic constituents exceeds a critical threshold the solid-fluid transition becomes abrupt and a hysteresis of the deformation states is observed even at the asymptotic limit of steady forcing. Quite remarkably, in spite of the limited number of parameters involved, the predictions of our model are in a good qualitative agreement with macro rheological experimental results on the solid-fluid transition in various yield stress materials subjected to an external stress.

Heterogeneous flow kinematics of cellulose nanofibril suspensions under shear

The rheology of NFC suspensions that exhibited different microstructures and colloidal stability, namely TEMPO and enzymatic NFC suspensions, was investigated at the macro and mesoscales using a transparent Couette rheometer combined with optical observations and ultrasonic speckle velocimetry (USV). Both NFC suspensions showed a complex rheology, which was typical of yield stress, non-linear and thixotropic fluids. Hysteresis loops and erratic evolutions of the macroscale shear stress were also observed, thereby suggesting important mesostructural changes and/or inhomogeneous flow conditions. The in situ optical observations revealed drastic mesostructural changes for the enzymatic NFC suspensions, whereas the TEMPO NFC suspensions did not exhibit mesoscale heterogeneities. However, for both suspensions, USV measurements showed that the flow was heterogeneous and exhibited complex situations with the coexistence of multiple flow bands, wall slippage and possibly multidimensional effects. Using USV measurements, we also showed that the fluidization of these suspensions could presumably be attributed to a progressive and spatially heterogeneous transition from a solid-like to a liquid-like behavior. As the shear rate was increased, the multiple coexisting shear bands progressively enlarged and nearly completely spanned over the rheometer gap, whereas the plug-like flow bands were eroded.

From colloidal spheres to nanofibrils: extensional flow properties of mineral pigment and mixtures with micro and nanofibrils under progressive double layer suppression

Suspensions of mineral pigment and cellulose fibrillar derivatives are materials regularly found in the forest products industries, particularly in paper and board production. Many manufacturing processes, including forming and coating employ flow geometries incorporating extensional flow. Traditionally, colloidal mineral pigment suspensions have been considered to show little to no non-linear behaviour in extensional viscosity. Additionally, recently, nanofibrillar materials, such as microfibrillar (MFC) and nanofibrillar cellulose (NFC), collectively termed MNFC, have been confirmed by their failure to follow the Cox-Merz rule to behave more as particulate material rather than showing polymeric rheological properties when dispersed in water. Such suspensions and their mixtures are currently intensively investigated to enable them to generate likely enhanced composite material properties. The processes frequently involve exposure to increasing levels of ionic strength, coming either from the weak solubility of pigments, such as calcium carbonate, or retained salts arising from the feed fibre source processing. By taking the simple case of polyacrylate stabilised calcium carbonate suspension and comparing the extensional viscosity as a function of post extension capillary-induced Hencky strain on a CaBER extensional rheometer over a range of increasing salt concentration, it has been shown that the regime of constriction changes as the classic DLVO double layer is progressively suppressed. This change is seen to lead to a characteristic double (bimodal) measured viscosity response for flocculated systems. With this novel characteristic established, more complex mixed suspensions of calcium carbonate, clay and MNFC have been studied, and the effects of fibrils versus flocculation identified and where possible separated. This technique is suggested to enable a better understanding of the origin of viscoelasticity in these important emerging water-based suspensions.

Dynamic hysteresis in the rheology of complex fluids

Recently, rheological hysteresis has been studied systematically in a wide range of complex fluids combining global rheology and time-resolved velocimetry. In this paper we present an analysis of the roles of the three most fundamental mechanisms in simple-yield-stress fluids: structure dynamics, viscoelastic response, and spatial flow heterogeneities, i.e., time-dependent shear bands. Dynamical hysteresis simulations are done analogously to rheological ramp-up and -down experiments on a coupled model which incorporates viscoelasticity and time-dependent structure evolution. Based on experimental data, a coupling between hysteresis measured from the local velocity profiles and that measured from the global flow curve has been suggested. According to the present model, even if transient shear banding appears during the shear ramps, in typical narrow-gap devices, only a small part of the hysteretic response can be attributed to heterogeneous flow. This results in decoupling of the hysteresis measured from the local velocity profiles and the global flow curve, demonstrating that for an arbitrary time-dependent rheological response this proposed coupling can be very weak.