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Due to rich rheological properties, dispersions of attractive colloidal particles are ubiquitous in industries. Specifically, upon experiencing a sudden reduction in shear rate, these dispersions may exhibit transient behaviors such as thixotropy-where viscosity increases over time-and anti-thixotropy, characterized by an initial viscosity decrease before reaching a steady state. While thixotropy has been described as a competition between structure buildup and disruption, the mechanisms of anti-thixotropy remain poorly understood. Here, we investigate the anti-thixotropic dynamics of carbon black particles dispersed in oil-a system known for exhibiting anti-thixotropy-through flow step-down experiments. Using a multi-technique approach combining rheology with velocimetry and structural characterizations, we show that viscosity decrease results from a decrease in wall slip concomitant to shear-induced structural rearrangements, indicating a transition from a dynamical network of fractal clusters into a network of loosely connected dense agglomerates. Additionally, after a characteristic anti-thixotropic time $\tau$, a steady flow is reached. This time $\tau$ diverges with increasing shear rate at a critical value corresponding to a Mason number of one, indicating that anti-thixotropy occurs only when colloidal attraction outweighs viscous forces. More precisely, we show that the structural rearrangement underpinning the viscosity decrease is mediated by elastic stresses $\sigma_e$, such that $\tau \propto \sigma_e^{-3}$. Finally, on long time scales, the steady state is linked to a microstructure with nearly zero yield stress, indicating a loss of flow memory. These findings provide a mechanism for anti-thixotropy and suggest pathways for controlling viscosity and yield stress in attractive colloidal dispersions.

Soft particulate glasses are dense suspensions of jammed particles that flow like liquids under external shear and recover their solid-like properties almost instantly upon flow cessation. Here, we consider a dense suspension of core-shell attractive particles whose polymer brush allows for a delayed recovery that we monitor by time-resolved mechanical spectroscopy. Viscoelastic spectra recorded upon flow cessation show a striking power-law behavior and can be rescaled onto a master curve that hints at a time-connectivity superposition principle. Additionally, the non-linear response of this soft glass, measured at various aging times, shows a ductile-to-brittle transition, which suggests that the interactions between the particles display a progressive repulsive-to-attractive transition. These results depict an original scenario for the delayed recovery involving a time-dependent interaction potential in which attractive hydrophobic forces are only activated when neighboring particles deform their polymer shell and come in close contact., Comment: 6 pages, 5 figures

The present work emphasizes the relevance of low-field NMR relaxometry to investigate colloid-polymer hydrogels by probing water dynamics across a wide range of formulations between $\rm 10^{\circ}C$ and $\rm 80^{\circ}C$. By examining the temperature dependence of the transverse relaxation time $T_2$, we demonstrate a clear link between the NMR response and the rheological behavior of the hydrogels. In particular, we show that NMR relaxometry targeting the solvent provides reliable insights into the hydrogel microstructure and allows the detection of phase transitions and aging processes. Our findings suggest that this solvent-focused technique could greatly benefit the soft matter community, complementing other experimental methods in the study of gels., Comment: 6 pages, 4 figures

Cellulose ethers represent a class of water-soluble polymers widely utilized across diverse sectors, spanning from healthcare to the construction industry. This experimental study specifically delves into aqueous suspensions of carboxymethylcellulose (CMC), a polymer that undergoes gel formation in acidic environments due to attractive interactions between hydrophobic patches along its molecular chain. We use rheometry to determine the linear viscoelastic properties of both CMC suspensions and acid-induced gels at various temperatures. Then, applying the time-temperature superposition principle, we construct master curves for the viscoelastic spectra, effectively described by fractional models. The horizontal shift factors exhibit an Arrhenius-like temperature dependence, allowing us to extract activation energies compatible with hydrophobic interactions. Furthermore, we show that acid-induced CMC gels are physical gels that display a reversible yielding transition under external shear. In particular, we discuss the influence of pH on the non-linear viscoelastic response under large-amplitude oscillatory shear. Overall, our results offer a comprehensive description of the linear and non-linear rheological properties of a compelling case of physical hydrogel involving hydrophobic interactions., Comment: 23 pages, 9 figures

Colloidal gels undergo a phenomenon known as physical aging, i.e., a continuous change of their physical properties with time after the gel point. To date, most of the research effort on aging in gels has been focused on suspensions of hard colloidal particles. In this letter, we tackle the case of soft colloidal "micelles" comprised of proteins, where gelation is induced by the addition of an enzyme. Using time-resolved mechanical spectroscopy, we monitor the viscoelastic properties of a suspension of colloidal micelles through the sol-gel transition and its subsequent aging. We show that the microscopic scenario underpinning the macroscopic aging dynamics comprises two sequential steps. First, the gel microstructure undergoes rapid coarsening, as observed by optical microscopy, followed by arrest. Second, aging occurs solely through a contact-driven mechanism, as evidenced by the square-root dependence of the yield stress with the elastic modulus measured at different ages of the gel. These results provide a comprehensive understanding of aging in enzymatic milk gels, which is crucial not only for a broad range of dairy products, but also for soft colloids in general.

The efficiency of supported catalysts depends on the porous microstructure of their solid support, which regulates mass transfer, exposure to the active phase, and mechanical strength. Here, we focus on the manufacturing of a specific type of catalytic support, $\gamma$-alumina extrudates, by a kneading-extrusion process. In this process, a paste is initially formed by blending and subsequently kneading a boehmite powder, an aluminum oxide hydroxide precursor of $\gamma$-alumina, with various liquids before undergoing extrusion. The crucial step in this process is the kneading step, which allows control over the textural and mechanical properties of the extrudate. The present experimental study aims to measure the impact of the kneading step on boehmite pastes prepared using a pilot kneader. The pastes are obtained by mixing boehmite powder with an acid and a basic solution in a two-step process known as peptization and neutralization. In this study, kneading is conducted at various mixing speeds and durations while monitoring the torque exerted by the boehmite paste on the kneader blades. Moreover, samples are extracted from the pilot kneader at various stages of the kneading process, and their textural properties are determined by both nitrogen sorption and mercury intrusion porosimetry. Our findings show that, at fixed composition, the textural properties of boehmite pastes are controlled by the overall deformation accumulated during kneading. Conversely, for a fixed accumulated deformation, the pH sets the textural properties. Finally, we identify an empirical control parameter that captures the combined effects of pH and accumulated deformation on the key textural attributes of boehmite pastes. These results set the stage for a systematic design approach of boehmite-based catalyst supports., Comment: 14 pages, 13 figures

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., Comment: 21 pages, 7 figures, perspective on the workshop 'Yield stress and fluidization in brittle and ductile amorphous systems' held from January 9 to 13, 2023 at the Lorentz Center in Leiden

The present work offers a comprehensive description of the acid-induced gelation of carboxymethylcellulose (CMC), a water-soluble derivative of cellulose broadly used in numerous applications ranging from food packaging to biomedical engineering. Linear viscoelastic properties measured at various pH and CMC contents allow us to build a sol-gel phase diagram, and show that CMC gels exhibit broad power-law viscoelastic spectra that can be rescaled onto a master curve following a time-composition superposition principle. These results demonstrate the microstructural self-similarity of CMC gels, and inspire a mean-field model based on hydrophobic inter-chain association that accounts for the sol-gel boundary over the entire range of CMC content under study. Neutron scattering experiments further confirm this picture and suggest that CMC gels comprise a fibrous network crosslinked by aggregates. Finally, low-field NMR measurements offer an original signature of acid-induced gelation from the solvent perspective. Altogether, these results open avenues for precise manipulation and control of CMC-based hydrogels., Comment: 7 pages, 4 figures and 4 figures as SI

We use time-resolved mechanical spectroscopy to offer a detailed picture of the gelation dynamics of cellulose nanocrystal (CNC) suspensions following shear cessation in the presence of salt. CNCs are charged, rodlike colloids that self-assemble into various phases, including physical gels serving as soft precursors for biosourced composites. Here, a series of linear viscoelastic spectra acquired across the sol-gel transition of CNC suspensions are rescaled onto two master curves, that correspond to a viscoelastic liquid state prior to gelation and to a soft solid state after gelation. These two states are separated by a critical gel point, where all rescaling parameters diverge in an asymmetric fashion, yet with exponents that obey hyperscaling relations consistent with previous works on isotropic colloids and polymer gels. Upon varying the salt content, we further show that these critical-like dynamics result in both time-connectivity and time-concentration superposition principles., Comment: 8 pages, 3 figures, supplementary information (2 pages, 2 figures, 2 tables)

Boehmite, an aluminum oxide hydroxide $\gamma$-AlO(OH), is broadly used in the form of particulate dispersions in industrial applications, e.g., for the fabrication of ceramics and catalyst supports or as a binder for extrusion processes. Under acidic conditions, colloidal boehmite dispersions at rest form gels, i.e., space-spanning percolated networks that behave as soft solids at rest, and yet yield and flow like liquids under large enough deformations. Like many other colloidal gels, the solid-like properties of boehmite gels at rest are very sensitive to their previous mechanical history. Our recent work [Sudreau et al., J. Rheol. 66, 91-104 (2022), and Phys. Rev. Material 6, L042601 (2022)] has revealed such \textit{memory effects}, where the shear experienced prior to flow cessation drives the elasticity of boehmite gels: while gels formed following application of a shear rate $\dot\gamma_{\rm p}$ larger than a critical value $\dot\gamma_{\rm c}$ are insensitive to shear history, gels formed after application of $\dot\gamma_{\rm p}<\dot\gamma_{\rm c}$ display reinforced viscoelastic properties and non-negligible residual stresses. Here, we provide a microstructural scenario for these striking observations by coupling rheometry and small-angle X-ray scattering. Time-resolved measurements for $\dot\gamma_{\rm p} <\dot\gamma_{\rm c}$ show that scattering patterns develop an anisotropic shape that persists upon flow cessation, whereas gels exposed to $\dot\gamma_{\rm p}>\dot\gamma_{\rm c}$ display isotropic scattering patterns upon flow cessation. Moreover, as the shear rate applied prior to flow cessation is decreased below $\dot\gamma_{\rm c}$, the level of anisotropy frozen in the sample microstructure grows similarly to the viscoelastic properties, thus providing a direct link between mechanical reinforcement and flow-induced microstructural anisotropy., Comment: 13 pages, 10 figures

Soft particulate gels include materials we can eat, squeeze, or 3D print. From foods to bio-inks to cement hydrates, these gels are composed of a small amount of particulate matter (proteins, polymers, colloidal particles, or agglomerates of various origins) embedded in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction $\phi$: however, the diverse range of different functional dependencies reported experimentally has, to date, challenged efforts to identify general scaling laws. Here we reveal a hidden hierarchical organization of fractal elements that controls the viscoelastic spectrum, and which is associated with the spatial heterogeneity of the solid matrix topology. The fractal elements form the foundations of a viscoelastic master curve, which we construct using large-scale 3D microscopic simulations of model gels, and can be described by a recursive rheological ladder model over a range of particle volume fractions and gelation rates. The hierarchy of the fractal elements provides the missing general framework required to predict the gel elasticity and the viscoelastic response of these ubiquitous complex materials.

Nanocomposites formed by mixing nanoparticles and polymers offer a limitless creative space for the design of functional advanced materials with a broad range of applications in materials and biological sciences. Here we focus on aqueous dispersions of hydrophobic colloidal soot particles, namely carbon black (CB) dispersed with a sodium salt of carboxymethylcellulose (CMC), a food additive known as cellulose gum that bears hydrophobic groups, which are liable to bind physically to CB particles. Varying the relative content of CB nanoparticles and cellulose gum allows us to explore a rich phase diagram that includes a gel phase. We investigate this hydrogel using rheometry and electrochemical impedance spectroscopy. CB-CMC hydrogels display two radically different types of mechanical behaviors that are separated by a critical CMC-to-CB mass ratio $r_c$. For $rr_c$ CB-CMC gels display a power-law viscoelastic spectrum that depends strongly on the CMC concentration. These relaxation spectra can be rescaled onto a master curve that exhibits a power-law scaling in the high-frequency limit, with an exponent that follows Zimm theory, showing that CMC plays a key role in the gel viscoelastic properties for $r>r_c$. Our results offer a characterization of CB-CMC dispersions that will be useful for designing nanocomposites based on hydrophobic interactions., Comment: 18 pages, 10 figures, and 6 supplemental figures

Soft Glassy Materials (SGM) consist in dense amorphous assemblies of colloidal particles of multiple shapes, elasticity, and interactions, which confer upon them solid-like properties at rest. They are ubiquitously encountered in modern engineering, including additive manufacturing, semi-solid flow cells, dip-coating, adhesive locomotion, where they are subjected to complex mechanical histories. Such processes often include a solid-to-liquid transition induced by large enough shear, which results in complex transient phenomena such as non-monotonic stress responses, i.e., stress overshoot, and spatially heterogeneous flows, e.g., shear-banding or brittle failure. In the present article, we propose a pedagogical introduction to a continuum model based on a spatially-resolved fluidity approach that we recently introduced to rationalize shear-induced yielding in SGMs. Our model, which relies upon non-local effects, quantitatively captures salient features associated with such complex flows, including the rate dependence of the stress overshoot, as well as transient shear-banded flows together with nontrivial scaling laws for fluidization times. This approach offers a versatile framework to account for subtle effects, such as avalanche-like phenomena, or the impact of boundary conditions, which we illustrate by including in our model the elasto-hydrodynamic slippage of soft particles compressed against solid surfaces., Comment: 8 pages, 4 figures

Colloidal gels are out of equilibrium soft solids composed of attractive Brownian particles that form a space-spanning network at low volume fractions. The elastic properties of these systems result from the network microstructure, which is very sensitive to shear history. Here, we take advantage of such sensitivity to tune the viscoelastic properties of a colloidal gel made of carbon black nanoparticles. Starting from a fluidized state under an applied shear rate $\dot \gamma_0$, we use an abrupt flow cessation to trigger a liquid-to-solid transition. We observe that the resulting gel is all the more elastic when the shear rate $\dot \gamma_0$ is low and that the viscoelastic spectra can be mapped on a master curve. Moreover, coupling rheometry to small angle X-ray scattering allows us to show that the gel microstructure is different from gels solely formed by thermal agitation where only two length scales are observed: the dimension of the colloidal and the dimension the fractal aggregates. Competition between shear and thermal energy leads to gels with three characteristic length scales. Such gels structure in a percolated network of fractal clusters that interpenetrate each other. Experiments on gels prepared with various shear histories reveal that cluster interpenetration increases with decreasing values of the shear rate $\dot \gamma_0$ applied before flow cessation. These observations strongly suggest that cluster interpenetration drives the gel elasticity, which we confirm using a structural model. Our results, which are in stark contrast with previous literature, where gel elasticity was either linked to cluster connectivity or to bending modes, highlight a novel local parameter controlling the macroscopic viscoelastic properties of colloidal gels.

Cellulose nanocrystals (CNCs) are rodlike biosourced colloidal particles used as key building blocks in a growing number of materials with innovative mechanical or optical properties. While CNCs form stable suspensions at low volume fractions in pure water, they aggregate in the presence of salt and form colloidal gels with time-dependent properties. Here, we study the impact of salt concentration on the slow aging dynamics of CNC gels following the cessation of a high-shear flow that fully fluidizes the sample. We show that the higher the salt content, the faster the recovery of elasticity upon flow cessation. Most remarkably, the elastic modulus $G'$ obeys a time-composition superposition principle: the temporal evolution of $G'$ can be rescaled onto a universal sigmoidal master curve spanning 13 orders of magnitude in time for a wide range of salt concentrations. Such a rescaling is obtained through a time-shift factor that follows a steep power-law decay with increasing salt concentration, until it saturates at large salt content. These findings are robust to changes in the type of salt and in the CNC content. We further show that both linear and nonlinear rheological properties of CNC gels of various compositions, including, e.g., the frequency-dependence of viscoelastic spectra and the yield strain, can be rescaled based on the sample age along the general master curve. Our results provide strong evidence for universality in the aging dynamics of CNC gels, and call for microstructural investigations during recovery as well as theoretical modelling of time-composition superposition in rodlike colloids., Comment: 11 pages, 5 figures and 6 supplemental figures

Colloidal gels respond like soft solids at rest, whereas they flow like liquids under external shear. Starting from a fluidized state under an applied shear rate $\dot\gamma_{p}$, abrupt flow cessation triggers a liquid-to-solid transition during which the stress relaxes towards a so-called \textit{residual stress} $\sigma_{\rm res}$ that tallies a macroscopic signature of previous shear history. Here, we report on the liquid-to-solid transition in gels of boehmite, an aluminum oxide, that shows a remarkable non-monotonic stress relaxation towards a residual stress $\sigma_{\rm res}(\dot\gamma_{p})$ characterized by a dual behavior relative to a critical value $\dot\gamma_{c}$ of the shear rate $\dot\gamma_{p}$. Following shear at $\dot\gamma_{p}>\dot\gamma_{c}$, the gel obtained upon flow cessation is insensitive to shear history, and the residual stress is negligible. However, for $\dot\gamma_{p}<\dot\gamma_{c}$, the gel encodes some memory of the shear history, and $\sigma_{\rm res}$ increases for decreasing shear rate, directly contributing to reinforcing the gel viscoelastic properties. Moreover, we show that both $\sigma_{\rm res}$ and the gel viscoelastic properties increase logarithmically with the strain accumulated during the shear period preceding flow cessation. Such a shear-induced "overaging" phenomenon bears great potential for tuning the rheological properties of colloidal gels., Comment: 5 pages, 4 figures

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate $\dot \gamma_c$. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the flow profile of the flowing band is set by the applied shear rate $\gd$ instead of $\dot \gamma_c$. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom., Comment: 12 pages, 9 figures

Due to their exceptional mechanical and chemical properties and their natural abundance, cellulose nanocrystals (CNCs) are promising building blocks of sustainable polymer composites. However, the rapid gelation of CNC dispersions has generally limited CNC-based composites to low CNC fractions, in which polymer remains the dominant phase. Here we report on the formulation and processing of crosslinked CNC-epoxy composites with a CNC fraction exceeding 50 wt.%. The microstructure comprises sub-micrometer aggregates of CNCs crosslinked to polymer, which are analogous to the lamellar structure of nacre and promotes toughening mechanisms associated with bulk ductile behavior, despite the brittle behavior of the aggregates at the nanoscale. At 63 wt.% CNCs, the composites exhibit a hardness of 0.66 GPa and a fracture toughness of 5.2 MPa.m$^{1/2}$. The hardness of this all-organic material is comparable to aluminum alloys, and the fracture toughness at the centimeter scale is comparable to that of wood cell wall. We show that CNC-epoxy composite objects can be shaped from the gel precursors by direct-write printing and by casting, while the cured composites can be machined into complex 3D shapes. The formulation, processing route, and the insights on toughening mechanisms gained from our multiscale approach can be applied broadly to highly loaded nanocomposites.

Soft glassy materials such as mayonnaise, wet clays, or dense microgels display under external shear a solid-to-liquid transition. Such a shear-induced transition is often associated with a non-monotonic stress response, in the form of a stress maximum referred to as "stress overshoot". This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress $\sigma_\text{M}$ and strain $\gamma_\text{M}$ that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon start-up of shear from the local flow behavior to the global rheological observables., Comment: 5 pages, 4 figures, supplemental materials with 2 figures

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a yield stress such that YSFs are solid below the yield stress, whereas they flow like liquids above it. Under an applied shear rate $\dot\gamma$, the solid-to-liquid transition is associated with a complex spatiotemporal scenario. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot", followed by stress relaxation towards a steady state. Such relaxation can be either long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady-state, or abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. Here we use a continuum model based on a spatially-resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. Our model provides a scaling for the coordinates of the stress maximum as a function of $\dot\gamma$, which shows excellent agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that such a scaling is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet, such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling of the stress maximum with $\dot\gamma$. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to non-local effects., Comment: 24 pages, 19 figures

Colloidal gels are formed by the aggregation of Brownian particles into clusters that are, in turn, part of a space-spanning percolated network. In practice, the microstructure of colloidal gels, which dictates their mechanical properties, strongly depends on the particle concentration and on the nature of their interactions. Yet another critical control parameter is the shear history experienced by the sample, which controls the size and density of the cluster population, via particle aggregation, cluster breakup, and restructuring. Here we investigate the impact of shear history on acid-induced gels of boehmite, an aluminum oxide. We show that following a primary gelation, these gels display a dual response depending on the shear rate $\dot\gamma_{\rm p}$ used to rejuvenate their microstructure. We identify a critical shear rate $\dot\gamma_{\rm c}$, above which boehmite gels display a gel-like viscoelastic spectrum upon flow cessation, similar to that obtained following the primary gelation. However, upon flow cessation after shear rejuvenation below $\dot\gamma_{\rm c}$, boehmite gels display a glassy-like viscoelastic spectrum together with enhanced elastic properties. Moreover, the nonlinear rheological properties of boehmite gels also differ on both sides of $\dot\gamma_{\rm c}$: weak gels obtained after rejuvenation at $\dot\gamma_{\rm p}>\dot\gamma_{\rm c}$ show a yield strain that is constant, independent of $\dot\gamma_{\rm p}$, whereas strong gels obtained with $\dot\gamma_{\rm p}<\dot\gamma_{\rm c}$ display a yield strain that significantly increases with $\dot\gamma_{\rm p}$. Our results can be interpreted in light of previous literature on shear-induced anisotropy, while we rationalize the critical shear rate in terms of a dimensionless quantity, the Mason number, comparing the strength of the shear flow to the interparticle bond force., Comment: 15 pages and 14 figures

From paints to food products, solvent evaporation is ubiquitous and critically impacts product rheological properties. It affects Newtonian fluids by concentrating any non-volatile components and viscoelastic materials, which hardens up. In both of these cases, solvent evaporation leads to a change in the sample volume, which makes any rheological measurements particularly challenging with traditional shear geometries. Here we show that the rheological properties of a sample experiencing `slow' evaporation can be monitored in a time-resolved fashion by using a zero normal-force controlled protocol in a parallel-plate geometry. Solvent evaporation from the sample leads to a decrease of the normal force, which is compensated at all times by a decrease of the gap height between the plates. As a result, the sample maintains a constant contact area with the plates despite the significant decrease of its volume. We validate the method under both oscillatory and continuous shear by accurately monitoring the viscosity of water-glycerol mixtures experiencing evaporation and a relative volume decrease as large as 70%. Moreover, we apply this protocol to dehydrating suspensions. Specifically, we monitor a dispersion of charged silica nanoparticles undergoing a glass transition induced by evaporation. While the decrease in gap height provides a direct estimate of the increasing particle volume fraction, oscillatory and continuous shear measurements allow us to monitor the suspension's evolving viscoelastic properties in real-time. Overall, our study shows that a zero normal-force protocol provides a simple approach to bulk and time-resolved rheological characterization for systems experiencing slow volume variations., Comment: 10 pages, 6+4 figures

Colloidal gels are formed through the aggregation of attractive particles, whose size ranges from 10~nm to a few micrometers, suspended in a liquid. Such gels are ubiquitous in everyday life applications, from food products to paints or construction materials, in particular thanks to their ability to easily "yield", i.e., to turn from a solid to a liquid under the application of a weak external load. Understanding and controlling the mechanical response of colloidal gels is therefore of prime importance. Depending on the details of the system, however, the resulting gel networks present different microstructural organisations that may lead to widely different mechanical responses. This raises important challenges in fully characterizing yielding and in uncovering the mechanisms of nonlinear response in colloidal gels. In this paper, we distinguish between two classes of colloidal gels showing respectively reversible yielding, where the gel network reforms upon load release, and irreversible yielding, where the network is fully destroyed through fractures and phase separation. This broad, empirical distinction is achieved through rheology and local experiments at a mesoscopic scale, intermediate between the network characteristic size and the sample size. We further discuss how the observables derived from creep and fatigue experiments may be modelled to predict yielding and highlight open questions and future research directions in the domain.

From soft polymeric gels to hardened cement paste, amorphous solids under constant load exhibit a pronounced time-dependent deformation called creep. The microscopic mechanism of such a phenomenon is poorly understood in amorphous materials and constitutes an even greater challenge in densely packed and chemically reactive granular systems. Both features are prominently present in hydrating cement pastes composed of calcium silicate hydrate (C-S-H) nanoparticles, whose packing density increases as a function of time, while cement hydration is taking place. Performing nano-indentation tests and porosity measurements on a large collection of samples at various stages of hydration, we show that the creep response of hydrating cement paste is mainly controlled by the inter-particle distance and results from slippage between (C-S-H) nanoparticles. Our findings provide a unique insight into the microscopic mechanism underpinning the creep response in aging granular materials, thus paving the way for the design of concrete with improved creep resistance., Comment: 14 pages, 8 figures

We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: ($i$) stable flows during which the gel undergoes a tensile deformation without yielding, and ($ii$) unstable flows characterized by the radial growth of air fingers into the gel. We show that the unstable regime occurs beyond a critical energy input, independent of the gel's macroscopic yield stress. This implies a local fluidization of the gel at the tip of the growing fingers and results in the most unstable wavelength of the patterns exhibiting the characteristic scalings of the classical viscous fingering instability. Our work provides a quantitative criterion for the onset of fingering in colloidal gels based on a local shear-induced yielding, in agreement with the delayed failure framework., Comment: 5 pages, 4 figures

Shear thickening denotes the reversible increase in viscosity of a suspension of rigid particles under external shear. This ubiquitous phenomenon has been documented in a broad variety of multiphase particulate systems, while its microscopic origin has been successively attributed to hydrodynamic interactions and frictional contact between particles. The relative contribution of these two phenomena to the magnitude of shear thickening is still highly debated and we report here a discriminating experimental study using a model shear-thickening suspension that allows us to tune independently both the surface chemistry and the surface roughness of the particles. We show here that both properties matter when it comes to continuous shear thickening (CST) and that the presence of hydrogen bonds between the particles is essential to achieve discontinuous shear thickening (DST) by enhancing solid friction between closely contacting particles. Moreover, a simple argument allows us to predict the onset of CST, which for these very rough particles occurs at a critical volume fraction much lower than that previously reported in the literature. Finally, we demonstrate how mixtures of particles with opposing surface chemistry make it possible to finely tune the shear-thickening response of the suspension at a fixed volume fraction, paving the way for a fine control of the shear-thickening transition in engineering applications., Comment: 16 pages, 16 figures

Dense emulsions, colloidal gels, microgels, and foams all display a solid-like behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization, $\tau_\text{f}$, has been reported to decay as a power-law of the shear rate $\dot \gamma$ and of the shear stress $\sigma$ with respective exponents $\alpha$ and $\beta$. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a "free energy", that captures quantitatively all the salient features associated with such \textit{transient} shear-banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids., Comment: 5 pages, 4 figures - supplemental 6 pages, 4 figures

Cellulose nanocrystals (CNC) are naturally-derived nanostructures of growing importance for the production of composites having attractive mechanical properties, and offer improved sustainability over purely petroleum-based alternatives. Fabrication of CNC composites typically involves extrusion of CNC suspensions and gels in a variety of solvents, in the presence of additives such as polymers and curing agents. However, most studies so far have focused on aqueous CNC gels, yet the behavior of CNC-polymer gels in organic solvents is important to their wider processability. Here, we study the rheological behavior of composite polymer-CNC gels in dimethylformamide, which include additives for both UV and thermal crosslinking. Using rheometry coupled with in-situ infrared spectroscopy, we show that under external shear, CNC-polymer gels display progressive and irreversible failure of the hydrogen bond network that is responsible for their pronounced elastic properties. In the absence of cross-linking additives, the polymer-CNC gels show negligible recovery upon cessation of flow, while the presence of additives allows the gels to recover via van der Waals interactions. By exploring a broad range of shear history and CNC concentrations, we construct master curves for the temporal evolution of the viscoelastic properties of the polymer-CNC gels, illustrating universality of the observed dynamics with respect to gel composition and flow conditions. We therefore find that polymer-CNC composite gels display a number of the distinctive features of colloidal glasses and, strikingly, that their response to the flow conditions encountered during processing can be tuned by chemical additives. These findings have implications for processing of dense CNC-polymer composites in solvent casting, 3D printing, and other manufacturing techniques., Comment: 12 pages, 10 figures, Supplemental: 6 pages, 8 figures

We use molecular dynamics simulations of a model three-dimensional particulate gel, to investigate the linear viscoelastic response. The numerical simulations are combined with a novel test protocol (the optimally- windowed chirp or OWCh), in which a continuous exponentially-varying frequency sweep windowed by a tapered cosine function is applied. The mechanical response of the gel is then analyzed in the Fourier domain. We show that i) OWCh leads to an accurate computation of the full frequency spectrum at a rate significantly faster than with the traditional discrete frequency sweeps, and with a reasonably high signal-to-noise ratio, and ii) the bulk viscoelastic response of the microscopic model can be described in terms of a simple mesoscopic constitutive model. The simulated gel response is in fact well described by a mechanical model corresponding to a fractional Kelvin-Voigt model with a single Scott-Blair (or springpot) element and a spring in parallel. By varying the viscous damping and the particle mass used in the microscopic simulations over a wide range of values, we demonstrate the existence of a single master curve for the frequency dependence of the viscoelastic response of the gel that is fully predicted by the constitutive model. By developing a fast and robust protocol for evaluating the linear viscoelastic spectrum of these soft solids, we open the path towards novel multiscale insight into the rheological response for such complex materials.

The ability to measure the bulk dynamic behavior of soft materials with combined time- and frequency-resolution is instrumental for improving our fundamental understanding of connections between the microstructural dynamics and the macroscopic mechanical response. Current state-of-the-art techniques are often limited by a compromise between resolution in the time and frequency domain, mainly due to the use of elementary input signals that have not been designed for fast time-evolving systems such as materials undergoing gelation, curing or self-healing. In this work, we develop an optimized and robust excitation signal for time-resolved mechanical spectroscopy through the introduction of joint frequency- and amplitude-modulated exponential chirps. Inspired by the biosonar signals of bats and dolphins, we optimize the signal profile to maximize the signal-to-noise ratio while minimizing spectral leakage with a carefully-designed modulation of the envelope of the chirp. A combined experimental and numerical investigation reveals that there exists an optimal range of window profiles that minimizes the error with respect to standard single frequency sweep methods. The minimum error is set by the noise floor of the instrument, suggesting that the accuracy of an optimally windowed chirp signal is directly comparable to that achievable with a standard frequency sweep, while the acquisition time can be reduced by up to two orders of magnitude, for comparable spectral content. Finally, we demonstrate the ability of this optimized signal to provide time- and frequency-resolved rheometric data by studying the fast gelation process of an acid-induced protein gel. The use of optimally windowed chirps enables a robust rheological characterization of a wide range of soft materials undergoing rapid mutation and has the potential to become an invaluable tool for researchers across different disciplines.

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., Comment: 20 pages, 13 figures

Hydrogels behave as viscoelastic soft solids and display a porous microstructure filled with water with typical amounts of 90\%~w/w or more. As such, these materials are highly sensitive to water loss through evaporation, which impacts their mechanical properties. Yet, aside from scattered empirical observations, little is known about the gel drying kinetics for which there is a lack of temporally and spatially resolved measurements. Here we report a benchmark study of the slow drying of agarose gels cast in cylindrical Petri dishes. The weak adhesion of the gel to the lateral wall of the dish guarantees that the gel diameter remains constant during the drying process and that the gel shrinkage is purely vertical. The thinning rate is monitored by in-situ interferometry using a Michelson interferometer. The displacement of interference fringes are analyzed using an original spatiotemporal filtering method, which allows us to measure local thinning rates of about 10~nm/s with high accuracy. Experiments conducted at different positions along the gel radius show that the gel thins locally with a constant velocity before experiencing a sudden collapse at the end of the drying process. We further use the thinning rate measured at the center of the dish during the early stage of the drying process as a robust observable to quantify the role of additives on the gel drying kinetics and compare gels of different compositions. Our work exemplifies interferometry as a powerful tool to quantify the impact of minute amounts of additives on the drying of biopolymer gels., Comment: 11 pages, 9+4 figures, under review

Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon ($i$) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and ($ii$) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical response to a shear start-up experiment, up to the onset of macroscopic failure. Moreover, as the gel failure involves the irreversible growth of macroscopic cracks, we couple the latter stress response with Bailey's durability criterion for brittle solids in order to predict the critical values of the stress $\sigma_c$ and strain $\gamma_c$ at the failure point, and how they scale with the applied shear rate. The excellent agreement between theory and experiments suggests that the crack growth in this soft viscoelastic gel is a Markovian process, and that Baileys' criterion extends well beyond hard materials such as metals, glasses, or minerals., Comment: 6 pages, 4 figures and 1 pages of supplemental materials

We introduce a novel apparatus designed for stress-controlled rheometers to perform simultaneous rheological and electrical measurements on strongly conductive complex fluids under shear. By means of a non-toxic liquid metal at room temperature, the electrical connection to the rotating shaft is completed with minimal additional mechanical friction, allowing for simultaneous stress measurements as low as 1 Pa. We use the capabilities of this design to perform an extensive set of rheo-electric experiments on gels formulated from attractive carbon black particles, at concentrations ranging from 4 to 15% wt. First, experiments on gels at rest prepared with different shear history show a robust power-law scaling between the elastic modulus $G'_0$ and the conductivity $\sigma_0$ of the gels, i.e. $G'_0 \sim \sigma_0^\alpha$, with $\alpha =1.65 \pm 0.04$ independently of the gel concentration. Second, conductivity measurements performed simultaneously with creep experiments reveal for the first time that plastic events take place in the bulk while the shear rate decreases as a weak power law of time in the early stage of the experiment. The subsequent evolution of the conductivity and shear rate allows us to propose a local yielding scenario that is in agreement with previous velocimetry measurements. Finally, we determine the constitutive rheological and electrical behavior of carbon black gels. Corrections first introduced for mechanical measurements are carefully extended to electrical measurements to accurately distinguish between bulk and surface contributions to the conductivity. As an illustrative example, we examine the constitutive rheo-electric properties of five carbon black gels of different grades, and demonstrate the relevance of the novel rheo-electric apparatus as a versatile characterization tool for strongly conductive complex fluids and their applications., Comment: 15 pages, 10 figures + supplemental material

Thermoreversible hydrogels are commonly prepared by cooling down to ambient temperature, aqueous polymer solutions first brought to a boil. The incubation time of the polymer solution at such a high temperature is traditionally kept to a minimum to minimize its impact on the subsequent gelation. Here we study the effect of a prolonged heating of a 1.5\% w/w agar solution at $T=80^{\circ}$C, well above the gelling temperature. The incubation time $\mathcal{T}$ of the polysaccharide solution is varied from a few hours up to five days. We show that the agar solution ages as the result of both the hydrolysis and the intramolecular oxidation of the polysaccharides. As a consequence, both the viscosity and the pH of the solution decrease continuously during the incubation period. Furthermore, samples withdrew at different incubation times are cooled down to form gels which structure and mechanical properties are systematically determined. Cryo-microscopy and X-ray diffraction experiments reveal that agar gels formed from solutions of increasing incubation times, display a coarser microstructure composed of micron-sized foils which result from the condensation of the polysaccharides and contrast with the fibrous-like microstructure of gels prepared from a fresh agar solution. Along with structural changes, a prolonged incubation time of the polymer solution at $T=80^{\circ}$C leads to weaker agar gels of significantly lower shear elastic modulus. Moreover, extensive macro-indentation experiments coupled to direct visualization show that increasing the incubation time of the agar solution up to a few days decreases the yield strain of the gel, while the rupture scenario turns continuously from brittle to ductile-like. Our study suggests that the incubation time of agar solutions at high temperature could be used to tune the mechanical properties of agar-based gels., Comment: 15 pages, 15 figures

Flows of suspensions are often affected by wall slip, that is the fluid velocity $v_{f}$ in the vicinity of a boundary differs from the wall velocity $v_{w}$ due to the presence of a lubrication layer. While the slip velocity $v_s=\vert v_{f}-v_{w}\vert$ robustly scales linearly with the stress $\sigma$ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a $v_s\propto\sigma^p$ with exponents $p$ inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that $v_s$ actually scales as a power law of the viscous stress $\sigma-\sigma_c$, where $\sigma_c$ denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions $\phi$ on both sides of the jamming point and that the exponent $p$ increases continuously with $\phi$, from $p=1$ in the case of dilute suspensions to $p=2$ for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and paves the way for a continuous description of wall slip above and below jamming., Comment: 6 pages, 4 figures - accepted for publication as a Rapid Communication in Phys. Rev. E