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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 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.

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., 8 pages, 4 figures

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., 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}, Comment: 5 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.

International audience; 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 organizations 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 modeled to predict yielding and highlight open questions and future research directions in the domain.

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

Correction for ‘Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation’ by Noémie Dagès et al., Soft Matter, 2022, 18, 6645–6659, https://doi.org/10.1039/D2SM00481J.

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 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}, Comment: 15 pages and 14 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.

© 2021 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences Mechanical properties, such as the hardness H, Young's modulus E, creep modulus C, and fracture toughness Kc, are essential parameters in the design of hydraulic fracturing systems for prospective shale gas formations. In this study, a practical methodology is presented for obtaining these properties through microindentation experiments combined with quantitative observations of the mineralogical phases using X-ray diffraction (XRD), scanning electron microscopy (SEM) with backscattered electron (BSE) imaging, and energy-dispersive X-ray spectroscopy (EDS) analyses. We apply this method in the case of three types of Longmaxi shales with different mineralogies (i.e. carbonate-, clay-, and quartz-rich, respectively), which allows us to determine the characteristic indentation depth, hc = 8–10 μm, beyond which the mechanical response of the carbonate-rich shale is homogeneous and independent of its complex heterogeneous microstructure. Moreover, exploiting the results of a large number of indentation tests, we demonstrate that the indentation modulus M of the shale increases as a power-law of hardness H, and its creep modulus C increases linearly with H. We also compute the fracture toughness Kc from the indentation data by assuming a perfectly plastic behavior of the sample. Our results are in good agreement with independent measurements of Kc determined by microscratch tests. Finally, further tests on quartz- and clay-rich samples of the Longmaxi shale suggest further variations in the samples’ mechanical properties depending on their burial conditions and the mechanical properties of their dominant mineral phases.

Nacre’s structure-property relationships have been a source of inspiration for designing advanced functional materials with both high strength and toughness. These outstanding mechanical properties have been mostly attributed to the interplay between aragonite platelets and organic matrices in the typical brick-and-mortar structure. Here, we show that crystallographically co-oriented stacks of aragonite platelets, in both columnar and sheet nacre, define another hierarchical level that contributes to the toughening of nacre. By correlating piezo-Raman and micro-indentation results, we quantify the residual strain energy associated with strain hardening capacity. Our findings suggest that the aragonite stacks, with characteristic dimensions of around 20 µm, effectively store energy through cooperative plastic deformation. The existence of a larger length scale beyond the brick-and-mortar structure offers an opportunity for a more efficient implementation of biomimetic design. The hierarchical structure of nacre is known to contribute to its high strength and toughness, providing inspiration for many biomimetic materials. Here, co-oriented 20 µm stacks of aragonite platelets are shown to contribute to the toughness of nacre, defining a new characteristic length scale.

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., 5 pages, 4 figures

International audience; The first study dealing with the self-assembly of an α-amino acid derivative in perfluorocarbons is reported. Rheology, microscopy, and spectroscopy studies revealed that the fluorous sodium Lprolinate derivative 1 self-assembles in perfluorocarbons to form a three-dimensional network of left-handed nano-helices resulting in solvent gelation. Singlet oxygen lifetime measured in a gel of perfluorodecalin was ~ 1000 times longer than in pure water. Low molecular weight gelators (LMWG) are a unique and important class of chemicals that can self-assemble in solution to form a gel, i.e. an entangled network of fibers trapping solvent molecules. These self-assembled soft materials have great potential in various applications, including cosmetics, catalysis, organic electronics, regenerative medicine, drug delivery and cell culture. 1,2 Among the various families of LMWGs discovered so far, those based on α-amino acids have received considerable attention. 2,3 Indeed, α-amino acids

International audience; Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time-connectivity superposition principle a series of rapidly-acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times appearing glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time-connectivity superposition principle for this class of soft glassy materials and provide a new compact description for the dichotomous viscoelastic nature of weak colloidal gels

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

International audience; Dilute suspensions of repulsive particles exhibit a Newtonian response to flow that can be accurately predicted by the particle volume fraction and the viscosity of the suspending fluid. However, such a description fails when the particles are weakly attractive. In a simple shear flow, suspensions of attractive particles exhibit complex, anisotropic microstructures and flow instabilities that are poorly understood and plague industrial processes. One such phenomenon, the formation of log-rolling flocs, which is ubiquitously observed in suspensions of attractive particles that are sheared while confined between parallel plates, is an exemplar of this phenomenology. Combining experiments and discrete element simulations, we demonstrate that this shear-induced structuring is driven by hydrodynamic coupling between the flocs and the confining boundaries. Clusters of particles trigger the formation of viscous eddies that are spaced periodically and whose centers act as stable regions where particles aggregate to form flocs spanning the vorticity direction. Simulation results for the wavelength of the periodic pattern of stripes formed by the logs and for the log diameter are in quantitative agreement with experimental observations on both colloidal and noncolloidal suspensions. Numerical and experimental results are successfully combined by means of rescaling in terms of a Mason number that describes the strength of the shear flow relative to the rupture force between contacting particles in the flocs. The introduction of this dimensionless group leads to a universal stability diagram for the log-rolling structures and allows for application of shear-induced structuring as a tool for assembling and patterning suspensions of attractive particles.

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., 12 pages, 10 figures, Supplemental: 6 pages, 8 figures

Thermoreversible gels are commonly prepared by cooling down to ambient temperature, aqueous polymer solutions first brought to a boil for a short time. Here, we study the effect of the latter duration on the subsequent gelation of an agar solution. Increasing the incubation time at high temperature ( T = 80 °C) from hours to a few days leads to the hydrolysis and the oxidation of the polysaccharides, and results in the decrease of the viscosity and the pH of the solution. Samples withdrew at different incubation times are cooled down to form gels whose structure and mechanical properties are systematically determined. Cryoelectron 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 agar solution at T = 80 °C leads to weaker gels than those made from fresher solutions, and extensive macro-indentation experiments coupled to direct visualization show that the gel rupture scenario turns from brittle to ductile-like as the incubation time increases. Our study suggests that the incubation time of agar solutions at high temperature could be used as an external control parameter to tune the mechanical properties of agar-based gels.

Celitement is a new type of cement that is based on hydraulic calcium-hydrosilicate (hCHS) that possesses a potential for minimizing the ratio C/S from above 3 in OPC down to 1, which significantly reduces the amount of CO$_2$ released during processing. The reaction kinetics of hCHS differs from that of classical clinker phases due to the presence of highly reactive silicate species, which involve silanol groups instead of pure calcium silicates and aluminates and aluminoferrites. In contrast to Portland cement, no calcium hydroxide is formed during hydration, which otherwise regulates the Ca concentration. Without the buffering role of Ca(OH)$_2$ the concentration of the dissolved species c(Ca$^{2+}$) and c(SiO$_4^{4-}$) and the corresponding pH must be controlled to ensure a reproducible reaction. Pure hCHS reacts isochemically with water, resulting in a C-S-H phase with the same chemical composition as a single hydration product, with a homogeneous distribution of the main elements Ca and Si throughout the sample. Here we study via nanoindentation the mechanical properties of two different types of hardened pastes made out of Celitement (C/S=1.28), with varying amounts of hCHS and variable water to cement ratio. We couple nanoindentation grids with Raman mappings to link the nanoscale mechanical properties to individual microstructural components, yielding in-depth insight into the mechanics of the mineralogical phases constituting the hardened cement paste. We show that we can identify in hardened Celitement paste both fresh C-S-H with varying density, and C-S-H from the raw material using their specific Raman spectra, while simultaneously measuring their mechanical properties. Albeit not suitable for phase identification, EDX measurements provide valuable information about the distribution of alkalis, thus further helping to understand the reaction pattern of hCHS., Comment: 32 pages, 8 figures

Purpose To make the Boston keratoprosthesis (B-KPro), together with its carrier corneal graft, more easily procured, transported and stored, as well as less expensive, easier for the surgeon to implant and safer for the patient, it is proposed that the B-KPro-graft combination be pre-assembled by an expert technician, followed by sterilization with gamma ray irradiation (GI) allowing long-term storage at room temperature. For this to be possible, it must be shown that the B-KPro itself (not only the graft) remains unharmed by the irradiation. Methods Polymethyl methacrylate (PMMA) discs and B-KPros were submitted to either ethylene oxide sterilization or different doses of GI. Cell biocompatibility, mechanical strength and optical quality were evaluated. The feasibility of assembling the B-KPro to a corneal graft, and gamma-radiate afterwards, was also assessed. Results There were no differences in cell biocompatibility between the samples. The optical evaluation showed high levels of transparency for all the groups. The absorbance of ultraviolet was higher for the groups treated with GI. The mechanical evaluation by nanoindentation showed no alterations of the PMMA discs after GI. The flexure test revealed a similar mechanical behavior. Technically, pre-assembly and GI of the B-KPro revealed no problems. Conclusions Sterilization of B-KPro using GI has no detrimental influence on the device. The pre-assembly of B-KPro to a donor cornea, followed by gamma sterilization, emerges as an efficient and safe procedure.

International audience; We use molecular dynamics simulations to investigate the linear viscoelastic response of a model three-dimensional particulate gel. 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 toward novel multiscale insight into the rheological response for such complex materials.

Agarose gels are viscoelastic soft solids that display a porous microstructure filled with water at 90% w/w or more. Despite an extensive use in food industry and microbiology, little is known about the drying kinetics of such squishy solids, which suffers from a lack of time-resolved local measurements. Moreover, only scattered empirical observations are available on the role of the gel composition on the drying kinetics. Here we study by in-situ interferometry the drying of agarose gels of various compositions cast in Petri dishes. The gel thinning is associated with the displacement of interference fringes that are analyzed using an efficient spatiotemporal filtering method, which allows us to assess local thinning rates as low as 10 nm/s with high accuracy. The gel thinning rate measured at the center of the dish appears as a robust observable to quantify the role of additives on the gel drying kinetics and compare the drying speed of agarose gels loaded with various non-gelling saccharides of increasing molecular weights. Our work shows that saccharides systematically decrease the agarose gel thinning rate up to a factor two, and exemplifies interferometry as a powerful tool to quantify the impact of additives on the drying kinetics of polymer gels.

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

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

A wide range of thermoreversible gels are prepared by cooling down to ambient temperature hot aqueous polymer solutions. During the sol-gel transition, such materials may experience a volume contraction which is traditionally overlooked as rheological measurements are usually performed in geometries of constant volume. In this article, we revisit the formation of 1.5\% wt. agar gels through a series of benchmark rheological experiments performed with a plate-plate geometry. We demonstrate on that particular gel of polysaccharides that the contraction associated with the sol/gel transition cannot be neglected. Indeed, imposing a constant gap width during the gelation results in the strain hardening of the sample, as evidenced by the large negative normal force that develops. Such hardening leads to the slow drift in time of the gel elastic modulus $G'$ towards ever larger values, and thus to an erroneous estimate of $G'$. As an alternative, we show that imposing a constant normal force equals to zero during the gelation, instead of a constant gap width, suppresses the hardening as the decrease of the gap compensates for the sample contraction. Using normal force controlled rheology, we then investigate the impact of thermal history on 1.5\% wt. agar gels. We show that neither the value of the cooling rate, nor the introduction of a constant temperature stage during the cooling process influence the gel elastic properties. Instead, $G'$ only depends on the terminal temperature reached at the end of the cooling ramp, as confirmed by direct imaging of the gel microstructure by cryoelectron microscopy. The present work offers an extensive review of the technical difficulties associated with the rheology of hydrogels and paves the way for a systematic use of normal force controlled rheology to monitor non-isochoric processes., 19 pages, 15 figures - accepted for publication in Journal of Rheology

International audience; Graphene oxide (GO), the main precursor of graphene-based materials made by solution processing, is known to be very stiff.Indeed, it has a Young’s modulus comparable to steel, on the order of 300 GPa. Despite its very high stiffness, we show here that GO is superflexible. We quantitatively measure the GO bending rigidity by characterizing the flattening of thermal undulations in response to shear forces in solution. Characterizations are performed by the combination of synchrotron X-ray diffraction at small angles and in situ rheology (rheo-SAXS) experiments using the high X-ray flux of a synchrotron source. The bending modulus is found to be 1 kT, which is about two orders of magnitude lower than the bending rigidity of neat graphene. This superflexibility compares with the fluidity of self-assembled liquid bilayers. This behavior is discussed by considering the mechanisms at play in bending and stretching deformations of atomic monolayers. The superflexibility of GO is a unique feature to develop bendable electronics after reduction, films, coatings, and fibers. This unique combination of properties of GO allows for flexibility in processing and fabrication coupled with a robustness in the fabricated structure.

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

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 during a time $t_w$ before being submitted to a constant shear rate $\dot \gamma$. We investigate in detail the effects of both $t_w$ and $\dot \gamma$ on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may either display 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 up to 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 values of $t_w$ and $\dot \gamma$, although the very details of the fluidization scenario vary with $\dot \gamma$. Finally, the critical shear rate $\dot \gamma^*$ that separates steady-state shear-banding from steady-state homogeneous flow depends on the width on the shear cell and exhibits a nonlinear dependence with $t_w$. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging which modeling constitutes a major challenge that has not been met yet., Comment: main: 12 pages, 10 figures; supplemental: 3 pages, 5 movies and 6 figures

Even in simple geometries many complex fluids display non-trivial flow fields, with regions where shear is concentrated. The possibility for such shear banding has been known since several decades, but the recent years have seen an upsurge of studies offering an ever more precise understanding of the phenomenon. The development of new techniques to probe the flow on multiple scales and with increasing spatial and temporal resolution has opened the possibility for a synthesis of the many phenomena that could only have been thought of separately before. In this review, we bring together recent research on shear banding in polymeric and on soft glassy materials, and highlight their similarities and disparities., Comment: 16 pages, 6 figures, 152 references. Submitted to Annual Review of Fluid Mechanics

Biogels made of crosslinked polymers such as proteins or polysaccharides behave as porous soft solids and store large amount of solvent. These gels undergo spontaneous aging, called syneresis that consists in the shrinkage of the gel matrix and the progressive expulsion of the solvent. As a result, a biogel originally casted in a container often lose contact with the container sidewalls, and the detachment time is a priori difficult to anticipate since it may occur over variable time spans (from hours to days). Here we report on the syneresis phenomena in agar plates that consist in Petri dishes filled with a gel mainly composed of agar. Direct observations and speckle pattern correlation analysis allow us to rationalize the delayed detachment of the gel from the sidewall of the Petri dish. The detachment time $t^*$ is surprisingly not controlled by the mass loss as one would intuitively expect. Instead, $t^*$ is strongly correlated to the gel minimum thickness $e_{min}$ measured along the sidewall of the plate, and increases as a robust function of $e_{min}$ independently of the prior mass-loss history. Time-resolved correlation spectroscopy atypically applied to such weakly diffusive media gives access to the local thinning rate of the gel. This technique also allows us to detect the gel micro-displacements that are triggered by the water evaporation prior to the detachment, and even to anticipate the latter from a few hours. Our work provides observables to predict the detachment time of agar gels in dishes, and highlights the relevance of speckle pattern correlation analysis for the quantitative investigation of the syneresis dynamics in biopolymer gels., 9 pages, 9 figures. Supplemental materials: 3 pages, 1 movie and 5 figures

We present a comprehensive review of the physical behavior of yield stress materials in soft condensed matter, which encompass a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces, due to the existence of a finite force threshold for flow to occur: the yield stress. We discuss both the physical origin and rheological consequences associated with this nonlinear behavior, and give an overview of experimental techniques available to measure the yield stress. We discuss recent progress concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing in particular the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and non-local effects in confined geometries., Comment: Review article: V1: 58 pages, 38 figs, 487 refs. V2: Final version 44 pages, 27 figs, 449 refs. Accepted for publication in Rev. Mod. Phys

Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a protein gel is reminiscent of brittle solids: after a primary creep regime characterized by a power-law behavior which exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captures the full rheological response. The failure time follows a decreasing power law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittle-like soft solids., Comment: 5 pages, 4 figures - Supplemental material: 3 pages, 4 figures available at the following URL: http://www.crpp-bordeaux.cnrs.fr/~divoux/publications/PRL_14_Protein_Gels_SM.pdf

In this letter, we report results on the effect of temperature variations on a granular assembly through Molecular Dynamic simulations of a 2D granular column. Periodic dilation of the grains are shown to perfectly mimic such thermal cycling, and allows to rationalize the link between the compaction process, the local grains dynamics and finite size effects. Here we show that the individual grain properties, namely their roughness and elastic modulus define a minimal cycling amplitude of temperature \Delta Tc below which the dynamics is intermittent and spatially heterogeneous while confined into localized regions recently coined "hot spot" [Amon et al., Phys. Rev. Lett. 108, 135502 (2012)]. Above \Delta Tc, the whole column flows while the grains dynamics ranges continuously from cage-like at the bottom of the column to purely diffusive at the top. Our results provide a solid framework for the futur use of thermal cycling as an alternate driving method for soft glassy materials., Comment: 5 pages, 5 figures, submitted

The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled to local velocity measurements. Under an applied shear stress, the fluidization of gels made of attractive carbon black particles suspended in a mineral oil is shown to involve a previously unreported shear rate response $\dot \gamma (t)$ characterized by two well-defined and separated timescales $\tau_c$ and $\tau_f$. First $\dot \gamma(t)$ decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the "Andrade creep." We show that the bulk deformation remains homogeneous at the micron scale, which demonstrates that if plastic events take place or if any shear transformation zone exists, such phenomena occur at a smaller scale. As a key result of this paper, the duration $\tau_c$ of this creep regime decreases as a power law of the viscous stress, defined as the difference between the applied stress and the yield stress with an exponent ranging between 2 and 3 depending on the gel concentration. The end of this first regime is marked by a jump of the shear rate by several orders of magnitude, while the gel slowly slides as a solid block experiencing strong wall slip at both walls, despite rough boundary conditions. Finally, a second sudden increase of the shear rate is concomitant to the full fluidization of the material which ends up being homogeneously sheared. The corresponding fluidization time $\tau_f$ robustly follows an exponential decay with the applied shear stress as already reported for smooth boundary conditions. Finally, we highlight a few features that are common to attractive colloidal gels and to solid materials by discussing our results in the framework of theoretical approaches of solid rupture (kinetic, fiber bundle, and transient network models)., Comment: Main: 18 pages, 15 figures - Supplemental: 5 pages, 6 figures - Accepted for publication in Soft Matter (Nov. 2013)

This work reports on an experimental study of elastic turbulence in a semi-dilute wormlike micelle system made of a highly elastic betaine surfactant solution. The temporal evolution of both rheological quantities and local flow properties is monitored by combining global rheology, optical visualization, and ultrasonic velocimetry. Even at the smallest applied shear rates or shear stresses, we find that the micellar sample develops large Weissenberg (Wi) numbers, leading the flow to undergo a transition to elastic turbulence. Three-dimensional flows are indeed observed all along the flow curve, which therefore cannot be interpreted in the framework of classical shear banding. Strong fluctuations are also recorded in the rheological quantities, in the reflected light intensity, and in velocity profiles. We show that the power spectral densities (PSDs) of these fluctuations display power law behaviours with exponents ranging from −1 to −3 depending on the applied shear stress or shear rate. The exponents inferred from local velocity measurements are found to be spatially dependent, pointing to inhomogeneous turbulence. The nature of the instability and of the transition to elastic turbulence is further discussed in light of recent experimental and theoretical works on wormlike micelles and polymers.

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatiotemporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the shear-banding flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. The criterion for purely elastic Taylor–Couette instability adapted to shear-banding flows suggested three categories of shear-banding depending on their stability. In the present study, we report on a large set of experimental data which demonstrates the existence of the three categories of shear-banding flows in various surfactant solutions. Consistent with theoretical predictions, increases in the surfactant concentration or in the curvature of the geometry destabilize the flow, whereas an increase in temperature stabilizes the flow. However, experiments also exhibit some interesting behaviors going beyond the purely elastic instability criterion., National Science Foundation (U.S.). Graduate Research Fellowship Program

The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., {\it Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration $\tau_f$ decreases as a power law of the applied shear rate $\gp$. Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width $e$ and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time $\tau_f$, different fluidization processes are observed depending on $\gp$ and $e$: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of $\gp$ or $e$, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears as very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition., Comment: 16 pages, 14+2 figures, published in Soft Matter

We report on the flow dynamics of a wormlike micellar system (CPCl/NaSal/brine) undergoing a shear-banding transition using a combination of global rheology, 1D ultrasonic velocimetry and 2D optical visualisation. The different measurements being performed in a single Taylor–Couette geometry, we find a strong correlation between the induced turbid band observed optically and the high shear rate band. This correspondence reveals that fluctuations observed in the 1D velocity profiles are related to elastic instabilities triggered in the high shear rate band: 3D coherent (laminar) flow and 3D turbulent flow successively develop as the applied shear rate is increased. The specific characteristics of the resulting complex dynamics are found to depend on subtle changes in the sample, due to temporary light exposure. The CPCl molecules exhibit a photochemistry mainly influenced by the photo-induced cleavage of the pyridine ring that yields an unstable aldehyde enamine, which further decays by thermally activated processes. The products of the reaction possibly build up a lubrication layer responsible for pathological flow dynamics. Overall, our results bridge the gap between previous independent optical and local velocity measurements and explain most of the observed fluctuations in terms of a sequence of elastic instabilities which turns out to be widespread among semidilute wormlike micellar systems.

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton {\it et al., Rheol Acta}, 2008, {\bf 47}, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress $\sigma$ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration $\tau_f$ of this fluidization process scales as $\tau_f \propto 1/(\sigma - \sigma_c)^{\beta}$, where $\sigma_c$ stands for the yield stress of the microgel, and $\beta$ is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux {\it et al., Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the {\it steady-state} HB exponent appears as the ratio of the two fluidization exponents extracted separately from the {\it transient} fluidization processes respectively under controlled shear rate and under controlled shear stress.

Many volcanoes exhibit temporal changes in their degassing process, from rapid gas puffing to lava fountaining and long-lasting quiescent passive degassing periods. This range of behaviors has been explained in terms of changes in gas flux and/or magma input rate. We report here a simple laboratory experiment which shows that the non- Newtonian rheology of magma can be responsible, alone, for such intriguing behavior, even in a stationary gas flux regime. We inject a constant gas flow-rate Q at the bottom of a non-Newtonian fluid column, and demonstrate the existence of a critical flow rate Q* above which the system spontaneously alternates between a bubbling and a channeling regime, where a gas channel crosses the entire fluid column. The threshold Q* depends on the fluid rheological properties which are controlled, in particular, by the gas volume fraction (or void fraction) {\phi}. When {\phi} increases, Q* decreases and the degassing regime changes. Non-Newtonian properties of magma might therefore play a crucial role in volcanic eruption dynamics.

We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress $\sigma(t)$ and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear rate $\dot\gamma$. (i) At small strains ($\gamma \dot\gamma_w$ [...]., Comment: 18 pages, 14 figures, accepted for publication in Soft Matter

In order to assess the physical mechanisms at stake when giant gas bubbles burst at the top of a magma conduit, laboratory experiments have been performed. An overpressurized gas cavity is initially closed by a thin liquid film, which suddenly bursts. The acoustic signal produced by the bursting is investigated. The key result is that the amplitude and energy of the acoustic signal strongly depend on the film rupture time. As the rupture time is uncontrolled in the experiments and in the field, the measurement of the acoustic excess pressure in the atmosphere, alone, cannot provide any information on the overpressure inside the bubble before explosion. This could explain the low energy partitioning between infrasound, seismic and explosive dynamics often observed on volcanoes.