Yield of reversible colloidal gels during flow start-up: release from kinetic arrest

Elucidating the role of physicochemical interactions on gel rheology

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

Predicting yielding in attractive colloidal gels

One of the defining characteristics of soft glassy materials is their ability to exhibit a yield stress, which can result in an overall elasto-visco-plastic mechanics. To design soft materials with specific properties, it is essential to gain a comprehensive understanding of the topological and structural failure points that occur during yielding. However, predicting these failure points, which lead to yielding, is challenging due to the dynamic nature of structure development and its cooccurrence with other complicated processes, such as local rearrangements and anisotropy. In this study, we employ a series of tools from network science to investigate colloidal gels as a model for soft glassy materials during yielding. Our findings reveal that edge betweenness centrality can be utilized as a universal predictor for yielding across various state variables, including the volume fraction of solids, the strength, and the range of attraction between colloids.

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.

Topological origins of yielding in short-ranged weakly attractive colloidal gels

Yielding of the particulate network in colloidal gels under applied deformation is accompanied by various microstructural changes, including rearrangement, bond rupture, anisotropy, and reformation of secondary structures. While much work has been done to understand the physical underpinnings of yielding in colloidal gels, its topological origins remain poorly understood. Here, employing a series of tools from network science, we characterize the bonds using their orientation and network centrality. We find that bonds with higher centralities in the network are ruptured the most at all applied deformation rates. This suggests that a network analysis of the particulate structure can be used to predict the failure points in colloidal gels a priori.

Biomass-based hydrogels with high ductility, self-adhesion and conductivity inspired by starch paste for strain sensing

Currently, hydrogel sensors for health monitoring require external tapes, bandages or adhesives to immobilize them on the surface of human skin. However, these external fixation methods easily lead to skin allergic reactions and the decline of monitoring accuracy. A simple strategy to solve this problem is to endow hydrogel sensors with good adhesion. Inspired by the starch paste adhesion mechanism, a biomass-based hydrogel with good conductivity and high repetitive adhesion strength was prepared by introducing modified starch into polyacrylic acid hydrogel system. The properties of biomass-based hydrogels could be controlled by changing the proportion of amylose and amylopectin. The biomass-based hydrogel exhibited a variety of excellent properties, including good stretchability (1290 %), high adhesion strength (pig skin: 46.51 kPa) and conductivity (2.3 S/m). Noticeably, the repeated adhesive strength of biomass-based hydrogel did not decrease with the increase of adhesion times. The strain sensor based on the biomass-based hydrogel could accurately monitor the large-scale and small movements of the human body, and had broad application prospects in the field of flexible wearable devices.

Continuum modeling of shear startup in soft glassy materials

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ_{y} such that YSFs are solid for stresses σ imposed below σ_{y}, whereas they flow like liquids for σ>σ_{y}. Under an applied shear rate γ[over ̇], the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. 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 (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, 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. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ_{M} and strain γ_{M} as a function of γ[over ̇], which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ_{M}(γ[over ̇]) 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, i.e., whether the steady-state flow profile is homogeneous or shear-banded. 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 σ_{M}(γ[over ̇]). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

Toward a flow-dependent phase-stability criterion: Osmotic pressure in sticky flowing suspensions

Equilibrium phase instability of colloids is robustly predicted by the Vliegenthart-Lekkerkerker (VL) critical value of the second virial efficient, but no such general criterion has been established for suspensions undergoing flow. A transition from positive to negative osmotic pressure is one mechanical hallmark of a change in phase stability in suspensions and provides a natural extension of the equilibrium osmotic pressure encoded in the second virial coefficient. Here, we propose to study the non-Newtonian rheology of an attractive colloidal suspension using the active microrheology framework as a model for focusing on the pair trajectories that underlie flow stability. We formulate and solve a Smoluchowski relation to understand the interplay between attractions, hydrodynamics, Brownian motion, and flow on particle microstructure in a semi-dilute suspension and utilize the results to study the viscosity and particle-phase osmotic pressure. We find that an interplay between attractions and hydrodynamics leads to dramatic changes in the nonequilibrium microstructure, which produces a two-stage flow-thinning of viscosity and leads to pronounced flow-induced negative osmotic pressure. We summarize these findings with an osmotic pressure heat map that predicts where hydrodynamic enhancement of attractive bonds encourages flow-induced aggregation or phase separation. We identify a critical isobar-a flow-induced critical pressure consistent with phase instability and a nonequilibrium extension of the VL criterion.

Stress Overshoots in Simple Yield Stress Fluids

Soft glassy materials such as mayonnaise, wet clays, or dense microgels display a solid-to-liquid transition under external shear. Such a shear-induced transition is often associated with a nonmonotonic 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 σ_{M} and strain γ_{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 startup of shear from the local flow behavior to the global rheological observables.

Gel breakdown in a formulated product via accumulated strain

Almost any formulated product is sufficiently complex that definitive elucidation of all interactions and microstructural evolutions is difficult at best and more likely intractable. Drilling fluids are no exception. Nevertheless, detailed experiment and comparison with simpler systems studied in the literature enable rational pictures to be deduced. We study the breakdown of a gelled formulated product, a drilling fluid, under the action of repeated deformation, i.e. weakly nonlinear oscillation. Our data may be rationalised by postulating that the fluid behaves as an arrested phase separating material whose natural slow structural evolution, aging and coarsening, is accelerated by the imposed sinusoidal strain consistent with previous work on well characterised systems. During the observed evolution the elastic modulus exhibits a maximum which appears correlated with a maximal connected heterogeneity of structure.

Migration and Morphology of Colloidal Gel Clusters in Cylindrical Channel Flow

We report the cluster-level structural parameters of colloidal thermogelling nanoemulsions in channel flow as a function of attractive interactions and local shear stress. The spatiotemporal evolution of the gel microstructure is obtained by directly visualizing the dispersed phase near the edge of a cylindrical channel. We observe the flow of the nanoemulsion gels in a range of radial positions (r) and shear stresses between 70 and 220 Pa, finding that the r-dependent cluster sizes are due to a balance between shear forces that yield bonds and attractive interactions that rebuild the inter-colloid bonds. In addition, the largest clusters appear to be affected by confinement and accumulate toward the central axis of the channel, resulting in a volume fraction gradient. Cluster size and volume fraction variabilities are most prominent when the attractive interactions are the strongest. Specifically, a distinct transition from sparse, fluidized clusters near the walls to concentrated, large clusters toward the center is observed. These two structural states coincide with a velocity-based transition from higher shear rates near the walls to lower shear rates toward the center of the channel. We find a compounding effect where larger gel clusters, formed under strong attractions and low shear stresses, are susceptible to shear-induced migration that intensifies r-dependent heterogeneity and deviations in the flow behavior from predictive models.

Machine learning of lubrication correction based on GPR for the coupled DPD-DEM simulation of colloidal suspensions

Hydrodynamic interactions have a major impact on the suspension properties, but they are absent in atomic and molecular fluids due to a lack of intervening medium at close range. To reproduce the correct hydrodynamic interactions, lubrication correction is essential to compensate the missing short-range hydrodynamics from the fluids. However, lubrication correction requires many simulations in particle-based simulations of colloidal suspensions. To address the problem, we employ an active learning strategy based on Gaussian process regression (GPR) for normal and tangential lubrication corrections to significantly reduce the number of necessary simulations and apply the correction to the coupled multiscale simulation of monodisperse hard-sphere colloidal suspensions. In particular, a single-particle dissipative particle dynamics (DPD) model with parameter correction is used to describe the solvent-solvent and colloid-solvent interactions, and a discrete element method (DEM) model to depict the colloid-colloid frictional contacts. The lubrication correction results demonstrate that only six and four independent simulations (observation points for GPR training) are required to achieve accurate normal and tangential lubrication corrections, respectively. To validate the machine learning of lubrication correction based on GPR, we investigate the self-diffusion coefficients of colloids, suspension rheology and microstructure using the coupled DPD-DEM model with GPR lubrication correction. Our simulation results show that the machine learning of lubrication correction based on GPR is effective and the lubrication corrected DPD-DEM model is indeed capable of accurately capturing hydrodynamic interactions and correctly reproducing dynamical and rheological properties of colloidal suspensions. Moreover, the machine learning of lubrication correction based on GPR is not limited to the coupled DPD-DEM simulation of colloidal suspensions presented here, but can be easily applied to other particle-based simulations of particulate suspensions.

Yielding and resolidification of colloidal gels under constant stress

We examine the macroscopic deformation of a colloidal depletion gel subjected to a step shear stress. Three regimes are identified depending on the magnitude of the applied stress: (i) for stresses below yield stress, the gel undergoes a weak creep in which the bulk deformation grows sublinearly with time similar to crystalline and amorphous solids. For stresses above yield stress, when the bulk deformation exceeds approximately the attraction range, the sublinear increase of deformation turns into a superlinear growth which signals the onset of non-linear rearrangements and yielding of the gel. However, the long-time creep after such superlinear growth shows two distinct behaviors: (ii) under strong stresses, a viscous flow is reached in which the strain increases linearly with time. This indicates a complete yielding and flow of the gel. In stark contrast, (iii) for weak stresses, the gel after yielding starts to resolidify. More homogenous gels that are produced through enhancement of either interparticle attraction strength or strain amplitude of the oscillatory preshear, resolidify gradually. In contrast, in gels that are more heterogeneous resolidification occurs abruptly. We also find that heterogenous gels produced by oscillatory preshear at intermediate strain amplitude yield in a two-step process. Finally, the characteristic time for the onset of delayed yielding is found to follow a two-step decrease with increasing stress. This is comprised of an exponential decrease at low stresses, during which bond reformation is decisive and resolidification is detected, and a power law decrease at higher stresses where bond breaking and particle rearrangements dominate.

Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation

Although dense colloidal gels with interparticle bonds of order several kT are typically described as resulting from an arrest of phase separation, they continue to coarsen with age, owing to the dynamics of their temporary bonds. Here, k is Boltzmann's constant and T is the absolute temperature. Computational studies of gel aging reveal particle-scale dynamics reminiscent of condensation that suggests very slow but ongoing phase separation. Subsequent studies of delayed yield reveal structural changes consistent with re-initiation of phase separation. In the present study we interrogate the idea that mechanical yield is connected to a release from phase arrest. We study aging and yield of moderately concentrated to dense reversible colloidal gels and focus on two macroscopic hallmarks of phase separation: increases in surface-area to volume ratio that accompanies condensation, and minimization of free energy. The interplay between externally imposed fields, Brownian motion, and interparticle forces during aging or yield, changes the distribution of bond lengths throughout the gel, altering macroscopic potential energy. The gradient of the microscopic potential (the interparticle force) gives a natural connection of potential energy to stress. We find that the free energy decreases with age, but this slows down as bonds get held stretched by glassy frustration. External perturbations break just enough bonds to liberate negative osmotic pressure, which we show drives a cascade of bond relaxation and rapid reduction of the potential energy, consistent with renewed phase separation. Overall, we show that mechanical yield of reversible colloidal gels releases kinetic arrest and can be viewed as non-equilibrium phase separation.

Microstructure of the near-wall layer of filtration-induced colloidal assembly

This paper describes an experimental study of filtration of a colloidal suspension using microfluidic devices. A suspension of micrometer-scale colloids flows through parallel slit-shaped pores at fixed pressure drop. Clogs and cakes are systematically observed at pore entrance, for variable applied pressure drop and ionic strength. Based on image analysis of the layer of colloids close to the device wall, global and local studies are performed to analyse in detail the near-wall layer microstructure. Whereas global porosity of this layer does not seem to be affected by ionic strength and applied pressure drop, a local study shows some heterogeneity: clogs are more porous at the vicinity of the pore than far away. An analysis of medium-range order using radial distribution function shows a slightly more organized state at high ionic strength. This is confirmed by a local analysis using two-dimension continuous wavelet decomposition: the typical size of crystals of colloids is larger for low ionic strength, and it increases with distance from the pores. We bring these results together in a phase diagram involving colloid-colloid repulsive interactions and fluid velocity.

Two step yielding in soft materials

A review is presented on the topic of two-step yielding observed in complex fluids that cover a broad variety of materials ranging from colloidal gels, attractive glasses, emulsions, suspensions, and several commercial paste-like materials. The common features in various systems displaying two-step yielding behavior are the presence of two characteristic forces between the interacting particles or two varying representative length or time scales. This focused review aims to provide physical insights, mechanistic understanding of the two-step yielding and other associated rheological consequences of this nonlinear behavior. A discussion is provided on the microstructural details with an overview of different experimental systems exhibiting double-yielding studied so far highlighting the similarities and differences among them. Particularly, the effects of continuous phase properties, dispersed particle phase factors (size, shape, softness and surface charge) and external force field (electric, magnetic, thermal and shear flows) on two-step yielding are considered.

Embedding orthogonal memories in a colloidal gel through oscillatory shear

It has recently been shown that in a broad class of disordered systems oscillatory shear training can embed memories of specific shear protocols in relevant physical parameters such as the yield strain. These shear protocols can be used to change the physical properties of the system and memories of the protocol can later be "read" out. Here we investigate shear training memories in colloidal gels, which include an attractive interaction and network structure, and discover that such systems can support memories both along and orthogonal to the training flow direction. We use oscillatory shear protocols to set and read out the yield strain memories and confocal microscopy to analyze the rearranging gel structure throughout the shear training. We find that the gel bonds remain largely isotropic in the shear-vorticity plane throughout the training process suggesting that structures formed to support shear along the training shear plane are also able to support shear along the orthogonal plane. Orthogonal memory extends the usefulness of shear memories to more applications and should apply to many other disordered systems as well.

Swimming to Stability: Structural and Dynamical Control via Active Doping

External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces-forces that are generated by driven components within a system-in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material.

Flow and fracture near the sol-gel transition of silica nanoparticle suspensions

We analyze the evolution of the mechanical response of a colloidal suspension to an external tensile stress, from fracture to flow, as a function of the distance from the sol-gel transition. We cease to observe cracks at a finite distance from the transition. In an intermediate region where the phenomenon is clearly hysteretic, we observe the coexistence of both flow and fracture. Even when cracks are observed, the material in fact flows over a distance that increases in the vicinity of the transition.