Volume 58, Issue 5, September 2014
Index of content:
58(2014); http://dx.doi.org/10.1122/1.4882021View Description Hide Description
We use numerical simulations and an athermal quasistatic shear protocol to investigate the yielding of a model colloidal gel. Under increasing deformation, the elastic regime is followed by a significant stiffening before yielding takes place. A space-resolved analysis of deformations and stresses unravel how the complex load curve observed is the result of stress localization and that the yielding can take place by breaking a very small fraction of the network connections. The stiffening corresponds to the stretching of the network chains, unbent, and aligned along the direction of maximum extension. It is characterized by a strong localization of tensile stresses that triggers the breaking of a few network nodes at around 30% of strain. Increasing deformation favors further breaking but also shear-induced bonding, eventually leading to a large-scale reorganization of the gel structure at the yielding. At low enough shear rates, density and velocity profiles display significant spatial inhomogeneity during yielding in agreement with experimental observations.
A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski's ratchet58(2014); http://dx.doi.org/10.1122/1.4892115View Description Hide Description
We study via theory and dynamical simulation the evolving structure, particle dynamics, and time-dependent rheological properties of an aging colloidal gel, with a focus on the micro-mechanics that drive coarsening and age-related changes in linear-response behavior. When colloids in suspension attract one another, the attractions can lead to phase separation into particle-rich and particle-poor regions separated by a single interface. But this transition is sometimes interrupted before full separation occurs. With certain particle concentrations and interparticle potentials, the attractions that promote phase separation also inhibit it, frustrating the separation and “freezing in” a nonequilibrium particle configuration, resulting in a space-spanning gel. With attractions on the order of a few kT, gelation can produce nonfractal bicontinuous morphologies. In such “reversible” gels, thermal fluctuations are strong enough to rupture bonds and reform new ones, allowing restructuring of the gel over time. But, because particle diffusion is dramatically slowed by interparticle attractions, the march toward equilibrium is frustrated. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times or heterogeneity. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, and crystalline), how restructuring takes place (via bulk diffusion, surface migration, and coalescence of large structures), and the impact of the evolution on rheology. In this study, we conduct dynamic simulations to elucidate the post-gelation evolution of a system of 750 000 Brownian spheres interacting via a hard-sphere repulsion and short-range attractions of order kT, as would be generated by a polymer depletant, for example. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski's ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of nonhydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on network length scale which, when carried out, collapses each modulus for all gel ages onto a single universal curve. A theoretical model inspired by the Rouse model is advanced and, from it, we have obtained an analytical expression that captures the effects of (finite) structural aging on rheology: The moduli are linear in the network size, suggesting that linear mechanical response can be determined at any age by measurement of dominant network length scale—or vice versa.
Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis58(2014); http://dx.doi.org/10.1122/1.4871474View Description Hide Description
The nonlinear rheology of glass-forming colloidal suspensions with short-ranged attractions is discussed within the integration-through transients framework combined with the mode-coupling theory of the glass transition. Calculations are based on the square-well system, as a model for colloid-polymer mixtures. The high-density regime featuring reentrant melting of the glass upon increasing the attraction strength and the crossover from repulsive glasses formed at weak attraction to attractive glasses formed at strong attraction are discussed. Flow curves are found in qualitative agreement with experimental data, featuring a strong increase in the yield stress and for suitable interaction parameters, the crossover between two yield stresses. The yield strain, defined as the position of the stress overshoot under startup flow, is found to be proportional to the attraction range for strong attraction. At weak and intermediate attraction strength, the combined effects of hard-core caging and attraction-driven bonding result in a richer dependence on the parameters. The first normal-stress difference exhibits a weaker dependence on short-ranged attractions as the shear stress, since the latter is more sensitive than the short-wavelength features of the static structure.
58(2014); http://dx.doi.org/10.1122/1.4892814View Description Hide Description
58(2014); http://dx.doi.org/10.1122/1.4881256View Description Hide Description
We present results from microscopic mode coupling theory generalized to colloidal dispersions under shear in an integration-through-transients formalism. Stress-strain curves in start-up shear, flow curves, and normal stresses are calculated with the equilibrium static structure factor as only input. Hard spheres close to their glass transition are considered, as are hard spheres with a short-ranged square-well attraction at their attraction dominated glass transition. The consequences of steric packing and physical bond formation on the linear elastic response, the stress release during yielding, and the steady plastic flow are discussed and compared to experimental data from concentrated model dispersions.
58(2014); http://dx.doi.org/10.1122/1.4878838View Description Hide Description
We propose a microscopic framework based on nonequilibrium statistical mechanics to connect the microscopic level of particle self-assembly with the macroscopic rheology of colloidal gelation. The method is based on the master kinetic equations for the time evolution of the colloidal cluster size distribution, from which the relaxation time spectrum during the gelation process can be extracted. The relaxation spectrum is a simple stretched-exponential for irreversible diffusion-limited colloidal aggregation gelation, with a stretching exponent df /3, where df is the mass fractal dimension. As opposed to glassy systems, the stretched-exponential relaxation does not result from quenched disorder in the relaxation times, but from the self-assembly kinetics in combination with the fractal character of the process. As the master kinetic equations for colloidal aggregation do not admit bond-percolation solutions, the arrest mechanism is driven by the interconnection among fractal clusters when excluded volume becomes active, i.e., at sufficiently high packing of clusters. The interconnections between rigid clusters decrease the soft modes of the system and drive a rigidity-percolation transition at the cluster level. Using the Boltzmann superposition principle, the creep and the full rheological response can be extracted for both irreversible and thermoreversible colloidal aggregation. In the case of thermoreversible gelation, the attraction energy is finite and plays the role of the control parameter driving a nonequilibrium phase transition into a nonequilibrium steady-state (the gel). A power-law spectrum coexisting with a stretched-exponential cut-off is predicted leading to power-law rheology at sufficiently high frequency. Our theory is in good agreement with experimental data of different systems published by other authors, for which no theory was available.
58(2014); http://dx.doi.org/10.1122/1.4891873View Description Hide Description
Wall adhesion effects during batch sedimentation of strongly flocculated colloidal gels are commonly assumed to be negligible. In this study, in-situ measurements of gel rheology and solids volume fraction distribution suggest the contrary, where significant wall adhesion effects are observed in a 110 mm diameter settling column. We develop and validate a mathematical model for the equilibrium stress state in the presence of wall adhesion under both viscoplastic and viscoelastic constitutive models. These formulations highlight fundamental issues regarding the constitutive modeling of colloidal gels, specifically the relative utility and validity of viscoplastic and viscoelastic rheological models under arbitrary tensorial loadings. The developed model is validated against experimental data, which points toward a novel method to estimate the shear and compressive yield strength of strongly flocculated colloidal gels from a series of equilibrium solids volume fraction profiles over various column widths.
Dynamic localization and shear-induced hopping of particles: A way to understand the rheology of dense colloidal dispersions58(2014); http://dx.doi.org/10.1122/1.4866038View Description Hide Description
For decades, attempts have been made to understand the formation of colloidal glasses and gels by linking suspension mechanics to particle properties where details of size, shape, and spatial dependencies of pair potentials present a bewildering array of variables that can be manipulated to achieve observed properties. Despite the range of variables that control suspension properties, one consistent observation is the remarkably similarity of flow properties observed as particle properties are varied. Understanding the underlying origins of the commonality in those behaviors (e.g., shear-thinning with increasing stress, diverging zero shear rate viscosity with increasing volume fraction, development of a dynamic yield stress plateau with increases in volume faction or strength of attraction, development of two characteristic relaxation times probed in linear viscoelasticity, the creation of a rubbery plateau modulus at high strain frequencies, and shear-thickening) remains a challenge. Recently, naïve mode coupling and dynamic localization theories have been developed to capture collective behavior giving rise to formation of colloidal glasses and gels. This approach characterizes suspension mechanics of strongly interacting particles in terms of sluggish long-range particle diffusion modulated by varying particle interactions and volume fraction. These theories capture the scaling of the modulus with the volume fraction and strength of interparticle attraction, the frequency dependence of the moduli at the onset of the gel/glass transition, together with the divergence of the zero shear rate viscosity and cessation of diffusivity for hard sphere systems as close packing is approached. In this study, we explore the generality of the predictions of dynamic localization theory for systems of particles composed of bimodal particle size distributions experiencing weak interactions. We find that the mechanical properties of these suspensions are well captured within the framework of dynamic localization theory and that suspension mechanics can be understood in terms of a dynamical potential barrier, the magnitude of which governs the zero shear rate viscosity, and onset of a dynamic yield stress plateau as volume fraction or strength of interaction is raised.
The microstructure and rheology of a model, thixotropic nanoparticle gel under steady shear and large amplitude oscillatory shear (LAOS)58(2014); http://dx.doi.org/10.1122/1.4878378View Description Hide Description
The microstructure-rheology relationship for a model, thermoreversible nanoparticle gel is investigated using a new technique of time-resolved neutron scattering under steady and time-resolved large amplitude oscillatory shear (LAOS) flows. A 21 vol. % gel is tested with varying strength of interparticle attraction. Shear-induced structural anisotropy is observed as butterfly scattering patterns and quantified through an alignment factor. Measurements in the plane of flow show significant, local anisotropy develops with alignment along the compressional axis of flow, providing new insights into how gels flow. The microstructure-rheology relationship is analyzed through a new type of structure-Lissajous plot that shows how the anisotropic microstructure is responsible for the observed LAOS response, which is beyond a response expected for a purely viscous gel with constant structure. The LAOS shear viscosities are observed to follow the “Delaware-Rutgers” rule. Rheological and microstructural data are successfully compared across a broad range of conditions by scaling the shear rate by the strength of attraction, providing a method to compare behavior between steady shear and LAOS experiments. However, important differences remain between the microstructures measured at comparatively high frequency in LAOS experiments and comparable steady shear experiments that illustrate the importance of measuring the microstructure to properly interpret the nonlinear, dynamic rheological response.
Time dependence in large amplitude oscillatory shear: A rheo-ultrasonic study of fatigue dynamics in a colloidal gel58(2014); http://dx.doi.org/10.1122/1.4887081View Description Hide Description
We report on the response of a yield stress material, namely, a colloidal gel made of attractive carbon black particles, submitted to large amplitude oscillatory shear stress (LAOStress) in a Couette geometry. At a constant stress amplitude well below its apparent yield stress, the gel displays fatigue and progressively turns from an elastic solid to a viscous fluid. The time-resolved analysis of the strain response, of the Fourier components, and of Lissajous plots allows one to define two different timescales associated with the yielding and fluidization of the gel. Coupling rheology to ultrasonic imaging further leads to a local picture of the LAOStress response in which the gel first fails at the walls at τw and then undergoes a slow heterogeneous fluidization involving solid–fluid coexistence until the whole sample is fluid at τf . Spatial heterogeneities are observed in both the gradient and vorticity directions and suggest a fragmentation of the initially solidlike gel into macroscopic domains eroded by the surrounding fluidized suspension.
Microstructure and nonlinear signatures of yielding in a heterogeneous colloidal gel under large amplitude oscillatory shear58(2014); http://dx.doi.org/10.1122/1.4882019View Description Hide Description
We investigate yielding in a colloidal gel that forms a heterogeneous structure, consisting of a two-phase bicontinuous network of colloid-rich domains of fractal clusters and colloid-poor domains. Combining large amplitude oscillatory shear measurements with simultaneous small and ultra-small angle neutron scattering (rheo-SANS/USANS), we characterize both the nonlinear mechanical processes and strain amplitude-dependent microstructure underlying yielding. We observe a broad, three-stage yielding process that evolves over an order of magnitude in strain amplitude between the onset of nonlinearity and flow. Analyzing the intracycle response as a sequence of physical processes reveals a transition from elastic straining to elastoplastic thinning (which dominates in region I) and eventually yielding (which evolves through region II) and flow (which saturates in region III), and allows quantification of instantaneous nonlinear parameters associated with yielding. These measures exhibit significant strain rate amplitude dependence above a characteristic frequency, which we argue is governed by poroelastic effects. Correlating these results with time-averaged rheo-USANS measurements reveals that the material passes through a cascade of structural breakdown from large to progressively smaller length scales. In region I, compression of the fractal domains leads to the formation of large voids. In regions II and III, cluster-cluster correlations become increasingly homogeneous, suggesting breakage and eventually depercolation of intercluster bonds at the yield point. All significant structural changes occur on the micron-scale, suggesting that large-scale rearrangements of hundreds or thousands of particles, rather than the homogeneous rearrangement of particle-particle bonds, dominate the initial yielding of heterogeneous colloidal gels.
58(2014); http://dx.doi.org/10.1122/1.4872059View Description Hide Description
We investigate the yielding behavior of colloid-polymer gels with intermediate volume fraction, which are subjected to large amplitude oscillatory shear, using rheology and light scattering echo (LS-Echo). Particular attention is given to the anharmonic contributions to the stress response and the characteristic timescale and extent of plastic rearrangements. Yielding is already observed at small strain amplitudes , where the network of interconnected clusters starts to break up and irreversible particle rearrangements are first observed. However, only at considerably larger strain amplitudes, , the network is completely disrupted and small clusters or individual particles flow. This complex yielding behavior is reflected in different regimes of in-cycle yielding, which were extracted from the analysis of the anharmonic contributions to the stress. In the range of strain amplitudes where bond breaking starts, in-cycle strain hardening and shear thickening are observed, with the strain hardening possibly caused by the shear-induced formation of more compact clusters. When the network is broken down, in-cycle shear thinning is observed with increasing strain amplitude, but still together with strain hardening. Both, the elastic and viscous nonlinear contributions, decrease with increasing strain amplitude, indicating the progressive fluidization of the system, consistent with the faster plastic rearrangements observed in LS-Echo. Two-distinct frequency-dependent regimes for the initial yielding at small strains are present: At small to moderate oscillation frequencies, the first yield strain increases with increasing frequency, while it decreases at large frequencies. This might be associated with the timescale for bond breaking, namely, the Brownian diffusion time at small frequencies and the inverse of the oscillation frequency at large frequencies.