Equilibrium concentration profiles and sedimentation kinetics of colloidal gels under gravitational stress
Stefano Buzzaccaro, Eleonora Secchi, Giovanni Brambilla, R. Piazza, Luca Cipelletti
备注：
This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version will be available online
We study the sedimentation of colloidal gels by using a combination of light scattering, polarimetry and video imaging. The asymptotic concentration profiles $φ(z,t\rightarrow \infty)$ exhibit remarkable scaling properties: profiles for gels prepared at different initial volume fractions and particle interactions can be superimposed onto a single master curve by using suitable reduced variables. We show theoretically that this behavior stems from a power law dependence of the compressive elastic modulus \textit{vs} $φ$, which we directly test experimentally. The sedimentation kinetics comprises an initial latency stage, followed by a rapid collapse where the gel height $h$ decreases at constant velocity, and a final compaction stage characterized by a stretched exponential relaxation of $h$ towards a plateau. Analogies and differences with previous works are briefly discussed.
Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "sk…
We study self-diffusion and sedimentation in colloidal suspensions of nearly-hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne--Prager--Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the…
Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. However, despite extensive work characterizing unfilled gels, little is known about how larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger `granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a `passive' regime where the filler fits into already-present voids, giving little …
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 differ…
Predicting the time-dependent yielding of colloidal gels under constant stress enables control of their mechanical stability and transport. Using rotational rheometry, we show that the shear rate of colloidal gels during an early stage of deformation known as primary creep can forecast an eventual yielding. Irrespective of whether the gel strain-softens or strain-hardens, the shear rate before failure exhibits a characteristic power-law decrease as a function of time, distinct from the linear viscoelastic response. We model this early-stage behavior as a series of uncorrelated local plastic ev…
Attractive colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and as the attraction between the particles grows, so does the elasticity of the colloidal network formed. The emergence of this rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attraction strengths is lacking. Moreover, recovering an accurate gelation phase diagram based on the …
The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different size. We show that the elastic properties vary in a highly non trivial way as consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its m…
Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between…
Shear history plays an important role in determining the linear and nonlinear rheological response of colloidal gels and can be used for tuning their structure and flow properties. Increasing colloidal particle aspect ratio lowers the critical volume fraction for gelation due to an increase of the particle excluded volume. Using a combination of rheology and confocal microscopy we investigate the effect of steady and oscillatory pre-shear history on the structure and rheology of colloidal gels formed by silica spheres and rods of length L and diameter D (L/D = 10) dispersed in 11 M CsCl soluti…
Locally (re)structuring colloidal gels $\unicode{x2013}$ micron-sized particles forming a connected network with arrested dynamics $\unicode{x2013}$ enables precise tuning of the micromechanical and -rheological properties of the system. A recent experimental study [B. Saint-Michel, G. Petekidis, and V. Garbin, Soft Matter $\boldsymbol{18}$, 2092 (2022)] showed that rapid restructuring can occur by acoustically modulating an embedded microbubble. Here, we perform Brownian dynamics simulations to understand the mechanical effect of an oscillating microbubble on the structure of the embedding co…
We investigate theoretically the effect of gravity on a plate-sphere colloidal mixture by means of an Onsager-like density functional to describe the bulk, and sedimentation path theory to incorporate gravity. We calculate the stacking diagram of the mixture for two sets of buoyant masses and different values of the sample height. Several stacking sequences appear due to the intricate interplay between gravity, the sample height, and bulk phase separation. These include the experimentally observed floating nematic sequence, which consists of a nematic layer sandwiched between two isotropic lay…
Colloidal gels possess a memory of previous shear events, both steady and oscillatory. This memory, embedded in the microstructure, affects the mechanical response of the gel, and therefore enables precise tuning of the material properties under careful preparation. Here we demonstrate how the dynamics of a deformable inclusion, namely a bubble, can be used to locally tune the microstructure of a colloidal gel. We examine two different phenomena of bubble dynamics that apply a local strain to the surrounding material: dissolution due to mass transfer, with a characteristic strain rate of $10^{…
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model - "sticky spheres". Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experi…
We study the driven collective dynamics of a colloidal monolayer sedimentating down an inclined plane. The action of the gravity force parallel to the bottom wall creates a flow around each colloid, and the hydrodynamic interactions among the colloids accelerate the sedimentation as the local density increases. This leads to the creation of a universal "triangular" inhomogeneous density profile, with a traveling density shock at the leading front moving in the downhill direction. Unlike density shocks in a colloidal monolayer driven by applied torques rather than forces [Phys. Rev. Fluids, 2(9…
Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regime…
The role of sample height in the stacking diagram of colloidal mixtures under gravity
体相分离是导致胶体混合物在沉降过程中出现不同层堆叠的原因。最近提出的理论（de las Heras and Schmidt 2013软物质9 8636）建立了体相行为和沉积-扩散-平衡之间的独特联系。该理论构建了一个堆叠图的所有可能的序列堆栈重力下的限制非常高（无限）的样品高度。在这里，我们研究了有限样品高度h下胶体混合物的堆积图。我们证明了h在胶体混合物的沉积扩散平衡中起着至关重要的作用。在堆积图中，给定的堆积序列所占据的区域取决于h。因此，具有不同高度但相同胶体浓度的两个样品可以形成不同的堆积序列。此外，不同高度的堆积图可以是定性不同的，因为一些堆积序列仅发生在样品高度的给定间隔中。我们使用的理论来研究堆积图的模型散装系统和混合物的补丁颗粒的数量或类型的补丁不同。
We study theoretically the effect of a gravitational field on the equilibrium behaviour of a colloidal suspension of rods with different length-to-width aspect ratios. The bulk phases of the system are described with analytical equations of state. The gravitational field is then incorporated via sedimentation path theory, which assumes a local equilibrium condition at each altitude of the sample. The bulk phenomenology is significantly enriched by the presence of the gravitational field. In a suspension of elongated rods with five stable phases in bulk, the gravitational field stabilizes up to…
