Session S8: Colloidal Rheology

Shear Thickening, Gel Elasticity and Internal Stresses in a Colloidal System with Attractive Interactions

Dilute dispersions of carbon particles in hydrocarbon fluids flocculate, forming colloidal gels with typical fractal scaling of shear modulus with particle volume fraction. Surprisingly, these systems exhibit shear thickening in two regimes. At low shear rates, shear thickening is concurrent with the formation of vorticity-aligned structures, a general phenomenon in attractively-interacting complex fluids, but not previously implicated in shear thickening. At high P\'{e}clet numbers, thickening involves degradation of particle clusters and an increase in effective volume fraction. This contrasts with the hard-sphere case where thickening is due to pseudo-jamming events that occur with the growth of hydro-clusters with persistent contacts. On cessation of high shear rate flow, these shear thickened gels display a power-law dependence of elasticity on pre-shear stress and the data can be re-scaled simply to provide a universal response for different particle volume fractions. We propose a mechanism and scaling argument that accounts for this behavior in terms of the stress dependence of the cluster number density during pre-shear. We characterize the internal stresses that result from a shear rate quench from the fluid to the gel state and find that the modulus is directly proportional to the internal stress in the system. At short times, t$\approx 10^3$s, the internal stress decays with a weak power law dependence on time.   

Microscopic Details of Plastically Sheared Colloidal Gels

We use fast confocal microscopy to study effects of different shear rates on colloidal depletion gels. Our samples consist of PMMA spheres in a refractive index matched solvent, with polymer added to produce a depletion interaction. We subject these samples to different rates of oscillatory shear with similar strain amplitudes. By tracking the three-dimensional trajectories of several thousand particles, we directly observe how shear modifies the gel's structure at the particle-level and how differences in local structure affect shear-induced dynamics. We find that increasing shear rate significantly increases the rate of plastic bond rearrangement, but that large clusters remain mostly intact, even when the observed deformations are highly non-affine.   

Delayed Collapse of Colloidal Gels

We study the behavior of colloidal gels under gravitational forces using a system of polystyrene beads and non-adsorbing polymer to induce depletion attraction between particles. As the interaction energy or the volume fraction decreases, a delayed collapse regime is observed, where the sedimentation of the gels starts with a slow initial compression followed, after a delay time, by a rapid collapse characterized by the coarsening of the structure. By means of changing the density mismatch between the network and the surrounding solvent, we are able to explore the dependence of the delay time and coarsening behavior with the gravitational stress. The results clearly show that, even though only the weakest gels undergo delayed collapse, the gravitational stress is not the trigger leading to the coarsening of the structure, although it certainly affects the time it takes the gel to completely sediment.   

Effect of Nanoparticle Shape and Size on Shear Rheology

The effect of nanoparticle shape and size on the shear rheology of nanoparticle suspensions was explored through non-equilibrium molecular dynamics simulations. Composite nanoparticles consisting of rigid Lennard-Jones particles in a Lennard-Jones explicit solvent were modeled using the M\"{u}ller-Plathe ``reverse'' perturbation method. A series of suspensions were modeled wherein the nanoparticle volume fraction was held constant while the shape and size of the nanoparticles were varied. Specifically, results for the shear viscosity of spherical, plate, and rod-like nanoparticles of size varying from tens to hundreds of interaction sites will be presented. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.   

Shear Thinning in Nanoparticle Suspensions

Results of large scale non-equilibrium molecular dynamics (NEMD) simulations are presented for nanoparticles in an explicit solvent. The nanoparticles are modeled as a uniform distribution of Lennard-Jones particles, while the solvent is represented by standard Lennard-Jones particles. Here we present results for the shear rheology of spherical nanoparticles of size 5 to 20 times that of the solvent for a range of nanoparticle volume fractions and interactions. Results from NEMD simulations suggest that for strongly interacting nanoparticle that form a colloidal gel, the shear rheology of the suspension depends only weakly on the size of the nanoparticle, even for nanoparticles as small as 5 times that of the solvent. However for hard sphere-like colloids the size of the nanoparticles strongly affects the shear rheology. The shear rheology for dumbbell nanoparticles made of two fused spheres is also compared to spherical nanoparticles and found to be similar except at very high volume fractions. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04- 94AL85000.   

Viscosity of confined suspensions.

In this work, we study experimentally and numerically the viscosity of non-brownian confined suspensions of hard spherical particles confined between two walls in a shear flow. By varying the wall-to-wall distance (gap), we show that the viscosity presents a remarkable behavior as a function of the confinement. A transition occurs from a 3D configuration (no confinement) to a quasi2D (Q2D) one when the wall-to-wall distance becomes smaller than twice the spheres diameter. We find, as expected, that the effective viscosity increases when the gap decreases. This is due to dissipation which is enhanced for smaller gaps. But, more precisely, when the wall-to-wall distance decreases, the linear term in volumic fraction (diluted case) increases while the quadratic term decreases to zero when the suspension reaches a Q2D regime and becomes negative for smaller gaps. In a Q2D suspension, it is proven that an anti-drag effect holds between two particles which move perpendicularly to their connecting line. Experimental measurements on diffusion coefficients have been achieved for colloidal Q2D suspensions by Cui et al [1] which shows this behavior without any ambiguity. We suspect that such anti-drag interactions can affect the viscosity of Q2D semi-diluted suspensions. [1] B. Cui, H. Diamant, B. Lin and S. Rice, Phys. Rev. Lett., vol. 92, 258301 (2004)   

Rate dependence, drag balance and role of disorder in linearly sheared foams.

We linearly shear a bidisperse foam monolayer sandwiched between a glass plate and a fluid surface over 3 orders of magnitude in driving velocity. We find strongly rate-dependent velocity profiles, which become increasingly shear banded with shear rate. We also confirm previous findings that monodisperse foam layers exhibit rate-{\it independent} velocity profiles. Both behaviors are quantitatively captured in a model that balances the viscous drag forces in the foam, provided that we assume the average drag force between bubbles in disordered foams to scale differently than the drag force at the bubble scale. We confirm the scaling of the drag forces in both mono- and bidisperse foams by independent rheological measurements, and confirm the crucial role of disorder on the flow of foams.   

Shear Modulus of a Depletion-Induced Colloidal Gel

Mechanical properties of a colloidal gel are of great interest because they are related to the processability of the colloidal dispersion and its stability. We measure the shear modulus for colloidal gel networks induced by depletion attraction and determine the relationship between the strength of the depletion attraction and the magnitude of the shear modulus.   

Irreversible flow-induced vitrification of nanoemulsions by extreme droplet rupturing

Some materials weaken through fracturing when subjected to extreme stresses. However, breaking down repulsive bits of condensed matter that are dispersed in a viscous liquid can also potentially cause a dramatic and irreversible increase in the dispersion's elasticity. Here, we demonstrate this principle using dispersions of one liquid in another immiscible liquid. Anionically stabilized microscale emulsions are subjected to a history of extreme high-pressure microfluidic flow, causing the droplets to rupture to nanoscale sizes. As the droplet radius decreases below 100 nm, the nanoemulsion can develop an unusually large elastic modulus, even at droplet volume fractions far below maximal random jamming of uniform hard spheres. Thus, through the history of applied flow, a liquid microscale emulsion can be transformed and vitrified into an elastic nanoemulsion of disordered repulsive droplets without altering the composition. Furthermore, we show that systematic macroscopic shear rheology of the nanoemulsion glass as a function of the droplet volume fraction can be effectively used as a surfaces forces apparatus to deduce the screened Debye interaction potential as a function of separation between the droplet interfaces.   

Hindered rising in aggregating polydisperse particle suspensions

We describe a direct simulation method that effectively determines the appropriate hindered rising behavior of polydisperse particle suspensions. Our method allows adequate representation of the hydrodynamic interactions as well as system specific colloidal interactions. Simulation results are in good agreement with experimental data obtained by MRI imaging. Our results demonstrate the importance of particle aggregation in the hindered rising suspensions.   

Self-organized criticality of slowly sedimenting sheared suspensions

Suspensions of neutrally buoyant particles driven by slow periodic shear can undergo a dynamical phase transition from an absorbing reversible steady state to a fluctuating irreversible state. For a given strain amplitude {\$}$\backslash $gamma{\$}, this transition occurs at a specific critical volume fraction {\$}$\backslash $Phi{\_}c{\$}. However, if the particles are not neutrally buoyant, they either sink to the bottom or float to the top of the container. New experiments and simulations show that under periodic shear, the particles resuspend, however, and that for a given strain amplitude {\$}$\backslash $gamma{\$}, the particles evolve towards the critical concentration {\$}$\backslash $Phi{\_}c{\$} without any external intervention. In that case, particle collisions nucleated at the bottom of the shear cell propagate through the sample and keep the system suspended close to the critical volume fraction {\$}$\backslash $Phi{\_}c($\backslash $gamma){\$}. Hence, slowly sedimenting particles under oscillatory shear appear as a new class of self-organized critical systems hitherto unreported.   

Random organization: A dynamical phase transition

We introduce a simple model motivated by recent experiments in sheared suspensions. We show that completely random displacements of colliding particles are sufficient to generate an organized state where further collisions are suppressed. This organization by self-activated random walkers presents a much more efficient process than when all particles are diffusing. It only occurs provided that the density in particle is lower than a critical value $\rho _{c}$ and is characterized by a dynamical phase transition. A mean-field description captures the existence of this transition. It suggests that the value of $\rho _{c}$ is determined by the ratio p$_{s}$/p$_{c}$, where p$_{s}$ is the probability for a pair of colliding particles to separate and p$_{c}$ is the probability that a ``quiet'' particle be collided. Our results also reveal that the ordering can be enhanced by straining the system periodically. However, these more organized states become less and less accessible as the strain amplitude is increased.   

X-ray photon correlation spectroscopy in a shear flow

X-ray photon correlation spectroscopy was used to measure the diffusive dynamics of colloidal suspensions in a shear flow. The results presented here show how the intensity autocorrelation functions measure a coupling between the diffusive dynamics of the particles and their flow-induced, convective motion. However, in the limit of low flow/shear rates, it is possible to obtain the diffusive component of the dynamics. The conditions under which this is possible are easier to achieve at higher values of the scattering wavevector q and this may provide an advantage of X-ray over, for e.g. light, photon correlation spectroscopy. In recent work (A. Fluerasu et al., submitted, 2007) we have shown this result to hold for dillute (particle volume fraction $\Phi \approx$ 10 \%) suspensions when the correlation functions probe, basically, the self-diffusion of individual, non-interacting particles. Here we will also adress the collective motion of concentrated suspensions of hard-sphere systems ($\Phi$ up to 50 \%) and study the coupling between the shear-induced response and the collective diffusion of the suspension. An important benefit of this experimental strategy over more traditional X-ray methods, is the minimization of X-ray induced beam damage, which makes the method suitable for the study of the dynamical properties of a large class of complex soft-matter and biological fluids.   

Electrophoretic ``Equilibrium'' Profile of Charged Colloids

We perform an electrophoresis experiment of a concentrated colloid against a semipermeable membrane. The electric field forces the charged particles against the membrane and sets up a concentration profile similar to that of a colloid in gravitational sedimentation equilibrium where gravitational forces compete against the osmotic pressure gradient. In the present case there is a current which flows through the electrolyte so the system reaches a steady state profile rather than equilibrium. The electric field, colloid and ionic concentrations adjust self consistently to produce the profile. We use 91 nm polystyrene spheres with sufficient charge that they crystallize and observe their Bragg scattering as a function of height to determine the lattice spacing and particle concentration. We also use 700nm spheres and obtain their concentration profile with X-ray absorption. The fluid flow is zero for a capped system. Connecting a return tube from the supernatant side above the electrophoretic sediment to below the filter yields an electroosmotic flow and circulation. The profile changes substantially and allows us to study the hydrodynamic interactions as a function of concentration for the electrophoresing particles.