Session P51: Colloids III: Shear and Hydrodynamics

Confined colloidal suspensions under simple shear

Here we report a study of a simple model system, a colloidal suspension of near hard spheres in an otherwise Newtonian fluid using Stokesian Dynamics (SD) simulations in combination with Non-Equilibrium Umbrella Sampling (NEUS) techniques. The suspension is confined by an external potential in the y direction and is driven far out of equilibrium with a simple shear flow. At moderate shear rate, the suspension forms layers normal to the flow gradient direction, in contrast to equilibrium. In addition to that, novel anisotropic structures (strings in vorticity direction at low density for example) are observed within each layer. We use Non-Equilibrium Umbrella Sampling to explore the relationship between this string structure and the strength of the layer formation. Furthermore we have also studied the relationship between the non-Newtonian behavior of the suspension and the strength of the layer structure.   

The nonlinear structural response of colloidal suspensions under large amplitude oscillatory shear

When a colloidal suspension is under oscillatory shear, the particle configuration has a flow-induced anisotropy. While these structural rearrangements have been intensively studied in the linear regime where the amplitude of the applied shear is small, the nonlinear structural response of suspensions under large amplitude oscillatory shear is poorly understood. Using a shear cell coupled to a fast confocal microscope, we directly measured the microscopic structure of colloidal suspensions under large amplitude oscillatory shear. To quantify the structural response, we integrated the pair correlation function over all contact positions; this quantity is proportional to the entropic stress of the suspension. We investigated the structural/stress response of colloidal suspensions systematically with increasing shear amplitudes. We observed strong nonlinear responses in both dense and dilute suspensions under large amplitude oscillatory shear. At even higher amplitudes, we found an overshoot of the stress response in dense suspensions. Our results provide insight on the microscopic structural origin of the nonlinear response of sheared colloidal suspensions.   

Imaging the microscopic structure of shear thinning and thickening colloidal suspensions

The viscosity of colloidal suspensions can vary by orders of magnitude depending on how quickly they are sheared. Although this non-Newtonian behavior is believed to arise from the arrangement of suspended particles and their mutual interactions, microscopic particle dynamics in such suspensions are difficult to measure directly. Here, by combining fast confocal microscopy with simultaneous force measurements, we systematically investigate a suspension's structure as it transitions through regimes of different flow signatures. Our measurements of the microscopic single-particle dynamics unambiguously show that shear thinning results from the decreased relative contribution of entropic forces and that shear thickening arises from particle clustering induced by inter-particle hydrodynamic lubrication forces. Furthermore, we explore out-of-equilibrium structures of sheared colloidal suspensions and report a novel string phase, where particles link into log-rolling strings normal to the plane of shear. Our techniques illustrate an approach that complements current methods for determining the microscopic origins of non-Newtonian flow behavior in complex fluids.   

Shear induced diffusion in hard sphere glasses

The response of dense hard sphere suspensions is examined during the application of steady and non-linear oscillatory shear using Brownian Dynamics (BD) simulations and experimental Light Scattering echo coupled with rheology. At rest, volume fractions around the glass transition exhibit long or infinite relaxation times. However, non-linear shear induces out of cage motions of comparable time scale to the applied rates. We found two distinct regimes in terms of stresses and dynamic response under shear. One regime for lower rates or frequencies of oscillation, governed by Brownian activated diffusion, and a second for higher rates related to shear activated diffusion. A linear dependence with rate was found for the diffusivity in the high rate regime, mirroring the viscous loss due to shear activated particle rearrangements, while diffusivities in the Brownian activated regime showed a power law exponent of less than unity. The exponent was found to increase with volume fraction. For applied rates inducing diffusivities above the in-cage diffusivity at rest, we find a time window of super-diffusive behavior, between the short time (in-cage) and long time (out-of cage) diffusivities under shear, a signature of a dynamic breaking and reforming of the cage.   

Diffusion in sheared athermal soft-particle suspensions: the role of inertia and dissipation mechanism

We perform numerical simulations to study diffusion in a model bi-disperse frictionless athermal soft-particle suspension of disks in two dimensions (2D). To model athermal shear, we damp the motion of a particle \emph{either} with respect to the globally imposed flow \emph{or} with respect to its near neighbors. We study shear flows at various rate $\dot{\gamma}$, system size $L$, and damping strength $b$ at packing fractions well above the random close packing point. At low $\dot{\gamma}$, we find a quasi-static effective transverse diffusion co-efficient, $D_{\rm eff}$, which has very weak dependence on $\phi$, $b$, or the damping mechanism yet has a pronounced linear dependence on $L$ in agreement with what is observed in conventional models of bulk metallic glasses. Away from the quasi-static regime, $D_{\rm eff}$ no longer depends on $L$, and $b$ has a profound impact on the scaling behavior of $D_{\rm eff}$ with $\dot{\gamma}$.   

Shear thinning in soft particle suspensions

Suspensions of soft deformable particles are encountered in a wide range of food and biological materials. Examples are biological cells, micelles, vesicles or microgel particles. While the behavior of suspenions of hard spheres - the classical model system of colloid science - is reasonably well understood, a full understanding of these soft particle suspensions remains elusive. The relation between single particle properties and macroscopic mechanical behavior still remains poorly understood in these materials. Here we examine the surprising shear thinning behavior that is observed in soft particle suspensions as a function of particle softness. We use poly-N-isopropylacrylamide (p-NIPAM) microgel particles as a model system to study this effect in detail. These soft spheres show significant shear thinning even at very large Peclet numbers, where this would not be observed for hard particles. The degree of shear thinning is directly related to the single particle elastic properties, which we characterize by the recently developed Capillary Micromechanics technique. We present a simple model that qualitatively accounts for the observed behavior.   

Anisotropic Diffusion of Colloidal Particles in a Shear Flow

Asymmetrically-shaped particles show anisotropic diffusive behavior along different particle axes. This anisotropic diffusion, however, is averaged out on long time scales due to the rotational diffusion of the particles. Here we report on an experimental study of anisotropic colloidal dimers suspended in an oscillatory shear flow. A preferred orientation of the dimers arises due to the applied oscillatory shear. This results in anisotropic particle diffusion that is persistent at long time scales. We compare our results to a simple model of diffusing particles in a shear flow, and comment briefly on the possibility of using this result for assembling out-of-equilibrium colloidal structures.   

Pattern formation in colloidal explosions: Theory and experiment

We study the nonequilibrium pattern formation that emerges when magnetically repelling colloids, trapped by optical tweezers, are abruptly released, forming colloidal explosions [EPL 94, 48008 (2011)]. For multiple colloids in a single trap, we observe a pattern of expanding concentric rings. For colloids individually trapped in a line, we observe explosions with a zigzag pattern that persists even when magnetic interactions are much weaker than those that break the linear symmetry in equilibrium. Theory and computer simulations quantitatively describe these phenomena both in and out of equilibrium. An analysis of the mode spectrum allows us to accurately quantify the nonharmonic nature of the optical traps. Colloidal explosions provide a new way to generate well-characterized nonequilibrium behavior in colloidal systems.   

Universal Scaling Law of Diffusion and Hydrodynamic Corrections in Colloidal Monolayers

Using dense monolayers of colloidal particles and the techniques of optical microscopy and particle tracking, we tested the universal scaling law of the diffusion constant of colloidal particles as a function of excess entropy. By varying the area fraction of the colloidal monolayer, we measured the diffusion constant and the corresponding pair correlation function of the colloidal particles, from which the excess entropy can be calculated. It is found that the universal scaling law applies to a monolayer of latex suspensions at an air-water interface when the inter-particle repulsions are dominant over the hydrodynamic interactions. For colloidal monolayers of hard spheres at the air-water interface and near a solid wall, the universal scaling law starts to deviate from its original form as the short-ranged hydrodynamic interactions increase.   

Long Range Hydrodynamic Correlations in Quasi-One-Dimensional Circular and Linear Geometries

We report the results of studies of the collective and pair diffusion coefficients of particles in two quasi-one-dimensional geometries: straight 2 mm long channels and rings with radii between 3 and 35 $\mu $m. We investigate, for both geometries, the observed density dependence in the collective diffusion coefficient as predicted by Frydel and Diamant (Phys. Rev. Letts. 104, 248302 (2010). The origin of this density dependence is the nonvanishing q = 0 component of the Green's function of the linearized one-dimensional hydrodynamic equation, which is indicative of the hydrodynamic coupling resulting from collective motion of particles in periodic or infinite quasi-one-dimensional geometries.   

Using artificial microswimmers for particle separation

Microscopic self-propelled swimmers capable of autonomous navigation through complex environments provide appealing opportunities for localization, pick-up and delivery of micro-and nanoscopic objects. Inspired by motile cells and bacteria, man-made microswimmers have been created, and their motion was studied experimentally in patterned surroundings [1]. We propose to use artificial microswimmers -- Janus spheres [2] illuminated by light -- as ``driving agents'' that move through a binary mixture of colloidal particles. We demonstrated [3] that binary mixtures can be effectively separated in this way. We analyzed the main features of the particle separation and explained mechanisms of different regimes including the one with a velocity inversion. Our finding can be readily verified in experiments with colloidal binary mixtures and could be of use for various biological and medical applications. \\[4pt] [1] G.~Volpe et al., Soft Matter {\bf 7}, 8810 (2011).\\[0pt] [2] Q.~Chen et al., Science {\bf 331}, 199 (2011).\\[0pt] [3] W.~Yang, V.R.~Misko, K.~Nelissen, M.~Kong, and F.M.~Peeters, arXiv:1109.5099 (2011).   

Diffusion in Dense Inhomogeneous Colloid Suspensions in Narrow Channels

We report the results of a study of single particle diffusion in dense colloid fluids confined in a ribbon channel geometry that is intermediate between quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D). In all of the systems studied the colloid density distribution transverse to the ribbon channel is stratified with peak amplitudes that depend on the colloid density. Although the virtual walls that confine a stratum are structured with a scale length of the colloid diameter, that structure does not have an apparent influence on the single particle diffusion, which shows the characteristic features of diffusion in a q1D channel with smooth walls. We find that for all channel widths and packing fractions studied the single particle transverse diffusion coefficient in a stratum is smaller than the single particle longitudinal diffusion coefficient in the same stratum, and that the single particle longitudinal diffusion coefficient varies very little from stratum to stratum, being only slightly smaller in the dense strata next to the walls than in central strata. The lack of variation of the longitudinal diffusion coefficient with apparent stratum density is explained by application of the Fischer-Methfessel approximation to the local density in an inhomogeneous liquid. The ratio of the transverse to longitudinal diffusion coefficients varies very slowly with ribbon width, implying a very slow transition from q1D to q2D behavior.   

Flow of concentrated emulsion in a microchannel: walls effects and roughness impact

Soft glassy materials have ubiquitous rheological properties. At small stress they deform elastically. For stress above a threshold they flow like liquids. At microscale, they are composed of highly disordered particles caged by the neighborhood. Flow happens by successive cage-jumps -or rearrangement. We study concentrated emulsion as a model fluid. When it flows in confined geometry, the viscosity does not correspond to the rheometer measurements but obeys to a non-local relation (Goyon-2008) due to rearrangement's correlation. As they impose viscosity's boundary conditions, walls modify the flow. We study carefully the conditions imposed by the walls and the impact of the roughness. In a microchannel, we create a Poiseuille flow. Using a fast confocal microscope we visualize the droplets and measure the velocity with high spatial resolution. At high stress, we observe one or two discontinuities of the velocity at respectively one and two droplets' diameters. They are due to stratification of the first droplets' layers. Far from them the non-local model remains valid. We create roughness by adding controlled size patterns. The roughness modifies the apparition of the stratifications and the limit conditions on the viscosity. We will compare these results with theory.   

Non-equilibrium dynamics in particle-interface systems

When a particle is at equilibrium at a fluid-fluid interface, its position can be calculated with Young's law (which has been used since 1805). The non-equilibrium behavior of particles at fluid-fluid interfaces, however, is only just beginning to be studied. In this talk, we will discuss the behavior of colloidal particles as they approach and meet an oil-water interface. A variety of different systems, such as approach from both the aqueous and oil phases and using aqueous phases of various salt concentrations will be compared. The motion of the polymer microspheres is captured using digital holographic microscopy in real time. As the holograms are simply two-dimensional images, the frame rate is limited only by the CMOS sensor and frame rates of up to 2000fps are used in this study. We then analyze the high frame rate data to recover the three-dimensional trajectory and fluctuations of the particles.   

Granular Fluid Kinetics Approach to Modeling Soft Colloid and Polymer Materials

The objective of this study is to understand the fundamental laws governing the Brownian motion of viscoelastic particles suspended in solvent at macroscopic equilibrium. Our hypothesis is that the internal degrees of freedom of the particles couple to their translational Brownian motion and affect their mean square displacement. Our system is similar to granular fluids with the important distinction that the energy absorbed by the particles during a collision is returned back thus maintaining a global thermodynamic equilibrium. We propose a new Molecular Dynamics model system that consists of tracer Brownian particles, solvent, and a virtual third component that serves as a thermal bath. The energy that is lost in an inelastic collision between Brownian and solvent particles is returned to the bath. The bath particles are undergoing elastic collisions among themselves and also with the solvent and Brownian particles. This provides a mechanism to restore and maintain an overall thermal equilibrium in the whole system. We report data on the effect of particle inelasticity on the translational diffusion.