Session K34: Rheology and Flow

A rheological signature of frictional interactions in shear thickening suspensions

We elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces to colloidal shear thickening by measuring both the viscosity $\eta$ and first normal stress difference $N_1$ in suspensions of silica spheres over a wide range of volume fractions. The first normal stress difference reveals a transition not apparent in the viscosity alone, from $N_1<0$ at moderate volume fractions $\phi \leq 0.52$ to $N_1 > 0$ at larger values of $\phi$. While the $N_1 <0$ behavior is consistent with hydrodynamic models, the $N_1 >0$ behavior (dilation) is instead a characteristic of frictional `granular' suspensions. Fitting our viscosity profiles $\eta(\sigma, \phi)$ to a model for friction-driven shear thickening, we capture the shear thickening for $\phi \geq 0.52$ but must adjust the adjust the maximum fraction of frictional contacts to fit at lower volume fractions. Our results bring together two contrasting theories for shear thickening; they show that friction drives shear thickening in concentrated colloidal suspensions, but also highlight the need to include hydrodynamic effects to fully describe the rheology at moderate concentrations.   

Microstructure of Brownian Particles under Cyclic Shear

We study the microstructure of a 2D colloidal system subject to cyclic shear. The system consists of $1\mu m$ particles which are purely repulsive and are adsorbed at an oil-water interface. The particles, which exhibit Brownian motion, provide a model system for thermal glasses under external shear. Cyclic shear is induced by a magnetized needle which is also placed at the interface. The particles are tracked through consecutive images taken within each cycle. By measuring the non-affine stroboscopic displacement of the particles, we identify the spatial distribution of rearrangements. Similar to nonthermal colloids ($4-6\mu m$), we observe localized regions of non-affine rearrangements. The number and size of these regions shrink as the Péclet number is increased. We also observe that similar to non-Brownian systems, a fraction of reversible cycles undergo plastic deformation. However, the spatial distribution of such Brownian particles is more homogeneous compared to non-Brownian system.   

Forces acting in quasi 2d emulsions

We study the forces in a quasi two dimensional emulsion system. Our samples are oil-in-water emulsions confined between two close-spaced parallel plates, so that the oil droplets are deformed into pancake shapes. By means of microscopy, we measure the droplet positions and their deformation, which we can relate to the contact forces due to surface tension. We improve over prior work in our lab, achieving a better force resolution. We use this result to measure and calibrate the viscous forces acting in our system, which fully determine all the forces on the droplets. Our results can be applied to study static configurations of emulsion, as well as faster flows.   

Flow in Smectic Liquid Crystal Films: Examining the Flow Field of a Smectic Liquid Crystal Film due to Fluid Ejected From a Small Nozzle

The rheological properties of 2D fluids are well-understood theoretically, but few experiments testing theoretical predictions have been carried out. We have used MX 12805, a smectic C liquid crystal at room temperature, to create quasi-2D films with which to study high-Reynolds number flow. We map the flow field as the fluid is ejected from a thin nozzle into a large reservoir, probing both laminar and turbulent flow. We also attempt to carry out the experiment in a vacuum to study the true 2D-regime; despite encountering experimental difficulties, some useful information can still be gleaned.   

Effect of Confinement on Suspension Rheology

Confined systems are ubiquitous in nature and occur at widely separated length scales from the atomic to granular. While the flow properties of both atomic and granular systems has been well studied, examining the rheology of the intermediate length scale in colloidal suspensions is challenging. We use a confocal rheoscope to image the particle configuration in a suspension of silica microspheres while simultaneously measuring its stress responses. The confocal rheoscope has two precisely-aligned parallel plates that can confine the suspension with a variable gap size ranging from 3 to 30 particle diameters, allowing us to measure the response of the system as a function of the gap size. We find that the viscosity of the system decreases with confinement in sharp contrast to the increase reported in atomic and granular systems. The microscopy images indicate that this decrease in viscosity is due to the formation of particle layers in this shear regime where hydrodynamic forces dominate particle interactions. We discuss these results and their implications.   

Orientation of dilute multi-walled carbon nanotube suspensions in shear and planar extensional flow

Small-angle x-ray scattering is used to study flow-induced orientation in suspensions of multi-walled carbon nanotubes in viscous, uncured epoxies. Shear flow studies are performed in an annular cone and plate shear cell in which fluid structure is probed in the flow-gradient (1-2) plane, allowing measures of both the degree and direction of nanotube orientation. General orientation behavior is consistent with expectations of Brownian dispersions of elongated particles. At high Peclet number, the degree of orientation saturates, and the orientation angle approaches the flow direction. Interestingly, otherwise identical suspensions in two different epoxies of different viscosity yield dramatically different degrees of orientation, even when compared at comparable Peclet number. The same suspensions are studied in planar extensional flow, using a cross-slot flow cell, in order to probe the relative effectiveness of shear and extensional flow at promoting nanotube orientation.   

Alignment and rotation of anisotropic particles in complex flows

Anisotropic particles in fluid flows develop orientational order that strongly affects both particle rotation statistics and rheology of multi-phase flows. We have measured the motion and rotation of non-brownian particles in chaotic and turbulent flows using video particle tracking to reconstruct 3D particle trajectories. The preferential alignment of particles of many different shapes can be understood using a simple picture that considers the stretching a particle has recently experienced. The stretching can be quantified using the Cauchy-Green strain tensors. Particle rotation statistics can be understood as a result of the preferential alignment of fluid vorticity and the particles by stretching. The Cauchy-Green eigenvalue fields have been widely used to identify Lagrangian coherent structures that affect fluid mixing. We show how their eigenvector fields can help understand the complex orientational order that occurs in these flows.   

Flow Induced by an Oscillating Sphere in Probing Complex Viscosity of Nonadsorbing Polymer Solutions

Theoretical investigation is presented for a linear viscoelastic flow induced by an oscillatory colloidal particle in nonadsorbing polymer solutions. The dilute to semi-dilute polymer solutions are treated as linear viscoelastic fluids. At small-amplitude oscillation, the polymer distribution is assumed at equilibrium and forms a depletion zone around the particle based on the mean field approximation. The analytical result based on the two-layer approximation is compared with numerical results using a continuous depletion profile to describe the nonuniform complex viscosity in the flow field. Depending on the polymer concentration, solution conditions and depletion thickness, the obtaining apparent complex viscosity or friction coefficient sensed by the particle could deviate significantly from the actual viscosity of the bulk polymer solution. The models developed can be applied, along with active and passive colloidal probing methods, for microrheological measurements of complex fluids that take depletion into account.   

How does inertia affect the steady-shear rheology of disordered solids?

We study the finite-shear-rate rheology of disordered solids with molecular dynamics simulations in two dimensions. By systematically varying the damping strength $\zeta$, we identify two well defined flow regimes, separated by a thin crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $\mathrm{Wi}\propto\zeta\dot{\gamma}$; the macroscopic stress $\Sigma$ follows the frequently encountered Herschel-Bulkley law $\Sigma=\Sigma_{0}+k\sqrt{\mathrm{Wi}}$, with yield stress $\Sigma_{0}>0$. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes nonmonotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably and proportional to the driving. By thermostatting more or less underdamped systems, we are able to link quantitatively the rheology to the kinetic temperature $T_k$, while the damping strength enters only indirectly by setting $T_k$.   

The flow and fracture of concentrated colloidal suspensions

Concentrated colloidal suspensions display dramatic rises in viscosity, leading to jamming and granulation, with increasing shear rate. It has been proposed that these effects result from inter particle friction, as lubrication forces are overcome. This suggests the jamming of concentrated colloidal suspensions should exhibit some shared phenomenology with macroscopic granular systems where friction leads to two different types of jammed state. Here we show that transient rheological measurements can be used to probe the processes of granulation in concentrated colloidal suspensions [1]. Our results support the idea that frictional contacts are created between jammed particles. The jamming behaviour displays two qualitatively different regimes separated by a critical strain rate with qualitatively different types of fracture/break up behaviour. In the lower strain rate regime, it is found that vibrations can be used to control jamming and granulation, resulting in a flowable fluid. [1] Nature Sci. Rep. 5:14175 (2015)   

Fragility in dense suspensions

Dense suspensions can jam under shear when the volume fraction of solid material is large enough. In this work we investigate the mechanical properties of shear jammed suspensions with numerical simulations. In particular, we address the issue of the fragility of these systems, i.e., the type of mechanical response (elastic or plastic) they show when subject to a mechanical load differing from the one applied during their preparation history.   

Role of inertia in the rheology of amorphous sys- tems: a finite element based elasto plastic model

A simple Finite Element analysis with varying damping strength is used to model the athermal shear rheology of densely packed glassy systems at a continuum level. We focus on the influence of dissipation mechanism on bulk rheological properties. Our numerical studies, done over a wide range of damping coefficients, identify two well-separated rheological regimes along with a cross-over region controlled by a critical damping. In the overdamped limit, inertial effects are negligible and the rheological response is well described by the commonly observed Herschel-Bulkley equation. In stark contrast, inertial vibrations in the underdamped regime prompt a significant drop in the mean-stress level, leading to a non-monotonic constitutive relation. The observed negative slope in the flow curve, which is a signature of mechanical instability and thus permanent shear-banding, arises from the sole influence of inertia, in qualitative agreement with the recent molecular dynamics study of Nicolas \emph{et al.} (\emph{arXiv preprint arXiv:1508.06067}, 2015 ).   

Experimental Timescales of Fracture-Healing Rheological Behavior of Thermoreversible Gels

Acrylic thermoreversible physical gels were used as a model soft material system to investigate fracture-healing behavior by shear rheometry. By using shear start-up experiments, gels at various concentrations and temperatures were measured to determine shear stress responses, and fracture was indicated by a decrease in shear stress (confirmed with rheophysical flow visualization experiments). Fractured gels were allowed to recover in the rheometer for set periods of time and were tested again using the same shear start-up procedure to evaluate the recovery kinetics of network strength. Relationships between the network recovery and the normalized ratio of the resting times and characteristic relaxation times of the gels were determined. It was found that resting times for fully healed networks needed to be 2 or 3 orders of magnitude greater than the relaxation times. The extent of fracture was also investigated. Gels that were deformed to smaller total strain magnitudes were suspected to have incomplete (or partial) fracture as results showed various responses for given resting times.   

Rich Janus Colloid Phase Behavior Under Steady Shear

We study the assembly of single-patch Janus colloids under steady shear via Brownian dynamic simulations. Under quiescent conditions, varying the patch size, the range, and strength of the interaction potential we observe different aggregates such as micelles, wormlike clusters, vesicles and lamellae. Under shear conditions we observe rearrangement, deformation, and break-up of aggregates. At large P\'{e}clet (Pe) numbers the shear forces dominate over Brownian forces and aggregates dissociate in a gas for all structures studied. At small and intermediate Pe, the competition between rearrangement, deformation, and break-up favors the growth of micelles and vesicles with Pe, resulting in mean cluster size increases, consistent with a previous study of Janus particles under shear. After the initial shear-induced growth, micelles and vesicles dissociate into a gas. Wormlike aggregates initially break-up into micelles, and proceed to finally reach a gas phase. Lamellar structures initially break into smaller lamellae that align with the flow direction and finally dissociate into a gas. This work opens new actuation routes for re-configurable materials and applications where different types of aggregates will be present under quiescent conditions while others will form under shear.