# Highly Anisotropic Vorticity Aligned Structures in a Shear Thickening Attractive Colloidal System

Entry by Helen Wu, AP225 Fall 2010

## Reference

"Highly anisotropic vorticity aligned structures in a shear thickening attractive colloidal system"

C. O. Osuji, D. A. Weitz, Soft Matter, 4, 1388-1392 (2008).

## Overview Figure 2. Microstructure under shear (a) cylindrical flocs at $\dot\gamma = 6.67 s^{-1}$, (b) $\dot\gamma = 133 s^{-1}$, (c) math>\dot\gamma = 1330 s^{-1}[/itex]. Figure 4. Quenched samples starting at zero shear rate and going up to math>\dot\gamma = 10 s^{-1}[/itex]. Vorticity is indicated by the white line in the first panel. Figure 5. (a) Optical micrographs over time. (b) the FFTs of images in (a). Figure 6. Microstructure after shear thickening in parallel plate geometry with gap sizes, (a) $d = 25 \mu m$, (b) $d = 50 \mu m$, (c) $d = 100 \mu m$, (d) $d = 250 \mu m$.

Soft materials and complex fluids often form structures in response to flow around them. In Brownian systems with hard spheres, distortion will occur when the timescale for flow is less than for the particles' diffusion, as described by the Péclet number (represents flow force over thermal/diffusive). In a system where flow dominates, the particles separate in one direction and aggregate in another, forming strings in dilute solutions. Shear thickening happens in more concentrated solutions, but usually not in colloidal systems with attractive interactions (they tend to form flocculated gels).

The authors studied steady state flow behavior of dilute, simple hydrocarbon dispersions of carbon black particles and were actually able to observe shear thickening under certain conditions (above a critical flow rate $\dot \gamma_c\approx 10^2-10^3 s^{-1}$. They also found that the shear modulus of the gels had a power law dependence on the pre-shear stress in the system, and deforming the thickened gells at lower shear rates created ordered vorticity aligned aggregates that broke down into small isotropic clusters given enough time (~300s).

## Results and discussion

Samples under steady shear displayed thixotropy, meaning they are normally thick and highly viscous but flow when stressed. The curves also indicate a composition-dependent shear thickening transition, mentioned previously. Optically observing the systems showed that at low shear stress, the system contained large pieces of broken gel that broke into subsequently smaller pieces when shear was increased. The system's viscosity began to increase at $\dot \gamma\approx 10^0-10^1 s^{-1}$ and clusters of particles aggregated along the vorticity axis (Figure 2a). This was considered to be the steady state response of the system.. They then found that as the shear rate increased, the structures went from being cylindrical to isotropic clusters that become more and more dense until the aggregates break and the transition to shear thickening flow happens.

The system was found to have large negative normal stresses at high shear rates (no changes seen at low rates). If the shear was stopped suddenly (quenching), the effect persisted for long times unless shear flow was applied again, in which case it went back to the original state quickly. This relaxation of internal shear stresses was determined to have a power law dependence $\sigma_i ~ t^{-0.1}$.

Deforming quenched shear thickened gels quickly resulted in highly anisotropic vorticity aligned structures that were much more defined than the steady state response the authors looked at first (Figure 4). The aspect ratios of the cylinders were greater than the macroscopic portions of the shear cell as well. They studied this phenomenon using Fourier transformations of the images to monitor the development of alignment in the system (Figure 5) - it turned out to be rapid and peaked at 20s with $\gamma=200$.

The authors observed that the width of the cylindrical structures was slightly larger than and proportional to the gap but periodicity doesn't change much, meaning the flocs become less dense as they become thicker.

Structure dissolution occurred first at the outside edge of the rheometer geometry both when using a parallel plate (highest shear at edge) as well as with an angled cone (constant shear across plate), so the authors suggest that confinement is important for stabilization of the flocs. (Figure 6)

The frequency and strain dependence of the elastic modulus of the flocs was different from the shear thickened gel, but both showed strong elastic responses. Yield strain was lower for structures than for gel and its presence indicates that the rolling of the flocs is not sufficient to account for the displacement and deformation that comes from the applied shear.

The observations made by the authors of this paper are similar to an elastic instability associated with what is seen in semi-dilute non-Brownian nanotubes that are undergoing clustering due to flow. Also, these results provide insight as to the effect of confinement and composition on the mechanics of such structures.

## Experimental Setup

Tetradecane dispersions of 8% 0.5 $\mu$m carbon black particles were used. Experiments were done using rheometers, sometimes combined with an optical observation component.