Cluster Crystals under Shear

We show that a distinct class of colloidal crystals, which consist of mutually overlapping particles, has a novel and universal response to steady shear. After a shear-banding regime at low shear rates, strings parallel to the flow direction form as shear grows, which order on a hexagonal crystal in the gradient-vorticity plane. At even higher shear, lateral fluctuations of the strings, enhanced by hydrodynamics, lead to a disordered, fluid state. Our results are based on appropriate simulation techniques that correctly account for hydrodynamics. We also find that shear vastly accelerates the nucleation rates of supercooled fluids into the cluster crystals.

Figure 1

(a) Vorticity-gradient and (b) flow-gradient views of the strings formed in an cluster crystal under shear with a shear rate $\dot{\gamma }\in [{\dot{\gamma }}_{\min },{\dot{\gamma }}_c]$ (see the text). Blue spheres (not drawn to scale) represent GEM particles. In (a), a few centers of mass of the strings are connected by straight lines, and the red shading of the resulting hexagonal tiles reflects the distance from the arbitrarily chosen central string; $a^{\prime }$ is the lattice constant of the triangular lattice formed by the strings.

Figure 2

Shear stress ${\sigma }_{xz}(\dot{\gamma })$, reduced by the yield stress ${\sigma }_0$, as obtained from the MPCD simulations, for shear at the [100] orientation. The full lines (string state) and the dashed lines (molten state) are fits according to the Bingham plastic. The inset shows the flux $\Psi (\dot{\gamma })$ of particles across the simulation box, as obtained from full MPCD (lines) and from Brownian dynamics without hydrodynamics (symbols).

Figure 3

Free volume fraction of the GEM particles, $\Phi (\dot{\gamma })$, for the three systems investigated (as labeled). Minima in $d\Phi /d\dot{\gamma }$ are indicated by vertical arrows.