Shear-Induced Configurations of Confined Colloidal Suspensions

We show that geometric confinement dramatically affects the shear-induced configurations of dense monodisperse colloidal suspensions; a new structure emerges, where layers of particles buckle to stack in a more efficient packing. The volume fraction in the shear zone is controlled by a balance between the viscous stresses and the osmotic pressure of a contacting reservoir of unsheared particles. We present a model that accounts for our observations and helps elucidate the complex interplay between particle packing and shear stress for confined suspensions.

Figure 1

Structure of a sheared suspension with $\gamma =0.38$, $f=30\mathrm{H}\mathrm{z}$, and $\varphi =0.61$. The plate moves in the $x$ direction. (a) shows a confocal micrograph of a sheared suspension forming hcp layers when $D=80\mu \mathrm{m}$. (b)–(e) show micrographs of the suspension in the buckled state. The gap is set slightly below the height commensurate with confinement of four flat hcp layers. (b) shows an $x\mathrm{\text{−}}y$ image slice of the suspension near the upper plate. (c)–(e) show slices that are, respectively, 1.3, 2.6, and $3.9\mu \mathrm{m}$ below the slice in (b). The images are presented side by side so that the strip alignment can be compared. The $y^{\prime }$ direction is aligned with one of the characteristic hcp lattice vectors and forms a $60°$ angle with the $x$ direction. The $x$, $y$, and $y^{\prime }$ directions are indicated in the bottom left corner of (a).

Figure 2

Suspension structure in the $y^{\prime }\mathrm{\text{−}}z$ plane.

Figure 3

Transition mechanism predicting buckling in confined suspensions. The solid and dashed curves indicate ${\tau }_{\eta }$ versus the rescaled gap, $\tilde{D}$, for systems with up to ten layers. The solid curves correspond to flat hcp sheets moving in the straight flow configuration. The dashed curves correspond to the zigzag flow configurations and delineate the border between the zigzag and buckled phases. With increasing gap, the buckled region becomes smaller and eventually disappears when the dashed and solid curves cross. The horizontal dash-dotted line corresponds to the value of ${\Pi }_{\mathrm{r}\mathrm{e}\mathrm{s}}$.

Figure 4

Separation between the top and bottom layers, $\Delta {\tilde{D}}_{tb}$, for maximally buckled (open symbols) and straight (closed symbols) flow configurations with different numbers of layers. The measurement error is on the order of the symbol size. The shear rate $\gamma f=30{\mathrm{s}}^{-1}$. A crossover of the curves occurs when the layer number is 12.