Figure 1

(a) Optical micrograph of a quiescent semidilute dispersion (0.5% MWNT by mass). The inset ($\mathrm{\text{width}}=1.3\mu \mathrm{m}$) is an SEM image before dispersion. Optical micrographs (b) 30 min after quenching the fluid to ${\dot{\gamma }}_0$, (c) 2 h after the quench, and (d) 15 min after quenching the sample in (c) to ${\dot{\gamma }}_m$. The aggregates have “melted” and the tubes orient with the flow, as evident in the depolarized light-scattering pattern (inset, $\mathrm{\text{scale bar}}=1\mu {\mathrm{m}}^{\mathrm{-}\mathrm{1}}$). The red scale bar is $10\mu \mathrm{m}$ and $h=50\mu \mathrm{m}$.Reuse & Permissions

Figure 2

Evolution of a confined pattern for the sample depicted in Fig. 1 ($h=50\mu \mathrm{m}$). The lower images are the corresponding $c(\mathbf{r})$ at each $t$, where the red scale bar ($125\mu \mathrm{m}$) applies to all six images. The inset to the lower left image is its FFT ($\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=1.2\mu {\mathrm{m}}^{-1}$), which gives the ubiquitous “butterfly” pattern.Reuse & Permissions

Figure 3

Projections of $c(\mathbf{r})$ along (a) $\widehat{\mathbf{x}}$ and (b) $\widehat{\mathbf{z}}$ for the data in Fig. 2, where $x$ and $z$ have been reduced by the corresponding correlation length, shown in the inset to (b) with $t^{1/2}$. The gray curve in (b) is an exponential decay. The inset to (a) shows the measured “pattern diagram” (0.5% MWNT by mass) in the $h\mathrm{\text{−}}\dot{\gamma }$ plane, with homogeneous (H), aggregated (A), and “striped” (S) regions. In region A, moderate aspect ratio domains are stable. In region S, these domains coarsen along $\widehat{\mathbf{z}}$ into stripes. The dashed curve marks a region of “metastability” in which the stripes are transient. Roughly 50 measurements in the $h\mathrm{\text{−}}\dot{\gamma }$ plane were used to deduce this diagram.Reuse & Permissions

Figure 4

(a) $\eta$, $N_1$, and $N$ vs $t$ at ${\dot{\gamma }}_0$. Inset images ($\mathrm{\text{width}}=430\mu \mathrm{m}$, $h=50\mu \mathrm{m}$) show the evolving morphology. (b) $\eta$ and $N_1$ vs $t$ following the quench of an aggregated sample (20 h at ${\dot{\gamma }}_0$) to ${\dot{\gamma }}_m$, where the clusters “melt.” The viscosity of the rehomogenized suspension, ${\eta }_0$, has been subtracted from $\eta$. The upper gray curve in (a) is ${\varphi }_d(t)$ scaled onto $\eta (t)$. Error bars show standard uncertainty.Reuse & Permissions

Figure 5

The complex shear modulus, $G^{*}(\omega )=G^{\prime }(\omega )+i{G}^{\prime \prime }(\omega )$, as a function of MWNT concentration for homogenized suspensions. The cartoon depicts the shear response of the compressible clusters, where internal streamlines are in tension due to elastic forces.Reuse & Permissions