Relation between dilation and stress fluctuations in discontinuous shear thickening suspensions

We investigate dilation-induced surface deformations in a discontinuous shear thickening (DST) suspension to determine the relationship between dilation and stresses in DST. Video is taken at two observation points on the surface of the suspension in a rheometer while shear and normal stresses are measured. A roughened surface of the suspension is observed as particles poke through the liquid-air interface, an indication of dilation in a suspension. These surface roughening events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and surface roughening is observed frequently in the high-stress state. On the other hand, a complete lack of surface roughening is observed when the stresses remain at low values for several seconds. Surface roughening is most prominent while the stresses grow from the low-stress state to the high-stress state, and the roughened surface tends to span the entire surface by the end of the stress growth period. Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.

Figure 1

Illustration of the experimental setup (not to scale). (a) Top view. (b) Side view. The suspension is sheared underneath the rheometer top plate. Dotted lines illustrate paths of light rays from the edges of the light source to the edges of the camera sensor. The camera views direct reflections as bright spots (red) on the suspension surface. When the suspension dilates, the roughened surface produces a diffuse reflection over a wider area of the suspension surface.

Figure 2

Side view of the suspension in the rheometer. (a) A suspension at rest with no surface roughening, indicated by the shiny surface. (b) A suspension under shear with a growing region of surface roughening, an indicator of overall dilation. Surface roughening is indicated by the speckled pattern, due to the rough surface reflecting light diffusively. (c) A suspension with a maximally roughened surface under shear. Lower images illustrate the cropping and thresholding used to identify the presence of surface roughening based on counts of the number of bright pixels. The red boxes in the top images outline the cropped region.

Figure 3

A series of images of the suspension at different times separated by 0.033 s, showing the propagation of a localized region of surface roughening (the faint speckled pattern) past the bright spot from left to right.

Figure 4

Number of bright pixels $n$ as a function of time for a single surface roughening event, showing the corresponding raw images in the experiment. The low values of $n$ correspond to when surface roughening is observed.

Figure 5

A time series showing the relation between surface roughening and stress. Left axis: shear stress $\tau$ (solid circles) and normal stress $\sigma$ (solid triangles). Right axis: number of bright pixels in each bright spot, $n_L$ (open squares) and $n_R$ (open diamonds). The start of stress growth events are indicated by large open circles. Both $n_L$ and $n_R$ drop to zero within a few seconds of each of these events, indicating the stress increases occur along with surface roughening. Vertical dashed lines: Times where both $n_L$ and $n_R$ increase simultaneously, a few seconds before both stresses drop to near zero, indicating that stress drops occur along with the end of surface roughening.

Figure 6

A viscosity curve showing shear and normal stress (left axis) and number of bright pixels $n$ on the surface (right axis), as a function of shear rate $\dot{\gamma }$. The high-stress range coincides with the range of intermittent surface roughening events.

Figure 7

(a) A viscosity curve $\eta \left(\tau \right)$. Solid line: line of slope 1/2 used to determine the onset of DST. Vertical line: $\tau ={\tau }_c$, corresponding to the onset of DST. (b) The probability of surface roughening $p_1$ as a function of controlled shear stress $\tau$. Surface roughening is found only for $\tau >{\tau }_c$, and the probability of surface roughening increases with stress in the shear thickening range.

Figure 8

Number of bright pixels $n$ as a function of time showing several surface roughening events when $n$ drops to near zero (indicated by the box).

Figure 9

Probability distribution of the number of bright pixels $n$. Different applied shear stresses $\tau$ are indicated in the legend. The broad peak at $n=n_p$ corresponds to a smooth suspension surface. Solid line: fit used to determine the peak location $n_p$. The sharp peak at $n=0$ corresponds to a dilated state with surface roughening. Data with no visible surface roughening at $\tau =1$ Pa do not have the peak at $n=0$ or the low-$p\left(n\right)$ plateau. Dotted line: standard threshold value $n_t/n_p$ below which surface roughening is counted.