Universal scaling of shear thickening suspensions under acoustic perturbation

TL;DR

The paper addresses how acoustic perturbations control the viscosity of dense shear-thickening suspensions. By embedding acoustic effects into a universal scaling framework with a two-jamming-point structure, the authors show that viscosity can be described by a crossover function $\mathcal{F}(x)$ of a scaling variable $x = \frac{C(\phi) e^{-\sigma^*_0/\sigma}}{\phi_0 - \phi}$, and that acoustics introduce an additional repulsive stress $\sigma^*_a(U_a)$ such that $\sigma^*_{\text{total}} = \sigma^*_0 + \sigma^*_a(U_a)$. They demonstrate data collapse across volume fraction, shear stress, and acoustic energy density when $\sigma^*_a(U_a) \approx U_a$, enabling quantitative predictions of viscosity under acoustic perturbations. The results unify unjamming/dethickening phenomena under a single critical-framework and provide a practical method to predict and tune suspension rheology for applications in smart fluids and fluid metamaterials.

Abstract

Tuning shear thickening behavior is a longstanding problem in the field of dense suspensions. Acoustic perturbations offer a convenient way to control shear thickening in real time, opening the door to a new class of smart materials. However, complete control over shear thickening requires a quantitative description for how suspension viscosity varies under acoustic perturbation. Here, we achieve this goal by experimentally probing suspensions with acoustic perturbations and incorporating their effect on the suspension viscosity into a universal scaling framework where the viscosity is described by a scaling function, which captures a crossover from the frictionless jamming critical point to a frictional shear jamming critical point. Our analysis reveals that the effect of acoustic perturbations may be explained by the introduction of an effective interparticle repulsion whose magnitude is roughly equal to the acoustic energy density. Furthermore, we demonstrate how this scaling framework may be leveraged to produce explicit predictions for the viscosity of a dense suspension under acoustic perturbation. Our results demonstrate the utility of the scaling framework for experimentally manipulating shear thickening systems.

Figures (4)

• Figure 1: Suspensions dethicken under acoustic perturbations. (a) Schematic of apparatus used to apply acoustic perturbations on the rheometer. (b) Viscosity $\eta$ versus shear stress $\sigma$ for various volume fractions $\phi$ of aluminosilicate microspheres in glycerol. (c) Viscosity versus time for a few example acoustic perturbations, applied on a suspension with volume fraction $\phi=0.61$ and under applied shear stress $\sigma=911\,$Pa. The color shows the acoustic energy density $U_a$ of each perturbation. (d) Viscosity versus acoustic energy density $U_a$ for a volume fraction of $\phi=0.52$. The applied shear stress $\sigma$ is shown by the color.
• Figure 2: Shear thickening is a precursor to shear jamming and is controlled by a crossover scaling function. (a) Viscosity data in the absence of an acoustic field ($U_a=0$) plotted as $\eta(\phi_0-\phi)^2$ versus $x= \frac{C(\phi)e^{-\sigma^*_0/\sigma}}{\phi_0-\phi}.$ As predicted by Equation \ref{['eqn:scaling_ansatz']}, the data collapse onto a single curve, $\mathcal{F}(x)$, whose shape is approximated by a fitting function shown as a red line. The inset shows the part of the scaling function near $x=x_c=1$, where the scaling function diverges. (b) $\eta(\phi_0-\phi)^2$ versus $x_c-x$, highlighting that $\mathcal{F}(x)$ diverges at $x_c$ as $\mathcal{F}\sim(x_c-x)^{-\delta}$ where $\delta=0.9\pm0.3$. (c) $C(\phi)$, the anisotropy factor plotted against volume fraction $\phi$.
• Figure 3: The effect of acoustic perturbations may be incorporated into a universal scaling framework. (a) $\eta(\phi_0-\phi)^2$ plotted against $x_c-x$ before incorporating the effects of acoustic perturbations. Acoustic energy density $U_a$ is shown by the color bar. Volume fraction is shown by symbols (same symbols as Fig. \ref{['fig:rawdata']}b). The viscosity data do not collapse onto a single curve. Error bars are excluded for visual clarity. (b) After incorporating the effects of acoustic perturbations into the scaling variable $x_a$, the data now collapse onto the curve $\mathcal{F}(x_a)$. (c) The acoustic contribution $\sigma^*_a$ to the interparticle repulsive stress versus acoustic energy density $U_a$. The circles are the values that produce the best collapse of the viscosity data, and the dotted line is $\sigma^*_a=U_a.$
• Figure 4: Comparison between experimental measurements (symbols) and predictions of the scaling framework (lines) for suspension viscosity $\eta$ as a function of volume fraction $\phi$, shear stress $\sigma$, and acoustic energy density $U_a,$ for $U_a=0$, $0.43$ Pa, $6.88$ Pa, and $27.5$ Pa. Results for other acoustic energy densities can be found in the Supplementary Material.