Boundary compliance selects heterogeneous dynamics in shear-thickening suspensions

TL;DR

This work shows that boundary compliance, tunable via a viscous oil layer, critically shapes heterogeneous dynamics in shear-thickening suspensions. By adjusting the oil viscosity $\eta_o$, the authors identify two regimes: compliant boundaries yield long-lived density inhomogeneities, while resistant confinement promotes transient, spanning load-bearing clusters accompanied by rapid stress waves; a dimensionless ratio $\epsilon=\eta_o/\eta_s$ governs the regime transition, with the DST onset stress $\tau_c$ remaining constant at high $\eta_o$. The findings connect the macroscopic flow response to the microstructural evolution of frictional contact networks and percolation phenomena, offering practical strategies to control DST and shear jamming in confined settings. The approach also provides a means to amplify and observe short-lived microscopic processes that are otherwise hidden under rigid confinement, deepening understanding of the interplay between suspension microstructure, flow instabilities, and confinement mechanics.

Abstract

The mechanical properties of confining boundaries can fundamentally alter the flow behaviour of shear-thickening suspensions. We study a dense cornstarch suspension sheared beneath a viscous silicone-oil layer, using the oil viscosity to tune boundary compliance. Flow visualisation and rheometry reveal two distinct regimes. With compliant boundaries, long-lived heterogeneities emerge via density waves or persistent clusters, maintained by a balance between interface deformation and particle rearrangement. With more resistant confinement, we observe transient jamming events, marked by abrupt spanning of load-bearing structures across the suspension thickness and the emergence of secondary stress waves. The onset stress of these events remains constant at the DST threshold, independent of bounding viscosity. Our results reveal that boundary compliance selects the lifetime and morphology of heterogeneous structures, offering a means to amplify otherwise short-lived microscopic processes and providing new insight into the interplay between shear thickening, shear jamming, and confinement mechanics.

Figures (6)

• Figure 1: (a) A schematic of the experimental setup. (b) Rheogram of the dense cornstarch suspension for $\Phi=0.42$. For detailed description, see the text. (c-e) Snapshots of three different states of inhomogeneity (see Movies S1, S2, and S3 for multimedia views). The red arrows indicate the instantaneous drive direction. The blue arrow refers to the instantaneous directions of high-$\phi$ regions' motion. The yellow one indicates the propagating event in the vorticity direction. Inset of panel (b): Comparison of independently measured rheological curves, $\eta_s(\dot{\gamma}_s)$, and results obtained in our experiments with silicone oils of different viscosities.
• Figure 2: (a-c) Local flow fields corresponding to state 1, state 2 and state 3, respectively. Note that $\widetilde{U}_0=\frac{\lvert\vec{U}_0(x,y)\rvert}{U}$ refers the scaled interface velocity, and $u_h$ denotes the speed of the heterogeneous structure.
• Figure 3: (a) State diagram illustrating distinct unsteady regimes observed at varying silicone oil viscosities and their relation to the particle Reynolds number. Symbols represent different dynamical states: $\circ$ represents the uniform state, $\blacktriangle$ denotes state 1, $\blacklozenge$ indicates state 2, and $\bigstar$ corresponds to state 3. (b) Normalized shear stress plotted against the suspension Reynolds number, with data and symbols consistent with those in (a). (c) Comparison of wavelengths $\lambda$ (defined as the distance between adjacent low-density regions along the mainstream): $+$ indicates the theoretical prediction from Eq. \ref{['eq.verticle_balance']}, while $\ast$ shows experimentally measured values. Note that the shear stress $\tau$ is varied by adjusting the thickness of the silicone oil layer while keeping the driving velocity fixed. (d) Variation of onset stress with silicone oil viscosity.
• Figure 4: The characteristics of heterogeneous in different value of the dimensionless number $\epsilon=\dot{\gamma}_s/\dot{\gamma}_o$. The data and symbols here are consistent with those in figure \ref{['fig:phase_diagram']}. Inset: A discontinuous drop in local $\epsilon$ for $\eta_{o}=10~Pa\cdot s$. Note that, to determine $\epsilon$ locally, the averaged velocity was measured within a fixed $1~mm^2$ area.
• Figure 5: Snapshot of the stress field of a transient event along the vorticity direction. The red arrow indicate the instantaneous drive direction. The stress field was derived from the measured local interfacial velocity field, $\vec{U}(x,y)$, obtained via PIV analysis. In the present experiment, $\eta_{o} = 10Pa~s^{-1}$ and the average shear rate is 38 s^-1.