Strain-transport superposition in shear-thinning dense non-Brownian suspensions

TL;DR

The study addresses how shear thinning arises in dense non-Brownian suspensions without relying on interaction-specific microstructural relaxation. It uses three-dimensional particle-resolved simulations across diverse mechanisms—attraction, repulsion, and load-dependent friction—under steady shear to quantify microstructure, velocity correlations, nonaffine velocities, and transport. A central finding is that the magnitude of nonaffine velocity fluctuations is set by the imposed shear rate $\dot{\gamma}$, independent of coordination number, structural anisotropy, or interaction details, and transverse MSD follows a universal master curve when scaled by $\langle|\bm{v}_{\mathrm{na}}|^2\rangle$ and accumulated strain $\gamma=\dot{\gamma}\Delta t$, i.e., $\mathrm{MSD}_{yz}(\Delta t) = \frac{\langle|\bm{v}_{\mathrm{na}}|^2\rangle}{\dot{\gamma}^2} F(\dot{\gamma}\Delta t)$ with a ballistic-to-diffusive crossover around $\gamma \sim \mathcal{O}(1)$. This strain--transport superposition shows a decoupling of kinematics and stress, revealing nonaffine velocity fluctuations as the emergent dynamical scale that governs shear-driven transport.

Abstract

Shear thinning in dense non-Brownian suspensions is often attributed to shear-induced microstructural evolution, including changes in alignment, anisotropy, and near-contact statistics, yet how these changes influence particle-scale dynamics remains unclear. Using particle-resolved simulations of dense suspensions that shear thin through diverse microscopic mechanisms, including short-range attraction, repulsion, and load-dependent friction, we show that the magnitude of nonaffine particle velocities is controlled solely by the imposed shear rate, independent of coordination number, structural anisotropy, and interaction details. In contrast, macroscopic stress and viscosity remain strongly sensitive to the underlying interactions. When mean-squared displacements transverse to the flow are rescaled by accumulated strain and the nonaffine velocity variance, all data collapse onto a single master curve, revealing strain-controlled transport with a robust ballistic-to-diffusive crossover. These results demonstrate a fundamental decoupling between particle-scale kinematics and macroscopic rheology and identify nonaffine velocity fluctuations as the emergent dynamical scale governing shear-driven transport.

Figures (4)

• Figure 1: (Color online) Microscopic interaction models and resulting shear-thinning rheology in dense suspensions. (a) Schematic of the short-range pairwise force laws used in the simulations, including attractive and repulsive interactions of varying strength and a load-dependent friction model. (b) Relative viscosity $\eta_r=\eta/\eta_0$ as a function of dimensionless shear rate $\dot{\gamma}/\dot{\gamma}_0$ for frictionless particles ($\mu=0$). (c) Relative viscosity $\eta_r$ versus $\dot{\gamma}/\dot{\gamma}_0$ for frictional particles ($\mu=1$). Despite their distinct microscopic origins, all interaction models exhibit pronounced shear thinning, while differing substantially in the magnitude and shear-rate dependence of the stress response. Lines in (b) and (c) are guides to the eye only.
• Figure 2: Shear-induced structural isotropy in dense suspensions. (a) Two-dimensional projections of the structure factor $S(\mathbf{k})$ in the flow--gradient plane for increasing dimensionless shear rate $\dot{\gamma}/\dot{\gamma}_0$ for strongly attractive suspension A10. Strong anisotropy is observed at low shear rates and progressively diminishes as shear rate increases. (b) Scalar structural anisotropy parameter $A$ as a function of $\dot{\gamma}/\dot{\gamma}_0$ for different interaction models and for frictionless ($\mu=0$, open symbols) and frictional ($\mu=1$, filled symbols) particles. Structural anisotropy decreases monotonically with shear rate across all cases, indicating shear-driven loss of microstructural order.
• Figure 3: Coordination number and velocity correlations under shear. (a) Mean coordination number $\langle Z\rangle$ as a function of dimensionless shear rate for different interaction models. Coordination decreases with shear rate in an interaction-dependent manner. (b) Normalized spatial velocity correlation $C_v(r)$ for frictional systems ($\mu=1$), for various shear rates denoted by increasing shade of the line. Despite large variations in microscopic coordination number, velocity correlations exhibit a similar spatial decay across interaction models, indicating emergent kinematic organization at mesoscale.
• Figure 4: Strain--transport superposition of particle motion across interaction models and shear rates. (a,b) Mean-squared displacement in the gradient--vorticity ($yz$) plane, normalized by the non-affine velocity variance, plotted against accumulated strain $\gamma=\dot{\gamma}\Delta t$ for frictionless ($\mu=0$) and frictional ($\mu=1$) systems, respectively. Fourteen distinct interaction models are shown, spanning hard-sphere, attractive (A0.1, A1, A10), repulsive (R100, R1000), and load-dependent friction (LD-$\mu$) suspensions, over eleven shear rates in the range $\dot{\gamma}=10^{-3}$--$10^{3}$. Panels (a) and (b) contain data that overlap but are displayed separately to avoid visual overcrowding. Different shear rates are indicated by progressively darker shading; however, the curves collapse so closely that individual shades are largely indistinguishable, highlighting the robustness of the superposition. Thick solid and dotted lines indicate reference slopes corresponding to ballistic ($\sim\gamma^{2}$) and diffusive ($\sim\gamma$) regimes, respectively. (c) non-affine velocity variance $\langle|\bm{v}_{\mathrm{na}}|^2\rangle$ plotted against $\dot{\gamma}^2$ for all interactions, demonstrating the scaling that underpins the strain--transport superposition. Filled (hollow) symbols correspond to $\mu=1$ ($\mu=0$), and crosses denote load-dependent friction.