Microscopic Mechanism for Shear Thickening of Non-Brownian Suspensions

We propose a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, that links the transition from continuous to discontinuous shear thickening in dense granular pastes to distinct lubrication regimes in the particle contacts. We identify a local Sommerfeld number that determines the transition from Newtonian to shear-thickening flows, and then show that the suspension’s volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.

Figure 1

(a) Schematic Stribeck curve. Evolution of the friction coefficient $\mu$ versus the Sommerfeld number $s$ for a lubricated contact. (b) Apparent viscosity $\eta$ versus the shear rate $\dot{\gamma }$ from the numerical simulations. (c) Friction law used in the numerical simulations (black line) and probability distributions of $s$, $P(s)$, for all contacts at several shear stresses as defined in (b). (d) Frequencies of BL contacts $P_{\mathrm{BL}}$ and HD contacts $P_{\mathrm{HD}}=1-P_{\mathrm{BL}}$, as a function of $\dot{\gamma }$ for the stresses defined in (b). The simulations data in (b)–(d) have $\varphi =0.58$, ${\mu }_0=0.1$, and $s_c=5\times {10}^{-5}$.

Figure 2

Apparent viscosity versus $\dot{\gamma }$ for different ${\mu }_0$ and $s_c=5\times {10}^{-5}$ in simulations. In the Newtonian regime, the viscosity does not depend on ${\mu }_0$ but on $\varphi$. At $\varphi =0.58$, for ${\mu }_0\le 0.3$, the system experiences CST, where the viscosity depends on the friction coefficient. For ${\mu }_0\ge 0.35$, the system jams at sufficiently large $\dot{\gamma }$. Data points for $\varphi =0.59$ show DST for ${\mu }_0=0.3$. Inset: Zoom of the transition zone.

Figure 3

(a) Sediment heights for the different polymers after centrifugation. (b) Viscosity versus shear rate with adsorbed polymer $A$ for various $\varphi$ of quartz microparticle suspensions. (c) Viscosity versus shear rate for the four adsorbed polymers at analogous $\varphi$ [$\varphi (A)=0.537$, $\varphi (B)=0.537$, $\varphi (C)=0.538$, and $\varphi (D)=0.535$]. (d) Oswald–de Waele exponent $n$ versus the reduced volume fraction [same symbols as in (c)]. Inset: Same data as in the log-log plot. The solid line is a power-law fit for ($n-1$) versus reduced volume fraction.

Figure 4

${\varphi }_{\max }^{\mathrm{BL}}$ as a function of the coefficient of friction in boundary regime ${\mu }_0$ for the four polymers (same symbols as in Fig. 3). The CST and DST regions are highlighted in the graph.