Particle Pressure in a Sheared Suspension: A Bridge from Osmosis to Granular Dilatancy

The normal stress exerted by particles in a sheared suspension is measured by analogy with a method used to measure osmotic pressure in solutions. Particles in a liquid are confined by a fine screen to a gap between two vertical concentric cylinders, the inner of which rotates. Pressure in the liquid is sensed either by a manometer or by a pressure transducer across the screen. The particles are large enough so that Brownian motion and equilibrium osmotic pressure are vanishingly small. The measured pressure yields the shear-induced particle pressure $\Pi$, the nonequilibrium continuation of equilibrium osmotic pressure. For volume fractions $0.3\le \varphi \le 0.5$, $\Pi$ is strongly dependent on $\varphi$, and linear in shear rate. Comparisons of the measured particle pressure with modeling and simulation show good agreement.

Figure 1

Left: $\mathsf{U}$ tube osmometer. Center: Schematic of the experimental apparatus. Right: Reynolds dilatancy.

Figure 2

Manometer approach for a suspension of $80\mu \mathrm{m}$ diameter particles at $\varphi =0.4$. Couette device is at right, with the upper surface of the suspension indicated by the dashed line. Meniscus levels are highlighted by arrows for screened (left tube) and open (right) holes at rest (top picture), and after 40 min of shear at $\dot{\gamma }=\Omega r_i/e=70{\mathrm{s}}^{-1}$ (bottom picture).

Figure 3

Measured difference in liquid pressure between resting and sheared states, $\Delta P$. Top: $40\mu \mathrm{m}$ diameter particle suspension at varying $\varphi$, as a function of ${\eta }_f\dot{\gamma }$. Error bars show the range of transducer measurements for a given condition. Bottom: $|\Delta P|/\dot{\gamma }{\eta }_f$ as a function of $\varphi$ for three particle sizes.

Figure 4

Comparison of experimental correlation, simulation, and modeling of the particle pressure with the experimental values obtained in this study taking $\Delta P\equiv \Pi$.