The characterization of the particle normal stresses of concentrated granular suspensions by local rheometry

Abstract

The normal and shear viscosities of non-Brownian suspensions are measured by optical suspension imaging for particle volume fractions $\phi$ between $0.3\phi _m$ and $0.98\phi _m$, where $\phi _m$ is the jamming fraction. Two distinct refractive-index-matched suspensions, made with the same polymethyl methacrylate spherical particles dispersed in a mixture of water and Triton X-100, are studied. One is density-matched while the other one is negatively buoyant. They are both sheared in a Couette rheometer where the velocity and particle volume fraction fields are measured. The shear viscosity and the second particle normal stress $\varSigma _{22}^p$ are determined through the study of these profiles in the neutrally buoyant suspension, while the third particle normal stress $\varSigma _{33}^p$ is deduced from the analysis of the vertical $\phi$ profiles measured in the negatively buoyant suspension. Our results indicate that the shear viscosity decreases with shear stress $\varSigma _{12}$, and that this shear-thinning behaviour can be captured by the variation of $\phi _m$ with $\varSigma _{12}$. We show that $\varSigma _{33}^p$ is proportional to $\varSigma _{12}$, and that $\varSigma _{33}^p/\eta _0\dot {\gamma }$ is a function of only $\phi /\phi _m(\varSigma _{12})$. The values of $\varSigma _{22}^p$ deduced from the radial $\phi$ profiles are consistent with the results of Zarraga et al. (J. Rheol., vol. 44, 2000, pp. 185–220). We conclude by discussing our results in the framework of the $\mu (J)$ rheology for viscous numbers $J$ ranging from $2\times 10^{-4}$ to $3\times 10^1$. We obtain very good agreement with the results obtained by Boyer et al. for $J\lesssim 10^{-1}$ (Phys. Rev. Lett., vol. 107, 2011, 188301) and by Zarraga et al. for $J\gtrsim 10^{-1}$.