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

The normal and shear viscosities of non-Brownian suspensions are measured by optical suspension imaging for particle volume fractions f between 0.3fm and 0.98fm, where fm 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 S p 22 are determined through the study of these profiles in the neutrally buoyant suspension, while the third particle normal stress S p 33 is deduced from the analysis of the vertical f profiles measured in the negatively buoyant suspension. Our results indicate that the shear viscosity decreases with shear stress S12, and that this shear-thinning behaviour can be captured by the variation of fm with S12. We show that S p 33 is proportional to S12, and that S p 33/.0.. is a function of only f/fm(S12). The values of S p 22 deduced from the radial f 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 x 10-4 to 3 x 101. We obtain very good agreement with the results obtained by Boyer et al. for J 10-1 (Phys. Rev. Lett., vol. 107, 2011, 188301) and by Zarraga et al. for J 10-1.