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We study both experimentally and theoretically the rheological behavior ofisotropic bidisperse suspensions of noncolloidal particles in yield stressfluids. We focus on materials in which noncolloidal particles interact with thesuspending fluid only through hydrodynamical interactions. We observe that boththe elastic modulus and yield stress of bidisperse suspensions are lower thanthose of monodisperse suspensions of same solid volume fraction. Moreover, weshow that the dimensionless yield stress of such suspensions is linked to theirdimensionless elastic modulus and to their solid volume fraction through thesimple equation of Chateau et al.[J. rheol. 52, 489-506 (2008)]. We also showthat the effect of the particle size heterogeneity can be described by means ofa packing model developed to estimate random loose packing of assemblies of dryparticles. All these observations finally allow us to propose simple closedform estimates for both the elastic modulus and the yield stress of bidispersesuspensions: while the elastic modulus is a function of the reduced volumefraction $\phi/\phi_m$ only, where $\phi_m$ is the estimated random loosepacking, the yield stress is a function of both the volume fraction $\phi$ andthe reduced volume fraction.

Macroscopic behavior of bidisperse suspensions of noncolloidal particles in yield stress fluids