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

We study both experimentally and theoretically the rheological behavior of isotropic bidisperse suspensions of noncolloidal particles in yield stress fluids. We focus on materials in which noncolloidal particles interact with the suspending fluid only through hydrodynamical interactions. We observe that both the elastic modulus and yield stress of bidisperse suspensions are lower than those of monodisperse suspensions of same solid volume fraction. Moreover, we show that the dimensionless yield stress of such suspensions is linked to their dimensionless elastic modulus and to their solid volume fraction through the simple equation of Chateau et al.[J. rheol. 52, 489-506 (2008)]. We also show that the effect of the particle size heterogeneity can be described by means of a packing model developed to estimate random loose packing of assemblies of dry particles. All these observations finally allow us to propose simple closed form estimates for both the elastic modulus and the yield stress of bidisperse suspensions: while the elastic modulus is a function of the reduced volume fraction $ϕ/ϕ_m$ only, where $ϕ_m$ is the estimated random loose packing, the yield stress is a function of both the volume fraction $ϕ$ and the reduced volume fraction.