Biaxial extensional rheology of granular suspensions: The HBP (Herschel-Bulkley for Pastes) model

Abstract

We show that a constitutive equation describing the extensional behavior of “soft” microcrystalline cellulose pastes [J. Rheology 51, 493–516 (2007)] can be applied to dense granular suspensions of “hard” spheres. Biaxial extension of ballotini (size ∼10μm) suspensions featuring a Newtonian liquid phase was investigated experimentally employing constant velocity squeeze flow with lubricated plates. All suspensions, featuring solid volume fraction 0.59≤ϕ≤0.62, exhibited elasto-viscoplasticity: they deformed as quasi-linear elastic solids prior to yielding and flowed as non-Newtonian (shear-thickening) liquids thereafter, with the transition occurring at a particular strain regardless of strain rate. The yield stress was dependent on the strain rate experienced by the material at yielding, the values being consistent with those obtained from separate limiting height experiments. The differences in the model parameters between hard and soft particle systems are discussed in terms of inter-particle interactio...