Interaction between a falling sphere and the structure of a non-Newtonian yield-stress fluid

Abstract We present an experimental study using mixtures of aqueous superabsorbent polymers (SAP) where we systematically investigate the influence of the size of grains that make up the fluid structure on the mixture effective rheology and its domain of validity. In water, SAP powder grains can swell up to 200 times and form gel grains, d g , whose sizes (typically between 1 and 8 mm) can be controlled by choosing the size of the initial powder grains. The rheology of this mixture (water and touching grains) combines viscous, elastic and plastic aspects. Here, they are characterized using the free-fall of spheres of different densities and diameters ( d s ). The latter were varied between 3 and 30 mm, therefore providing a range where they become comparable to the fluid gel grains. We observe five different regimes of motion: (1) A linear regime where the sphere has a rapid and straight fall and reaches a constant terminal velocity. (2) An irregular regime where the sphere’s velocity varies around a constant value. (3) An intermittent regime where periods of no-motion and periods of irregular falls follow one another. (4) A slow fall regime where the sphere’s speed progressively decreases in a logarithmic way. (5) A no-motion regime when spheres are not heavy enough to overcome the yield stress of the mixture, or are too small compared to the grain size. The sphere trajectories in regimes (1), (2) and (3) are all following a same trend which, in the framework of an Hershel-Bulkley fluid, allows to estimate the effective yield stress σ Y and consistency K v of the SAP mixtures. Both σ Y and K v increase with increasing gel grain size. Regimes (2) and (3) are due to the interactions between the falling sphere and individual gel grains, i.e. the fluid structure. Moreover, the critical Yield number ( Y c , which compares σ Y to the stress induced by the sphere net weight in the fluid) above which there is no motion decreases as d s ∕ d g becomes smaller than 2. So although the characteristic size of the fluid structure influences the magnitude of its rheological properties, the use of an Herschel-Bulkley rheology to describe the trajectories of the spheres breaks down only when the sphere diameter becomes very close to the SAP structure size.