Deformation of a macroscopic yield stress hydrogel during the free fall of a sphere

We investigate the deformation of a macroscopic yield stress fluid consisting of a mixture of water and hydrogel (superabsorbent polymer) with high solid volume fractions and different grain size distributions during the settling of a sphere. The fluid's rheology combines viscous, elastic, and plastic behaviors and is described by a shear-thinning yield stress model. Experiments were conducted in two motion regimes: the continuous fall, where the sphere reaches a constant terminal velocity, and the intermittent regime, with alternating periods of motion and no-motion. Particle image velocimetry and spatiotemporal images of laser-illuminated fluid cross sections were used to determine the yield surface and analyze local grain motion dynamics. In both regimes, a yield surface similar to an ovoid spheroid is observed. A scaling law is derived for lateral deformation (perpendicular to the fall direction), dependent on sphere size and Yield number (Y). This scaling law provides reliable estimations of maximum deformation widths, consistent with experiments in the literature using different yield stress fluids. For all fluid samples used, the flow within the yielded region shows a strong fore-aft asymmetry, characterized by a negative wake at the back of the sphere related to the elastic component of the bulk deformation. In the intermittent motion regime, we find that the transition from no-motion to motion is associated with reaching a maximum level of compression or triggering sufficient irreversible plastic events in the region of fluid under compression. This leads to a sudden avalanche-type of event where stresses are relaxed and the sphere starts moving downward again.