We investigate the buoyancy-driven motion and path instability of freely rising spheres in Newtonian fluids and in Laponite clay dispersions whose rheology evolves with clay concentration and aging. Three-dimensional particle tracking velocimetry resolves trajectories over Ga=10−245, and a principal component representation is used to characterize lateral deviations and identify the symmetry-breaking transition in situ within individual ascents. A complementary horizontal-acceleration diagnostic captures the dynamic growth of lateral motion and provides an unambiguous indicator of whether wake-induced perturbations amplify or remain suppressed. Frenet–Serret analysis further shows that increasing clay concentration or aging suppresses lateral excursions, reduces out-of-plane curvature, and yields trajectories that become nearly planar with minimal binormal deviation. Velocity and drag measurements reveal a systematic reduction in terminal speed, consistent with the formation of a thin shear-fluidized layer surrounding the rising sphere at high structural ages. The results demonstrate that time-dependent microstructure, arising from shear-thinning, thixotropy, and aging, reorganizes the wake and reshapes the instability landscape beyond that which Galileo or Reynolds numbers alone can predict. The combined geometric and dynamic approach provides a quantitative basis for assessing path instability in evolving complex fluids and supports extensions to non-Newtonian and anisotropic particulate environments.
Wang et al. (Sun,) studied this question.