Multiscale dynamics in yield stress fluids during homogeneous and shear-banded yielding
Whether homogeneous and shear-banded yielding involve distinct microscopic mechanisms remains unresolved. We combine oscillatory rheology with gradient-resolved particle tracking to compare a ductile Carbopol microgel that yields homogeneously with a more brittle dense emulsion that develops stationary shear bands. In both systems, we separate long-range correlated ballistic flow from local Fickian diffusion and find that the two act on the same tracers, rather than on distinct persistent populations. This finding challenges the distinct-population interpretation of earlier experiments, which could access only dynamics averaged over particles and along the velocity-gradient direction. We distinguish these contributions in Carbopol by varying the tracer radius $a$ and the observation-window size $L$ independently. The ballistic velocity is independent of $a$ but increases with $L$, indicating correlations beyond the field of view; the diffusion coefficient $D$ scales as $1/a$ and is independent of $L$. At fixed driving frequency and tracer size, emulsion measurements collapse onto a single $D(γ_L)$ curve, whether taken across the banded profile or at fixed height under varying applied amplitude. Local strain amplitude, rather than stress, therefore governs the mean diffusive mobility within our resolution. The increase of $D$ with $γ_L$ is steeper than in Carbopol, consistent with the emulsion's greater brittility. Diffusive displacements are nearly Gaussian in Carbopol, with no measurable cooperativity, while in the emulsion they are strongly non-Gaussian and cooperative. There, the four-point susceptibility is largest at the strain characterising the interband region. Homogeneous and shear-banded yielding therefore share the same dynamical ingredients, while differing in the statistics and spatial organisation of the residual diffusive motion.