Convective Flows in Sheared Packings of Spherical Particles

Abstract

Understanding how granular materials respond to shear stress remains a central challenge in soft matter physics. We report direct observations of persistent granular convection in the bulk shear zones of spherical particle packings -- a phenomenon previously associated primarily with particle shape anisotropy or boundary effects. By employing various bead-coloring techniques in a split-bottom geometry, we reveal internal flow fields within sheared granular packings. We find robust convection rolls, strikingly governed by system geometry: at low filling heights, two counter-rotating convection rolls emerge, while at higher filling heights, a single dominant convection roll forms, featuring radially outward flow at the surface. This transition is driven by the height-dependent broadening of the shear zone, which introduces shear rate asymmetry across its flanks. Notably, the transition occurs entirely within the open shear band regime. These findings underscore the pivotal role of system geometry in shaping secondary flow formation in dense packings of frictional particles, suggesting possible broader relevance to geophysical flow dynamics and industrial applications.

Figures (7)

• Figure 1: Schematic (left) and photograph (right) of the split-bottom setup used in the experiments.
• Figure 2: (a) Schematic of initial vertical plane of colored tracers embedded along one diameter of the cylinder and initial surface photo before shearing. (b) Deformed tracer line after shear reveals local angular displacement at different bulk heights $h$. (c) Angular velocity profiles $\omega(r)$ at various $h$ (solid lines) and corresponding error function fits (dashed lines). Inset: axial angular velocity $\omega_0$ vs $h$. The line represents a Gaussian fit. (d) Comparison of shear zone center $R_c$ and width $\delta$ in our setup (green) with prior rough-boundary data (purple). Solid lines and symbols represent $R_c$ and shaded regions indicate $\delta$; see text. (e) Variational model prediction of $R_c$ versus $\mu_\text{rel}$ for different $H$. (f) $\delta$ vs $h$ for different values of $H$. The dotted line represents $\delta{\sim}h^{0.58}$.
• Figure 3: (a) Top-view images at selected time points for various filling heights $H$, showing the dispersion of colored tracer grains initially placed in narrow radial bands on the surface. (b) Mean radial position $\langle r\rangle$ of tracers as a function of time, for different initial radii and filling heights. Changes in $\langle r\rangle$ reflect surface signatures of underlying convective flow.
• Figure 4: (a) Initial configuration of colored tracers placed at mid-height ($h{=}H{/}2$) for two filling levels, covered with a black tracer layer at the top. (b) Reconstructed bulk tracer positions after shear for $H{=}4\,\text{cm}$. (c) Tracer density map in the ($r, h$) plane for $H{=}4\,\text{cm}$ in the steady state, overlaid with the shear zone center and boundaries, indicating a single dominant convection roll. Inset: Side view of the initial arrangement of colored tracers. (d) Quantitative characterization of the vertical positions of the differently colored tracer particles shown in panel (c). Each point denotes the mean color-intensity-weighted position within a vertical strip and the error bars indicate the corresponding standard deviations.
• Figure 5: (a) Reconstructed bulk tracer positions after shear for $H{=}2\,\text{cm}$. (b) Individual tracer density maps for $H{=}2\,\text{cm}$ in the steady state, overlaid with the shear zone center and boundaries, indicating two counter-rotating convection rolls. Inset: Side view of the initial arrangement of colored tracers. (c) Tracer density maps for $H{=}2\,\text{cm}$ and bulk heights $h{=}0.5,\,1.0,\,2.0\,\text{cm}$ at an early time point $t\,{=}\,3\,\text{min}$. (d) Mean vertical positions (color-intensity-weighted) of the differently colored tracer particles shown in panel (c).