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Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force,$$F_{{L}}$$, and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities,$$u_{{s}}$$. The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However,$$F_{{L}}$$in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low$$u_{{s}}$$, reaches a maximum value and then decreases with increasing$$u_{{s}}$$, eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the$$F_{{L}}$$versus$$u_{{s}}$$data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases.
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This content will become publicly available on August 10, 2026
Thin-layer formation of ellipsoidal gyrotactic swimmers in time-dependent hydrodynamic shear
We investigated the dynamics of thin-layer formation by non-spherical motile phytoplankton in time-dependent shear flow, building on the seminal work of Durhamet al.(2009Sciencevol. 323, pp. 1067–1070), on spherical microswimmers in time-independent flows. By solving the torque balance equation for a microswimmer, we found that the system is highly damped for body sizes smaller than$$10^{-3}$$m, with initial rotational motion dissipating quickly. From this torque balance, we also derived the critical shear for ellipsoidal microswimmers, which we validated numerically. Simulations revealed that the peak density of microswimmers is slightly higher than the theoretical prediction due to the speed asymmetry of sinking and gyrotaxis above and below the predicted height. In addition, we observed that microswimmers with higher aspect ratios tend to form thicker layers due to slower angular velocity. Using linear stability analysis, we identified a thin-layer accumulation time scale, which contains two regimes. This theoretically predicted accumulation time scale was validated through simulations. In time-dependent flow with oscillating critical shear depth, we identified three accumulation regimes and a transitional regime based on the ratio of swimmer and flow time scales. Our results indicate that thin layers can form across time scale ratios spanning five orders of magnitude, which helps explain the widespread occurrence of thin phytoplankton layers in natural water bodies.
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- PAR ID:
- 10676180
- Publisher / Repository:
- Journal of Fluid Mechanics
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1016
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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