Wet granular bed eroded by a dry granular flow

Abstract

Using three-dimensional Discrete Element Method (DEM) simulations, we investigate the erosion dynamics of a cohesive bed composed of wet spherical particles subjected to the shear flow of an overlying non-cohesive granular layer. Cohesion is modeled through a capillary attraction law, where the erosion process is governed by the irreversible rupture of liquid bridges at the interface. By systematically varying the liquid-vapor surface tension and the inclination angle of the bed, we analyze the influence of cohesive strength and flow intensity on the mass entrainment rate. Our results identify two distinct erosion regimes: a slow, stochastic regime driven by granular temperature fluctuations, and a fast, collective regime characterized by a global mechanical instability of the interface. We propose a robust scaling law for the surface erosion rate in the fast erosion regime, based on the interplay between two dimensionless parameters: the inertial number ($I$) and the cohesion index ($ξ$). This framework reveals that the threshold for the fast erosion regime is determined by the ratio of the geometric mean of the driving stresses (kinetic and pressure) to the cohesive resistance. These findings provide a comprehensive description of the coupling between inertial and capillary forces, offering a predictive tool for the stability of cohesive interfaces in sheared granular flows.

Figures (8)

• Figure 1: Schematic representation of the system, consisting of two granular layers deposited on a rough, rigid plane inclined at an angle $\theta$ relative to the horizontal, within a vertical gravitational field $g$. The upper layer comprises a non-cohesive granular medium in a flow state driven by gravity. The underlying layer consists of a cohesive granular medium, initially at rest. The erosion process occurs at the interface between these two distinct phases, where particles are detached from the cohesive bed and entrained into the overlying dry flow.
• Figure 2: A snapshot of the granular bed in its initial configuration, consisting of 3,500 wet particles (blue) overlaid by a non-cohesive bed of 4,000 dry particles (red). Additionally, 1000 immobile particles are stuck to the bottom of the sample (grey). The gravity vector is rotated to an angle $\theta$ (above the angle of repose) to trigger the flow of the particles in the non-cohesive layer.
• Figure 3: Snapshots showing the time evolution of the erosion process for an inclination angle $\theta = 32°$. Velocity vector thickness is proportional to particle velocity. Time snapshots: (a) $t = 0.1$ s, (b) $t = 0.5$ s, (c) $t = 8$ s, (d) $t = 10$ s, and (e) $t = 13$ s. The corresponding velocity profiles are shown in Fig. \ref{['fig:VelocityProfiles']}. In these snapshots, the particles keep their initial color as shown in Fig. \ref{['fig:SampleImage']} although the blue eroded particles (dispersed inside the dry layer) are no more wet.
• Figure 4: Normalized velocity profiles, using the characteristic velocity $\sqrt{gd}$, along the direction of flow as a function of normalized height $z/d$ for a system of surface tension $\gamma_s = 0.03N \per m$ and inclination angle $\theta = 32°$ at several instants of time corresponding to the snapshots (a-e) in Fig. \ref{['fig:ErosionImage']}. The flow is initially at rest ($t = 0$ s), with the dry system beginning to flow while the velocity in the cohesive bed remains zero. As erosion progresses, the thickness of the static wet layer decreases. In the final stage, the entire sample flows as the cohesive layer becomes fully eroded.
• Figure 5: Temporal evolution of the number of eroded particles $N_e$, normalized by the average number of particles $N_s$ located at the interface between the cohesive and non-cohesive zones. The data are obtained from DEM simulations with a surface tension $\gamma_s = 0.03$ N/m and an inclination angle $\theta = 25^\circ$.