Particle impact on a cohesive granular media
Velotiana Jean-Luc Ralaiarisoa, Pascal Dupont, Ahmed Ould El Moctar, Florence Naaim-Bouvet, Luc Oger, Alexandre Valance
Abstract
We investigate numerically the impact process of a particle of diameter $d$ and velocity ${V}_{i}$ onto a cohesive granular packing made of similar particles via two-dimensional discrete element method simulations. The cohesion is ensured by liquid bridges between neighboring particles and described by short range attraction force based on capillary modeling. The outcome of the impact is analyzed through the production of ejected particles from the packing, referred to as the splash process. We quantify this production as a function of the impact velocity for various capillary strength $\mathrm{\ensuremath{\Gamma}}$ and liquid content $\mathrm{\ensuremath{\Omega}}$. The numerical data indicate that the splash process is modified when the dimensionless cohesion number $\text{Co}=6\mathrm{\ensuremath{\Gamma}}/{\ensuremath{\rho}}_{p}g{d}^{2}$ (where ${\ensuremath{\rho}}_{p}$ is the particle density, $d$ its diameter, and $g$ the gravitational acceleration) exceeds a critical value of the order of the unity. Above this value, we highlight that the ejection process is triggered above a threshold impact Froude number, $\text{Fr}={V}_{i}/\sqrt{gd}$, which depends both on $\mathrm{\ensuremath{\Gamma}}$ and $\mathrm{\ensuremath{\Omega}}$ and scales as ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{\beta}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{\delta}}$, where the values of the exponents are found close to $1/2$ and $1/6$, respectively, and can be derived from rational physical arguments. Importantly, we show that, above the threshold, the number of splashed particles follows a linear law with the impact Froude number as in the cohesionless case.