Energy absorption by the particle and the surface during impact

When a particle impacts a target its kinetic energy dissipates to different mechanisms. In the current study, we developed a novel particle-wall impact model, that allows to distinguish between three energy dissipation mechanisms: wall deformation, wall cutting, and particle deformation. For each mechanism a different model for a coefficient of restitution (COR) was established, which allows to compute the energy loss due to the specific mechanism. In order to relate to each mechanism separately, we considered the indentation hardness ratio of the materials as a criterion for quantifying which phenomena is more dominant. This assumption allowed formulating a complete scheme for evaluation of the energy loss when simultaneous surface erosion and particle breakage can occur. In addition, this model is a useful tool that can identify if energy dissipation to the wall or to the particle can be neglected based on their mechanical properties (indentation hardness, Young's modulus, Poisson's ratio and density) and the collision characteristics (impact velocity and angle). This model is also applicable for evaluating the COR for all ranges of hardness ratio, which implies that it can be integrated as a general model for computing the COR in terms of the materials properties and collision conditions for numerous particle-fluid applications. Extensive validation is conducted throughout the paper incorporating six different target materials and seven types of particles for the proposed model, verifying its applicability for accurate prediction of each mechanism. The model showed good agreement in predicting the tangential and normal COR. Furthermore, a broad analysis was conducted to study the model performance at various conditions with different combinations of particle and wall materials.