Dynamics of collision of a spherical ice crystal particle with a perfectly rigid substrate

Impact of single particle onto a rigid substrate leads to its deformation and fragmentation. The flow associated with the particle spreading on a solid substrate after impact is extremely complicated. In this theoretical study a simplified model for the plastic flow with the rate-dependent yield strength is developed. The flow in the particle is approximated by an incompressible inviscid flow past a thin rigid disk. The expression for the pressure field distribution is obtained in the vicinity of the impact axis. The total momentum balance of the particle is used to derive the equations of the particle deformation by impact. The theoretical predictions of the typical geometrical parameters of the particle, the peak force and the evolution of the force in time are compared with the existing experimental data. The agreement is rather good.