“…4 and 5 can be justified considering that (i) the reaction kinetics parameters k or 1=t f are in relation with the energy exchanged during shocks, (ii) this exchanged energy is proportional to the kinetic energy of the ball at the collision time, but not equal because collisions can be from frontal to tangential (impact mode or friction mode [20,21] with a statistical distribution of these modes with the time of grinding), (iii) for a given mass of the balls, the kinetic energy is a quadratic function of the ball velocity and therefore is a quadratic function of the rotation speed of the disc and of the eccentricity r d of the vial on the rotating disc (Eq. (12)).…”