The mobile particles collision frequency

The problem of particle collision frequency has been discussed where all particles are mobile. An arbitrary sphere, called sphere of collisions, whose radius is the sum of the radii of the two particles, is considered. The simultaneous sojourn of them in the sphere leads inevitably to collision. New relation for the collision frequency has been derived. The simultaneous collision of two, three and more particles is considered. The new relation provides a much lower value for the collision frequency than the previous one -- the great difference is caused by the very low probability for the particles to be found in the sphere of collisions simultaneously. Evaluation of bi-particle and three-particle collisions has been undertaken. At high particle densities the three-particle collisions seem to predominate over the bi-particle ones. These relations concern the rate of the nuclei formation and growth in a homogenous nucleation process