The rapid expansion of supercritical solution (RESS) is a promising process for the production of small particles with a narrow size distribution. It involves an expansion of a supercritical solution through a small nozzle to generate a rapid nucleation and then the formation of ultrafine particles. The particles are transported by a powerful jet developed in the expansion chamber. The particle size distribution (PSD) of the obtained fine powders depends on the hydrodynamic conditions in the pre- and post-expansion unit, the nature of solute-solvent system, as well as on the nozzle geometry, and diameter. In this work, we have developed a numerical simulation of both transport and Brownian coagulation of spherical particles in the expansion chamber by resolving the general dynamic equation (GDE). This simulation has permitted to control the temporal evolution of PSD characterizing each class of particles. These PSD field evolutions show that the particles of each class get round the Mach disk taking refuge on the jet boundaries where the Brownian coagulation is more pronounced. Therefore, these particles whose size depends on thermodynamic and geometrical conditions are deposited on the flat plate as a ring. We notice that the narrowest distribution function of the deposited particles on the flat plate is obtained for the largest nozzle orifice diameters and the lowest expansion pressure.