The two-dimensional self-assembling of mono-dispersed particles which were immersed in deuterium water was investigated under the sedimentation-free configuration. The diameters of particles ranged from 3 to 5 mu m. Since particles were floated on the free surface of deuterium water, the behaviour of particles could be observed using an optical microscope. The light scattering method was applied to measure Brownian movements of particles. The observation cell was designed to control the temperature and the evaporation rate of water by helium gas. The processes of self-assembling were very similar to those of crystal growth. Particle-particle interactions due to Brownian movements, clustering and growth of ordered lattices were observed. Using the light scattering method, the frequency spectra of Brownian particles were measured with respect to ordered and disordered configurations. It was clarified that the frequencies of phonon-like vibrations were a function of the gas-flow rate. The results indicate, the evaporation is essential to the assembling of particles. Fraction-like vibrations on percolation clusters were confirmed and explained by the formation of the clusters with long range correlation length at the critical density. The assembling forces were explained based on the interaction of Marangoni flows which were induced by evaporative cooling on the particles. The study reports a unique mechanism of particle self-assembling due to Marangoni flow.