Several coarsening models of three-dimensional solid-liquid mixtures were performed in the condition of statistically mean or randomly chosen position of uniform arrangement of the solute particles. These arrangements of the particles spacing imply that the two-phase mixtures are not stationary and must be realized by convection of the liquid matrix. Contrarily, any purely diffusion-controlled model for the three-dimensional coarsening in the stationary liquid matrix has not been clarified. The mean field model is numerically applied to represent the coarsening based on a non-convective, i.e. purely diffusive liquid in the present work. As the particles in the stationary liquid may tend to encounter each other owing to their radii changing during the coarsening, a simple model of particles spatially rearranged one another is proposed. This spatial rearranging model is derived from avoiding a geometrical overlap of two particles during coarsening calculation by transporting the particles to the positions, in which the surfaces of the par ticles jointly meet at the same point, due to a conservative rule, i.e. the total momentum of the encountered particles being zero. This coarsening model has shown the cubic law, which is a linear relation of the cube of the average radius and the holding time, of a a commonly coarsening behavior and the normalized particle size distribution left-skewed in the steady state as the conventional models based on the mean field theory. However, this model makes the rate conslant of the cubic law larger in the low volume fraction and smaller in the high volume fraction than the model for a randomly chosen position of uniform arrangement, i.e. Monte Carlo procedure of the particle.