The grain growth in presence of particles is controlled by the local evolution of grain boundaries around the considered grain and not by the average evolution of the totality of the matrix. Then, the curvature radii of the boundaries that surround growing grains cannot be ignored. In the present study, the curvature radius should be linked to the grain boundary nature by defining a minimal critical radius R-c for grain growth. This critical radius which is related to the average radius of the neighbourhood permits the exploration of possible growth sequence for small grains.