The effect of Ostwald ripening of metal particles attached to carbon nanotubes has been studied using density functional theory. It has been confirmed that Ostwald ripening may be responsible for the termination of growth of carbon nanotube forests. It was seen that the Ostwald ripening of metal particles attached to carbon nanotubes is governed by a critical factor that depends on both the cluster size and the carbon nanotube chirality. For example, clusters attached to armchair and zigzag nanotubes of similar diameters will have different critical factors although the exact behavior may depend on which molecules are present in the surrounding medium. The critical factor was also observed to have a critical point with the effect that clusters with a narrow size distribution close to the critical point may experience a narrowing rather than a widening of the size distribution, as is the case for free clusters.