Ostwald ripening

Ostwald ripening is an observed phenomenon in solid solutions or liquid sols that describes the change of an inhomogeneous structure over time, i.e., small crystals or sol particles dissolve, and redeposit onto larger crystals or sol particles.

Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described by Wilhelm Ostwald in 1896. Ostwald ripening is generally found in water-in-oil emulsions, while flocculation is found in oil-in-water emulsions.

This thermodynamically-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles. This stems from the fact that molecules on the surface of a particle are energetically less stable than the ones in the interior.

Consider a cubic crystal of atoms: all the atoms inside are bonded to 6 neighbors and are quite stable, but atoms on the surface are only bonded to 5 neighbors or fewer, which makes these surface atoms less stable. Large particles are more energetically favorable since, continuing with this example, more atoms are bonded to 6 neighbors and fewer atoms are at the unfavorable surface. As the system tries to lower its overall energy, molecules on the surface of a small particle (energetically unfavorable, with only 3 or 4 or 5 bonded neighbors) will tend to detach from the particle, as per the Kelvin equation, and diffuse into the solution. When all small particles do this, it increases the concentration of free molecules in solution. When the free molecules in solution are supersaturated, the free molecules have a tendency to condense on the surface of larger particles. Therefore, all smaller particles shrink, while larger particles grow, and overall the average size will increase. As time tends to infinity, the entire population of particles becomes one large spherical particle to minimize the total surface area.

The history of research progress in quantitatively modeling Ostwald ripening is long, with many derivations. In 1958, Lifshitz and Slyozov performed a mathematical investigation of Ostwald ripening in the case where diffusion of material is the slowest process. They began by stating how a single particle grows in a solution. This equation describes where the boundary is between small, shrinking particles and large, growing particles. They finally conclude that the average radius of the particles ⟨R⟩, grows as follows:

...
Wikipedia