Ostwald Ripening: Lifshitz-Slyozov Coarsening

Large droplets grow at the expense of small ones via diffusion through the matrix. The mean radius obeys ⟨R⟩³ ~ t (Lifshitz-Slyozov-Wagner law) and the size distribution converges to a universal self-similar shape.

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Statistics

N surviving
⟨R⟩
⟨R⟩³/t
Time t

About

Lifshitz-Slyozov (1961) & Wagner (1961): at late times, ⟨R(t)⟩³ − ⟨R(0)⟩³ = (4/9)κDt/c∞. The universal size distribution f(u), u=R/⟨R⟩, has a sharp cutoff at u=3/2. This coarsening underlies grain growth, phase separation, and cloud droplet evolution.