Coarsening of precipitation patterns in a moving reaction-diffusion front

Precipitation patterns emerging in a two-dimensional moving front are investigated on the example of NaOH diffusing into a gel containing ${\text{AlCl}}_{3}$. The time evolution of the precipitate $\text{Al}{(\text{OH})}_{3}$ can be observed since the precipitate redissolves in the excess outer electrolyte NaOH and thus it exists only in a narrow optically accessible region of the reaction front. The patterns display self-similar coarsening with a characteristic length $\ensuremath{\xi}$ increasing with time as $\ensuremath{\xi}(t)\ensuremath{\sim}\sqrt{t}$. A theory based on the Cahn-Hilliard phase-separation dynamics, including redissolution, is shown to yield agreement with the experiments.