The Equations of Ostwald Ripening for Dilute Systems

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We consider a dilute mixture in 3D of a finite number of particles initially close to spherical, but of varying sizes, and representing one of the phases evolving according to the quasistatic dynamics. Under the scaling hypotheses that (1) typical size/typical distance and (2) deviation from sphericity/typical size are small, we associate centers and radii to each particle for the whole evolution and derive rigorously a set of ODEs fo the radii which we relate to the Lifschitz–Slyosov–Wagner theory of coarsening.

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