Ostwald ripening: New relations between particle growth and particle size distribution

I. The critical radius Rc = uc R̄ one of the important parameters of Ostwald ripening, can be determined using the relation 3 H(uc) = uc h(uc). II. The ratio T = R03 / K has a physical meaning which has not yet been seen: After the time t = t0 + T the initial particle number density N0 has reduced by a factor two. With the scaled time t′ = (t - t0) /T it is N(t′) = N0 / (1 + t′). III. The scaled dissolution time of a particle with u(t0) = u0 simply is t′ex = F(u0) / H(u0), i.e. equal to the initial ratio of the particles which are smaller to the particles which are larger than the particle considered. IV. If u0 > uc the growth path culminates at a time t′ = t′cr when R (t′cr) = Rc (t′cr). The relation between t′cr and t′ex is: t′cr + 1 = (t′ex + 1) H(uc). V. The equation H[u(t′)] = (t′ + 1) H(u0) can be used to calculate u(t′). The growth path yields then according to R(t′) = u(t′) R̄(t′).