Using the population balance method we investigated the dependence of polydispersity on the growth law that governs the size increase of particles. Using a power-law kernel Ki ∼ iα (where i is the mass of the particle) explicit results are derived for two limiting cases of constant kernel α = 0.0 and proportional kernel α = 1.0. For the constant kernel the normalized variance decreases in time. For the proportional kernel the variance increases during growth. In the two transition regions of weak kernels α < 0.5 and strong kernels α > 0.5, the polydispersity approaches the asymptotic values of the constant and proportional kernels. In the transition regions the growth law cannot be deduced from the polydispersity.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Surfaces, Coatings and Films
- Colloid and Surface Chemistry