Diffusional Boundary Value Problems Involving Moving Boundaries, Connected with the Growth of Colloidal Particles

A method is suggested for treating problems of diffusion which involve moving boundaries. This method is applicable when the flux of material through any surface in the diffusion field is considerably greater than the rate of change of concentration on that surface. The method is applied to two problems dealing with the growth of monodispersed aerosols and hydrosols. The solution of the first of these problems indicates that, in a naphthalene‐like aerosol system growing by means of the diffusion of vapor toward sinks (nuclei) which cannot support supersaturation, spontaneous nucleation will not occur if the number density of nuclei exceeds 100/cc. The solution of the second problem permits the reproduction from theory of several curves due to Zaiser and La Mer which depict the rate of growth of sulfur hydrosols, therefore lending support to the idea that the particles grow by means of a simple diffusion mechanism rather than by a surface catalyzed deposition. The critical supersaturation concentration for sulfur in aqueous solution is $$c_0{\text{=4.7×10}}^{\text{−6}}\hspace{0.17em}\mathrm{g/atom/liter},$$ and the diffusion coefficient of S₈ is $${\text{D=2×10}}^{\text{−6}}\hspace{0.17em}{\mathrm{cm}}^2/\sec .$$ These values are in reasonable agreement with those estimated by independent means, although the diffusion coefficient seems to have about one‐half the expected value. This indicates that a unit larger than S₈ may be diffusing, e.g., a polythionate.