Slow and fast diffusion in a lead sulphate gravity separation process

A model for the growth of lead sulphate particles in a gravity separation system
from the crystal glassware industry is presented. The lead sulphate particles are an undesirable
byproduct, and thus the model is used to ascertain the optimal system temperature configuration
such that particle extraction is maximised. The model describes the evolution of a single,
spherical particle due to the mass flux of lead particles from a surrounding acid solution. We
divide the concentration field into two separate regions. Specifically, a relatively small boundary
layer region around the particle is characterised by fast diffusion, and is thus considered quasistatic.
In contrast, diffusion in the far-field is slower, and hence assumed to be time-dependent.
The final system consisting of two nonlinear, coupled ordinary differential equations for the
particle radius and lead concentration, is integrated numerically.