Slow and fast diffusion in a lead sulphate gravity separation process

8th Workshop on Multi-Rate Processes and Hysteresis;HSFS Workshop (Hysteresis and Slow-Fast Systems)

Cregan, Vincent^1 ; Lee, William T.^2

Centre de Recerca Matemá Tica, Campus de Bellaterra, Edifici C, Bellaterra, Barcelona

08193, Spain^1

Deptartment of Mathematics, University of Portsmouth, Winston Churchill Ave, Portsmouth

PO1 2UP, United Kingdom^2

关键词: Boundary-layer regions;    Concentration fields;    Gravity separation;    Lead concentration;    Particle extraction;    Particle radii;    Spherical particle;    System temperature;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012001/pdf
DOI  :  10.1088/1742-6596/811/1/012001

来源: IOP

【 摘 要 】

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 quasi-static. 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.