Mathematical Modeling of Heavy Metals Removal from Bio-film Coated Cylindrical Cement Base Waste Forms

Abstract

Abstract A mathematical description is presented for the leaching behavior of cobalt and chromium from their solidified/stabilized forms under the attack from biofilms commonly developed by acid forming bacteria such as Thiobacillus thiooxidans or Thiobacillus ferooxidans. The proposed model predicts the metals diffusion and subsequent removal from cylindrical cement waste forms using a Michaelis-Menten-type kinetics, as a special case of the widely accepted Langmuir-Hinshelwood mechanism at the surface of the encapsulating cylinder. The resulting nonlinear model is solved by applying boundary perturbation to reduce the nonlinear problem to an infinite series of linear problems that are solvable by Laplace transform methods. Model predictions compares well with published experimental data and confirms that a Michaelis-Menten-type kinetics is most probably the dominant mechanism for the leaching of heavy metals from cement based waste forms.