Date of Award
Doctor of Philosophy in Chemical Engineering - (Ph.D.)
Chemical, Biological and Pharmaceutical Engineering
Norman W. Loney
Angelo J. Perna
R. P. T. Tomkins.
A mathematical model is developed to predict bioleachi ng of heavy metals from long cylindrical shape cementitious samples. In this model, the metal concentration difference within the solid and its surface is considered as the main driving force for transport of metals to the surface of a sample at a given temperature and pressure. Fick’s first and second law are applied to explain the motion of contaminants in a long and uniform cylindrical solid. In addition, the model considers Michaelis-Menten type kinetics, a special case of the widely accepted Langmuir-Hinshelwood reaction mechanism, at the surface of the encapsulating cylinder. The resulting model is solved analytically by applying regular perturbation techniques and Laplace transform.
Specifically, the mathematical model consisting of a partial differential equation describing the mass transfer of the targeted species as it moves through the encapsulating cylinder toward the surroundings. The nature of the species interaction at the surface of the cylinder renders an otherwise linear problem to be nonlinear. However, by applying a boundary perturbation technique, a series of linear problems are generated that can then be solved using traditional methods such as the Laplace Transform. The Residue Theorem is used to carry out the inversions yielding closed form solutions of the targeted species concentration profile.
The model was benchmarked by using effective diffusivities and specific surface bio-reaction rate constants within published ranges. Values of the mass concentrations generated by the model for bioleaching of a number of metals namely cobalt, calcium, and chromium, from encapsulated cementitious cylindrical matrices are in reasonable agreement with those reported in the published literature.
Tabatabaie, Mojdeh, "Mathematical modeling of heavy metals diffusion and removal from cylindrical cement forms coated with bio-film" (2012). Dissertations. 354.