Articles via Databases
Articles via Journals
Online Catalog
E-books
Research & Information Literacy
Interlibrary loan
Theses & Dissertations
Collections
Policies
Services
About / Contact Us
Administration
Littman Architecture Library
This site will be removed in January 2019, please change your bookmarks.
This page will redirect to https://digitalcommons.njit.edu/dissertations/354 in 5 seconds

The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Mathematical modeling of heavy metals diffusion and removal from cylindrical cement forms coated with bio-film
Author: Tabatabaie, Mojdeh
View Online: njit-etd2013-060
(xiii, 108 pages ~ 1.7 MB pdf)
Department: Department of Chemical, Biological and Pharmaceutical Engineering
Degree: Doctor of Philosophy
Program: Chemical Engineering
Document Type: Dissertation
Advisory Committee: Loney, Norman W. (Committee chair)
Hanesian, Deran (Committee member)
Perna, Angelo J. (Committee member)
Simon, Laurent (Committee member)
Tomkins, R. P. T. (Committee member)
Nutakor, John (Committee member)
Date: 2013-01
Keywords: Math modeling
Diffusion in solids
Michaelis-Menten kinetics
Diffusion in cylinders
Availability: Unrestricted
Abstract:

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.


If you have any questions please contact the ETD Team, libetd@njit.edu.

 
ETD Information
Digital Commons @ NJIT
Theses and DIssertations
ETD Policies & Procedures
ETD FAQ's
ETD home

Request a Scan
NDLTD

NJIT's ETD project was given an ACRL/NJ Technology Innovation Honorable Mention Award in spring 2003