Date of Award

Summer 2000

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Raja Nassar


In this study free molecular flow in a micro-channel was modeled using a stochastic approach, namely the Kolmogorov forward equation in three dimensions. Model equations were discretized using Central Difference and Backward Difference methods and solved using the Jacobi method. Parameters were used that reflect the characteristic geometry of experimental work performed at the Louisiana Tech University Institute for Micromanufacturing.

The solution to the model equations provided the probability density function of the distance traveled by a particle in the micro-channel. From this distribution we obtained the distribution of the residence time of a particle in the micro-channel. Knowledge of Residence time will aid both chemical and biomedical engineers in the study of micro-reactors and biological systems, respectively. From the transition probability density obtained in our model and the initial particle density (or number concentration), one can calculate also the distribution of particle or solute concentration in the micro-channel. Model prediction of the distribution of distance traveled by a particle can be applied to experimental data on micro-channel flow being gathered at the Institute for Micromanufacturing at Louisiana Tech University.