Date of Award

Fall 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering

First Advisor

Brian A. Todd

Committee Chair

Brian A. Todd

Committee Member 1

Thomas M. Talavage

Committee Member 2

Daniel S. Elliot

Committee Member 3

Jan P. Allebach

Committee Member 4

Kenneth P. Ritchie


We develop a theory for encounter rates in a three-dimensional system of connected compartments. The model of connected compartments exhibits the length-scale dependent diffusion that is observed in many heterogeneous environments, such as porous catalysts and biological environments. We discovered a dimensionless number that is the dominant scaling variable and obtained, for the first time, an analytical expression for the encounter rate. The new theory generalizes the classic Smoluchowski diffusion limit to the case of heterogeneous environments. The new theory is tested using Brownian dynamics simulations.^ We also experimentally investigated the behavior of multivalent electrolyte near a charged solid-liquid interface. We used the streaming potential technique to measure electrical potentials near negatively charged glass surface as a function of trivalent ion (Co(NH3)6Cl3) concentration, monovalent ion (KCl) concentration, and pH. Charge inversion was observed. Measured electrical potentials were compared with predictions from a recent theory that models multivalent ions near the charged surface as two-dimensional strong coupled liquid (SCL). We found that SCL predictions agree quantitatively with our experimental data, which suggests that multivalent ions near charged surfaces form a two-dimensional highly correlated structure.