Date of Award
Fall 2014
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
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
Abstract
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.
Recommended Citation
Li, Ran, "Theory for diffusional encounters in heterogeneous environments and multivalent electrolyte screening of charged interface" (2014). Open Access Dissertations. 320.
https://docs.lib.purdue.edu/open_access_dissertations/320