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.
","abstract_html":"<p>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(NH<sub>3</sub>)<sub>6</sub>Cl<sub>3</sub>) 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.</p>","abstract_has_math":false,"creators":["Li, Ran"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Brian A. Todd","Thomas M. Talavage","Daniel S. Elliot","Jan P. Allebach","Kenneth P. Ritchie"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-10-01T07:00:00Z","date_published":"2014-10-01T07:00:00Z","updated_at":"2026-07-24T03:53:34Z","subjects":["Biomechanics and Biotransport","Biophysics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/320","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Brian A. Todd","Thomas M. Talavage","Daniel S. Elliot","Jan P. Allebach","Kenneth P. Ritchie"]},{"key":"dc:creator","label":"Author","values":["Li, Ran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Biomechanics and Biotransport","Biophysics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/320"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Theory for diffusional encounters in heterogeneous environments and multivalent electrolyte screening of charged interface"]}]}],"canonical_facts":{"dc:contributor":["Brian A. Todd","Thomas M. Talavage","Daniel S. Elliot","Jan P. Allebach","Kenneth P. Ritchie"],"dc:creator":["Li, Ran"],"dc:description.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.
"],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/320"],"dc:subject":["Biomechanics and Biotransport","Biophysics"],"dc:title":["Theory for diffusional encounters in heterogeneous environments and multivalent electrolyte screening of charged interface"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:53:34Z"}