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The use of mathematical models for predicting the concentration gradient of a molar species under electrophoretic and electroosmotic forces has been exploited in a variety of applications, including water desalination, electrokinetic remediation of soil pollutants, and modeling drug delivery methods. Many existing models are only suited for narrow applications and are rooted primarily in data analysis rather than the governing equations, limiting flexibility under parameter changes. This contribution provides a generalized mathematical model for the concentration gradient of a molar species undergoing electrophoretic and electroosmotic forces in a rectangular channel. The model couples electrostatic potential and velocity profile formulations to produce an accurate concentration profile, relying on solutions to fluid mechanics equations including the Poisson–Boltzmann equation, the Navier–Stokes equation, and the molar species continuity equation. The model treats diffusivity, susceptibility, and electrostatic potential as variable parameters rather than fixed constants, and it leverages area-averaging techniques to solve the molar species continuity equation in this context. The work includes analysis of the resulting model and describes useful parameter configurations, including behavior in highly convective systems.
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Concentration Profiles in a Cylindrical Cell under Electrophoretic and Electroosmotic Forces
Due to rising concerns with environmental issues, electroosmosis and electrokinetic techniques are currently being explored in various applications within the field of environmental engineering. Current techniques include desalination and the remediation of soil due to the necessity of non-polluted soil and safe water. Mathematical modeling approaches to electroosmosis and electrokinetic techniques have been proven to be effective; unfortunately, existing models are often specialized to a specific set of circumstances and lack flexibility for other situations (e.g., drug delivery and biomedical engineering). This work introduces a generalized mathematical model for describing the concentration gradient of a molar species within a cylindrical channel undergoing electroosmotic and electrokinetic influence. The model couples electrostatic potential in a cylindrical channel with the velocity profile to obtain concentration predictions. Core to the formulation are established fluid mechanics equations, including the Poisson–Boltzmann equation, the Navier–Stokes equation, and the molar species continuity equation, with parameters such as diffusivity, susceptibility, and electrostatic potential treated as variables. A distinct aspect of this study is its use of area-averaging techniques to resolve the molar continuity equation. The study provides analysis of the cylindrical model and highlights patterns under standard parameters (e.g., higher susceptibility yields a more uniform concentration gradient from the wall to the channel center), with further research directions discussed.
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- Award ID(s):
- 2345379
- PAR ID:
- 10662905
- Publisher / Repository:
- American Institute of Chemical Engineers (AIChE)
- Date Published:
- Edition / Version:
- 1
- Page Range / eLocation ID:
- 1-2
- Subject(s) / Keyword(s):
- electroosmosis electrokinetics electrophoresis area-averaging
- Format(s):
- Medium: X Size: 128KB Other: pdf
- Size(s):
- 128KB
- Location:
- Boston, MA, USA
- Sponsoring Org:
- National Science Foundation
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