An energetic variational approach for ION transport
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2014-03-06
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Abstract
The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system. All of the physics is included in the choices of corresponding energy law and kinematic transport of particles. The variational derivations give the coupled force balance equations in a unique and deterministic fashion. We also discuss the situations with different types of boundary conditions. Finally, we show that the Onsager's relation holds for the electrokinetics, near the initial time of a step function applied field. © 2014 International Press.
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Xu, S, P Sheng and C Liu (2014). An energetic variational approach for ION transport. Communications in Mathematical Sciences, 12(4). pp. 779–789. 10.4310/CMS.2014.v12.n4.a9 Retrieved from https://hdl.handle.net/10161/28786.
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Shixin Xu
Shixin Xu is an Assistant Professor of Mathematics whose research spans several dynamic and interconnected fields. His primary interests include machine learning and data-driven models for disease prediction, multiscale modeling of complex fluids, neurovascular coupling, homogenization theory, and numerical analysis. His current projects reflect a diverse and impactful portfolio:
- Developing predictive models based on image data to identify hemorrhagic transformation in acute ischemic stroke.
- Conducting electrodynamics modeling of saltatory conduction along myelinated axons to understand nerve impulse transmission.
- Engaging in electrochemical modeling to explore the interactions between electric fields and chemical processes.
- Investigating fluid-structure interactions with mass transport and reactions, crucial for understanding physiological and engineering systems.
These projects demonstrate his commitment to addressing complex problems through interdisciplinary approaches that bridge mathematics with biological and physical sciences.
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