Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 6460
Silong Zong | York University
An Electro-Neutral Model for ion transport
The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this talk, we present simplified electro-neutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First of all, it is much cheaper to solve them numerically. Secondly, EN models are easier to deal with compared to the original PNP system, therefore it would also be easier to derive macroscopic models for cellular structures using EN models. We will consider the general multi-ion case with either Dirichlet boundary conditions or flux boundary conditions. The derivation is based on matched asymptotics, and the key idea is to bring back higher order contributions into the effective boundary conditions. The EN model will be verified by some numerical examples, including a concrete example for neural axon to simulate action potential.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.