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Well‐Posed Treatment of Space‐Charge Layers in the Electroneutral Limit of Electrodiffusion
Author(s) -
Stinchcombe Adam R.,
Mori Yoichiro,
Peskin Charles S.
Publication year - 2016
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21611
Subject(s) - limit (mathematics) , space (punctuation) , point (geometry) , space charge , charge (physics) , boundary (topology) , depletion region , ionic bonding , boundary layer , boundary value problem , membrane , layer (electronics) , mathematics , mathematical analysis , statistical physics , physics , chemistry , mechanics , computer science , materials science , ion , nanotechnology , geometry , quantum mechanics , electron , operating system , biochemistry
The electroneutral model describes cellular electrical activity, accounting for ionic concentration dynamics without resolution of the fine spatial scales of the space‐charge layer. This is done by asserting that the ionic solution is electrically neutral at each point in space. However, electroneutrality is inconsistent with the original boundary conditions at cell membranes. We consider three separate methods of resolving this inconsistency that result in well‐posed models that are accurate approximations to a detailed model in which the space‐charge layer is fully resolved. A particular electrodiffusion problem is utilized to make the discussion specific.© 2015 Wiley Periodicals, Inc.