Abstract
We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies is dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1835-1852 |
| Number of pages | 18 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 240 |
| Issue number | 22 |
| DOIs | |
| State | Published - Nov 1 2011 |
| Externally published | Yes |
Bibliographical note
Funding Information:The authors gratefully acknowledge support from the following sources: National Science Foundation (NSF) grant DMS-0914963 , the Alfred P. Sloan Foundation and the McKnight Foundation (to YM), NSF grant DMS-0707594 (to CL), and National Institutes of Health grant GM076013 (to RSE). The authors are grateful to the Institute of Mathematics and its Application (IMA) at the University of Minnesota at which much of the discussion took place. YM thanks Charles S. Peskin for pointing to Ref. [64] and experimental observations on osmosis described therein. Appendix A
Keywords
- Electrodiffusion
- Electrophysiology
- Energetic structure
- Osmosis