| Abstract: |
| We analyze a one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through ion channels with oppositely charged ion species. A local hard-sphere potential is included to account for ion size effects on ionic flows. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this model. The existence of solutions to the boundary value problem for small ion sizes is established.Treating ion sizes as small parameters, we derive approximations of the individual fluxes, the I-V relation and identify some critical potentials for ion size effects. Under electroneutrality conditions, each of these critical potentials separates the potential into two regions over which ion size effects are qualitatively opposite to each other. Without electroneutrality conditions, the qualitative effects of ion sizes will depend not only on the critical potentials but also on boundary concentrations and relative ion valences. The flow properties of interest depend on multiple physical parameters such as boundary conditions and diffusion coefficients, in addition to ion sizes and valences. For the relatively simple setting and assumptions of the model, we are able to characterize the distinct effects of the nonlinear interplay between these physical parameters. |
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