Resumen de Geometric Singular Perturbation Approach to Poisson-Nernst-Planck Systems with Local Hard-Sphere Potential: Studies on Zero-Current Ionic Flows with Boundary Layers

Jianing Chen, Mingji Zhang

• We examine the dynamics of zero-current ionic flows via Poisson-Nernst-Planck systems with one cation, one anion and boundary layers. To account finite ion size effects in the analysis, we include Bikerman’s local hard-sphere model. Geometric singular perturbation theory is employed in our discussion, together with the specific structures of the model problem, we obtain the existence and local uniqueness result of the problem for zero-current state. More importantly, we are able to derive explicit expressions of the approximation to individual fluxes from the solutions. This allows us to further examine the effect on the zero-current ionic flows with boundary layers from finite ion sizes and diffusion coefficients by further employing regular perturbation analysis. The detailed analysis, particularly, the characterization of the nonlinear interplay between system parameters provides deep insights and better understandings of the internal dynamics of ionic flows through membrane channels.