2018/05/08 by Doron Elad, Elad, Doron, Nir Gavish +1
Chemistry · Physics and Astronomy · Decision Sciences · #Electrostatics and Colloid Interactions #Surface and Thin Film Phenomena #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1805.03332
Steady-state solutions of the Poisson-Nernst-Planck model are studied in the\nasymptotic limit of large, but finite domains. By using asymptotic matching for\nintegrals, we derive an approximate solution for the steady-state equation with\nexponentially small error with respect to the domain size. The approximation is\nused to quantify the extent of finite domain effects over the full parameter\nspace. Surprisingly, already for small applied voltages (several thermal\nvoltages), we found that finite domain effects are significant even for large\ndomains (on the scale of hundreds of Debye lengths). Namely, the solution near\nthe boundary, i.e., the boundary layer (electric double layer) structure, is\nsensitive to the domain size even when the domain size is many times larger\nthan the characteristic width of the boundary layer. We focus on this\nintermediate regime between confined domains and `essentially infinite'\ndomains, and study how the domain size effects the solution properties. We\nconclude by providing an outlook to higher dimensions with applications to ion\nchannels and porous electrodes.\n