Size-Modified Poisson-Nernst-Planck Model

• Main Authors: Jen-Ho Lo, 羅仁和
• Other Authors: Jinn-Liang Liu
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/96805650568180052217

碩士 === 國立新竹教育大學 === 應用數學系碩士班 === 100 === The Poisson-Nernst-Planck (PNP) model is a basic continuum model for simulating ionic flows in an open ion channel. The effects of finite particle size on electrostatics, density profile, and diffusion have been a long existing topic in the study of ionic solution [8]. The Poisson equation is derived from Coulomb's law in electrostatics and Gauss's theorem in calculus. The Nernst-Planck equation is equivalent to the convection-diffussion model. An entropy functional that accounts for the finite size effects of ions in electrolytes proposed by Borukhov et al. [1] for the Poisson-Boltzmann (PB) equation has been generalized by Lu and Zhou [8] to the PNP model. We obtain second-order convergent results for the finite size linear PNP model with exact solutions. For nonlinear finite size PNP model with exact solutions, the numerical errors are almost zero.