The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukh...

We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the wa...

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical...

An equation for ionophoresis in large tip microelectrodes is derived from Nernst-Planck equations for the general case of a completely dissociated electrolyte. The relation between the release of ions and the applied electric current is mainly determined by two parameters: the transference number of the ions under consideration and the diffusional leak of the microelectrode. Also it is shown ho...

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluch...

A new numerical model is presented for analyzing the propagation of ionic concentrations and electrical potential in space and time in the liquid junction and in the solution/ion-exchanging membrane system. In this model, diffusion and migration according to the Nernst-Planck (NP) flux equation govern the transport of ions, and the electrical interaction of the species is described by the Poiss...

Abstract In these notes, we have considered models of electrophysiology across several scales. The first was the membrane model. It assumes that action potential is similar whole cell membrane, and model represents as a function time alone. No spatial variable involved in pure models, so length scale does not make sense.

We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson–Nernst–Planck equations (PNP) and Sizemodified Poisson–Nernst–Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst–Planck e...

The optimal estimation of a general continuous-discrete system can be achieved through the solution of the Fokker-Planck equation and the Bayesian update. However, solving the Fokker-Planck equation numerically is prohibitive in most cases. Recently a nonlinear filtering algorithm using a direct quadrature method of moments was proposed by the authors, in which the associated Fokker-Planck equa...