The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the first author in [Transport Theory Statist. Phys. 31 (2002), 333–366], where a local existence-uniqueness theory was demonstrated, based upon Kato’s framework for examining evolution equations. In this article, the existence of a global weak solution is proved to hold for the model, in the case of the in...

The drift-diffusion (Poisson–Nernst–Planck) model—including a numerical model for cell membranes that resolves surface-charge boundary layers—is applied to the cone–horizontal cell synapse in the outer plexiform layer of the retina. Numerical simulations reproduce the experimental calcium current-voltage (IV) curves for the goldfish retina in response to a bright spot, with and without an illum...

Motivated by contact resistance on the front side of a crystalline silicon solar cell, we formulate and analyse a two-dimensional mathematical model for electron flow across a poorly conducting (glass) layer situated between silver electrodes, based on the driftdiffusion (Poisson-Nernst-Planck) equations. We devise and validate a novel spectral method to solve this model numerically. We find th...

In the framework of fundamentals of smart materials and structures, a proper mathematical modeling of electro-kinetic transport phenomena in micro-structures adhering to the law of conservation of mass is suggested. The reference multiphase medium is described by a nonlinear Poisson–Nernst–Planck model stated in a heterogeneous pore-particle space disjoint by the interface. For physical consist...

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to...

We present an effective numerical approach to simulate electrochemically mediated desalination of seawater. This new membraneless, energy efficient desalination method relies on the oxidation of chloride ions, which generates an ion depletion zone and local electric field gradient near the junction of a microchannel branch to redirect sea salt into the brine stream, consequently producing desal...

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, Nucl. Instrum Methods Phys. Res. B 184, 337 (2001); Z. Siwy, Europhys. Lett. 60, 349 (2002)]. Here, the ion current r...

The conductivity behavior of doped hydrocarbon systems is studied by applying impedance spectroscopy. In the case of 3,5-diisopropyl salicylato aluminum (III) the charge carriers are formed by dissociation of the compound and their concentration is proportional to the square root of the solute concentration. In hydrocarbon systems that consist of micelle forming compounds (sodium AOT/ lecithin)...