Until now, we have developed continuum models for the dynamics of electrolytes at the macroscopic scale, much larger than typical length scales for intermolecular forces. In particular, we have used principles of nonequlibrium thermodynamics, to arrive at general models of interfacial voltage (Nernst equation), reaction kinetics (Butler-Volmer equation), and transport (Poisson-Nernst-Planck equ...

Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. S...

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic ...

The a posteriori error estimates are studied for class of nonlinear stead-state Poisson–Nernst–Planck equations, which coupled system consisting the Nernst–Planck equation and Poisson equation. Both global upper bounds local lower estimators obtained by using averaging operator. Numerical experiments given to confirm reliability efficiency estimators.

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three domi...

In 1887, Walther Hermann Nernst (1864-1941; Nobel Laureate 1920) began his highly successful career as an assistant to Wilhelm Ostwald (1853-1932; Nobel Laureate 1909) at the University of Leipzig. Ostwald strongly supported the ionic theory and had extended it, especially to the dissociation of weak electrolytes. By 1889, Nernst had established the principles of electrode potential, familiariz...

With a microfluidic droplet-based liquid/liquid extraction setup, we demonstrate that the extraction of an ionic analyte from complex matrices can be modulated by the interfacial Galvani potential difference and the extraction equilibrium follows the classical Nernst equation.

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...

The transport of propidium iodide into electropermeabilized Chinese hamster ovary cells was monitored with a photomultiplier tube during and after the electric pulse. The influence of pulse amplitude and duration on the transport kinetics was investigated with time resolutions from 200 ns to 4 ms in intervals from 400 micros to 8 s. The transport became detectable as early as 60 micros after th...