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...

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...

Cellular Physiology 1. Define the distribution of solutes between the intracellular and extracellular compartments. 2. Define passive, active and secondary active transport across the cell membrane. 3. Define the equation and the variables that determine the flux of an uncharged solute by simple diffusion, i.e. Fick’s law of diffusion. 4. Define the role of membrane voltage, concentration gradi...

We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the field of microand nanofluidics, we consider the model in such generality that electrokinetic flows are included. This prohibits employing the assumption of el...

The concept of electrodiffusion based on the Nernst-Planck equations for ionic fluxes coupled with the Poisson equation expressing relation between gradient of the electric field and the charge density is widely used in many areas of natural sciences and engineering. In contrast to the steady-state solutions of the Nernst-Planck-Poisson (abbreviated as NPP or PNP) equations, little is known abo...

Cellular Physiology 1. Define the distribution of solutes between the intracellular and extracellular compartments. 2. Define passive, active and secondary active transport across the cell membrane. 3. Define the equation and the variables that determine the flux of an uncharged solute by simple diffusion, i.e. Fick’s law of diffusion. 4. Define the role of membrane voltage, concentration gradi...

Ionic diffusion coefficients in the membrane are needed for modelling of ion transport ion-exchange membranes (IEMs) with Nernst-Planck equation. We have determined ionic Na+, OH?, H+, Cl?, SO42?, NaSO4?, and HSO4? from experiments dilute NaCl, NaOH, HCl, Na2SO4, H2SO4 solutions through IEMs conductivity measured these solutions, using electrochemical impedance spectroscopy. The order fluxes ac...

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...