We study the electro-diffusion properties of a domain containing a cusp-shaped structure in three dimensions when one ionic specie is dominant. The mathematical problem consists in solving the steady-state Poisson-Nernst-Planck (PNP) equation with an integral constraint for the number of charges. A non-homogeneous Neumann boundary condition is imposed on the boundary. We construct an asymptotic...

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical re...

The biological effects of high-gradient magnetic fields (HGMFs) have steadily gained the increased attention of researchers from different disciplines, such as cell biology, cell therapy, targeted stem cell delivery and nanomedicine. We present a theoretical framework towards a fundamental understanding of the effects of HGMFs on intracellular processes, highlighting new directions for the stud...

In this work, the effect of extra-cellular conductivity on electroporation-mediated molecular delivery efficiency is investigated. A numerical model combining the Smoluchowski equation for membrane permeabilization and the Nernst-Planck equations for ion transport is used to simulate the evolution of ion concentration spatially and temporally. The results are compared with and used to interpret...

The bulk and interfacial transport properties of PANI free-standing membranes have been investigated in acidic media with chloride as common counter-ion and with di€erent co-ions, using the a.c. impedance technique with a four-electrode cell. The experimental data were compared to a recently proposed theoretical expression, based on use of the Nernst±Planck equation for mass transport and on sl...

Understanding the doping mechanism that involves substantial charge transfer between carbon nanotubes and chemical adsorbent is of critical importance for both basic scientific knowledge and nanodevice applications. Nevertheless, it is difficult to estimate the modification of electronic structures of the doped carbon nanotubes. Here we report measurements of electrochemical potentials of n-dop...

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and ...

Presence of wall at the vicinity of a moving particle through a flowing or stationary fluid hindered the motion of the particle by implying more drag on it. Presence of charge on the particle alone or on both the wall and particle hinders the motion more due to electrokinetic effect like relaxation and EDL overlap. Presence of charged surface heterogeneity make the scenario worse. A 3D finite e...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection–diffusion equations for potential flows, and...

Mutual diffusion coefficients D(12) of the ionic liquids 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C(2)MIM][NTf(2)]) and [C(4)MIM][NTf(2)] in highly diluted solutions of water and methanol have been measured at different temperatures between 288 K and 313 K using the Taylor dispersion technique. Tracer diffusion coefficients of the two cations [C(2)MIM](+) and [C(4)MIM](+...