In thesis we propose a mathematical model of electrolyte fluid and interface systems. The model is based on a coupling between the Navier-Stokes equations of an incompressible fluid, the Nernst-Plank-Poisson equations of a diffuse, binary electrolyte, and the phase field Allen-Cahn equation. The coupling is derived in the energetic variational framework and guarantees the consistent exchange of...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 1 Preliminary concepts and literature review . . . . . . . . . . . . . . . 11 1.1 Cellular excitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.1 Membranes, ionic gradients, and transport . . . . . . . . . . . . . 12 1.1.2 Electrical signaling and action potentials . . . . . . . . . . ...

The underlying theory of a new actuator concept based on hydrogel core flexible matrix composites (H-FMC) is presented. The key principle that underlines the H-FMC actuator operation is that the three-dimensional swelling of a hydrogel is partially constrained in order to improve the amount of useful work done. The partial constraint is applied to the hydrogel by a flexible matrix composite (FM...

A model for electro-diffusion is discussed, characterized by the NavierStokes/Poisson-Nernst-Planck system. In particular, we emphasize: (i) significant applications; (ii) existence for the initial/boundary-value problem; (iii) aspects of the steady problem.

Two different analyses of impedance data obtained from ultra-pure water allowed to equilibrate with the atmosphere have recently appeared. They both thus show much smaller low-frequency resistances than does ultra-pure water. Different fitting models were used in these analyses and led to appreciably different parameter estimates from their data fits. Their two “pure” water experimental data se...

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...

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.

Identification of the molecular interaction governing ion conduction through biological pores is one of the most important goals of modern electrophysiology. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) and three-dimensional Poisson-Nernst-Plank (3d-PNP) electrodiffusion algorithms offer powerful and general approaches to study of ion permeation through wide molecular pores. A detail...