Nernst Planck System Research Articles

Numerical simulation of pH-stimuli responsive hydrogel in buffer solutions

In this paper, the chemo-electro-mechanical behavior of the responsive hydrogel actuated by pH-stimuli is addressed. A chemo-electro-mechanical model, describing the hydrogel behavior with multi-field effects, is developed to simulate the swelling of the captivating biomaterials, and it is termed the multi-effect-coupling pH-stimulus (MECpH) model. This model delineates the effects of electric potential and mechanical deformations of the hydrogel as well as the transports of ionic fluxes within both the hydrogel and bath solution. The main contribution of this model laid on the incorporation of the relationship between the concentrations of the ionized fix-charge groups and the diffusive hydrogen ion, which follows a Langmuir isotherm theory, into the Poisson–Nernst–Planck system. In order to validate the MECpH model, one-dimensional steady-state simulations are conducted under varying pH conditions generated by buffer solution. The mathematical models are solved via a meshless Hermite–Cloud method and the numerical results are compared well with available experimental data. In conclusion, the presently developed MECpH model is able to predict the swelling behavior of the hydrogel precisely. This study provides a better understanding of the behavior of the pH-sensitive hydrogels.

Ionic diffusion through confined geometries: from Langevin equations to partial differentialequations

Ionic diffusion through and near small domains is of considerable importance inmolecular biophysics in applications such as permeation through protein channelsand diffusion near the charged active sites of macromolecules. The motion of theions in these settings depends on the specific nanoscale geometry and chargedistribution in and near the domain, so standard continuum type approaches haveobvious limitations. The standard machinery of equilibrium statistical mechanicsincludes microscopic details, but is also not applicable, because these systems areusually not in equilibrium due to concentration gradients and to the presence of anexternal applied potential, which drive a non-vanishing stationary current throughthe system. We present a stochastic molecular model for the diffusive motion ofinteracting particles in an external field of force and a derivation of effective partialdifferential equations and their boundary conditions that describe the stationarynon-equilibrium system. The interactions can include electrostatic, Lennard-Jones andother pairwise forces. The analysis yields a new type of Poisson–Nernst–Planck equations,that involves conditional and unconditional charge densities and potentials. Theconditional charge densities are the non-equilibrium analogues of the well studied paircorrelation functions of equilibrium statistical physics. Our proposed theory isan extension of equilibrium statistical mechanics of simple fluids to stationarynon-equilibrium problems. The proposed system of equations differs from thestandard Poisson–Nernst–Planck system in two important aspects. First, the forceterm depends on conditional densities and thus on the finite size of ions, andsecond, it contains the dielectric boundary force on a discrete ion near dielectricinterfaces. Recently, various authors have shown that both of these terms areimportant for diffusion through confined geometries in the context of ion channels.

ANALYTICAL APPROACHES TO CHARGE TRANSPORT IN A MOVING MEDIUM

ABSTRACT We consider electrodiffusion in an incompressible electrolyte medium which is in motion. The Cauchy problem is governed by a coupled Navier-Stokes/Poisson–Nernst–Planck system. We prove the existence of a unique smooth local solution for smooth initial data, with nonnegativity preserved for the ion concentrations. We make use of semigroup ideas, originally introduced by T. Kato in the 1970s for quasi-linear hyperbolic systems. The time interval is invariant under the inviscid limit to the Euler/Poisson–Nernst–Planck system.

Numerical simulation of multi-species diffusion

A numerical model has been developed to simulate the transport of several ionic species across a saturated concrete or mortar sample. The chloride binding as well as the electrical coupling between the different ionic fluxes are included in the model by using the Nernst-Planck system of equations. This model highlights which parameters affect substantially chloride penetration into reinforced concrete structures and then shows that the use of Fick’s first law in a predictive model for chloride penetration is strongly challenged. The simulations are in good agreement with diffusion-cell experiments and membrane potential measurements.

Modelling ion diffusion mechanisms in porous media

The main features of a numerical model aiming at predicting the drift of ions in electrolytic solutions are presented. The mechanisms of ionic diffusion are described by solving the Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Two algorithms using the finite element method for spatial discretization are compared for simple test cases. One is based on the Picard iteration method while the other is based on the Newton–Raphson scheme. Test results clearly indicate that the range of application is broader for the algorithm based on the Newton–Raphson method. Selected examples of the application of the algorithm to more complex 1-D and 2-D cases are given. Copyright © 1999 John Wiley & Sons, Ltd.

Modelling ion diffusion mechanisms in porous media

The main features of a numerical model aiming at predicting the drift of ions in electrolytic solutions are presented. The mechanisms of ionic diffusion are described by solving the Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Two algorithms using the finite element method for spatial discretization are compared for simple test cases. One is based on the Picard iteration method while the other is based on the Newton–Raphson scheme. Test results clearly indicate that the range of application is broader for the algorithm based on the Newton–Raphson method. Selected examples of the application of the algorithm to more complex 1-D and 2-D cases are given. Copyright © 1999 John Wiley & Sons, Ltd.

Numerical Solution of the Extended Nernst–Planck Model

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Numerical solution of the Nernst-Planck and poisson equation system with applications to membrane electrochemistry and solid state physics

An efficient finite difference simulation procedure for the steady state and transient solution of the Nernst-Planck and Poisson equation system is presented. The procedure is general and extremely efficient, containing refinements in time and distance scaling. The implicitly-formulated non-linear equations are solved with an iterative Newton-Raphson technique. The derivation is presented in sufficient detail for the reader to directly formulate similar computer codes. Steady state solutions, transient responses, and impedance-frequency responses are presented for a number of examples from the fields of membrane electrochemistry and solid state physics.