We develop a set of numerical schemes for the Poisson–Nernst–Planck equations. prove that our are mass conservative, uniquely solvable and keep positivity unconditionally. Furthermore, first-order scheme is proven to be unconditionally energy dissipative. These properties hold various spatial discretizations. Numerical results presented validate these properties. Moreover, indicate second-order...

We demonstrate the role of selectivity variation in the structure of the nonequilibrium extended space charge using one-dimensional analytic and two-dimensional numerical Poisson-Nernst-Planck models for the electro-diffusive transport of a symmetric electrolyte. This provides a deeper understanding of the underlying mechanism behind a previously observed maximum in the resistance-voltage curve...

We propose an anomalous diffusion approach to analyze the electrical impedance response of electrolytic cells using time-fractional derivatives. establish, in general terms, conservation laws connected a modified displacement current entering fractional formulation Poisson–Nernst–Planck (PNP) model. In this new formalism, we obtain analytical expressions for case blocking electrodes and presenc...

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...

This paper discusses the little-known fact that Donnan’s equilibrium criteria established over 100 years ago neglected coupling between ion concentrations and osmotic pressure. Such can be treated based on general thermodynamic considerations including solvent equilibrium, leading to a membrane potential consists of not only classical Donnan term but also an additional due pressure, existence e...

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.

In this work, the results concerning to the mean activity coefficient measurements for NaCl in the (glycerol + water) system using the potentiometric method are reported. The potentiometric measurements were performed on the galvanic cells without liquid junction of the type: Ag|AgCl|NaCl (m), glycerol (wt%), H2O (1 - wt)%|Na-ISE, in various mixed solvent systems containing 0, 5, 10,...

In nanofiltration (NF), solution and membrane chemistry determine the charge density. multi-component electrolytes solutions, it is important to consider interaction between ions NF membranes. For instance, in presence of divalent ions, reversal can take place due counterions with charged functional groups membrane. This paper presents a model based on state-of-the-art mean-field theory that in...