A Numerical Strategy for Nernst–Planck Systems with Solvation Effect

Abstract

A thermodynamically consistent model of an isothermal, incompressible ionic mixture in mechanical equilibrium is presented. It accounts for differing ion sizes and differing solvation numbers of the ionic species. For this model, a numerical solution procedure based on a two point flux finite volume ansatz on unstructured triangular meshes is developed. Based on a reformulation of the continuous problem in terms of absolute activities, the Scharfetter‐Gummel upwind scheme for semiconductor simulation is generalized to take into account finite ion size and solvation effects.

On Four Numerical Schemes for a Unipolar Degenerate Drift-Diffusion Model

“…The activity based flux is a restriction of the flux introduced in [7]. It relies on the expression (8). With frozen β (c), the flux J is linear w.r.t.…”

“…In (3), c dop describes the doping profile of the media. Such models occur in applications ranging from organic semiconductors [5], high-temperature fuel cells [13] or simplified models of ionic liquids [8]. Because of the singularity of h near 1, the density c remains in the interval (0, 1).…”

“…Let us notice that, even ν(c) = r(c) for our specific choice of h(c), the excess chemical potential and the diffusion enhancement arising respectively in (7) and (9) have a different physical sense so that we keep different notations. Each formulation (2), (7), (8) and (9) leads to a different scheme that we compared from a numerical analysis point of view. Notice that the flux J can also be expressed as J = −∇r(c)−c∇Φ.…”

A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model

“…It is the limit for vanishing disorder of the Gauss-Fermi integral [42,45] which is used to describe organic semiconductors [16]. A similar relationship is valid for the oxygen ion concentration in a solid oxide electrolyte [49] and a simple model of an ionic liquid [30].…”

Induced charge electroosmotic flow with finite ion size and solvation effects

“…Section 2 introduces a modified Nernst-Planck-Poisson-Navier-Stokes model which has its foundations in first principles of nonequilibrium thermodynamics [4,5,6] and takes into account ion-solvent interactions, finite ion size and solvation effects. Section 3 introduces a finite volume discretization approach for ion transport in a self-consistent electric field which is motivated by results from semiconductor device simulation [7]. Pressure robust mixed finite element methods for fluid flow [8], and a fix point approach for coupling to ion transport are introduced.…”