Multi-dimensional electrochemistry model

Global Well-Posedness and Stability of Electrokinetic Flows

“…Therefore, our approach generalizes the ones given, for instance, in [9,10,15,19,20,21], where electro(-reaction)-diffusion systems are considered, not taking into account convection induced by fluid motion or a coupling to the Navier-Stokes equations. In this context, we also want to stress the fact that our approach does not need the electro-neutrality assumption, as is assumed e.g.…”

“…Having this information at hand it is possible to prove that the L 2 (Ω)-norm of the concentrations c i is uniformly bounded in time, as it is done in [10]. Applying further energy estimates, the norm of the strong solutions (u, c) is shown to remain finite for finite time, whence the solution can be extended up to any time T .…”

“…For convenience we reproduce the computation from [10] correcting also a slight mistake. We use the same splitting into φ 1 and φ 2 for the potential φ as in (2.1) and (2.2).…”

“…Our proof of existence and uniqueness of steady states is much simpler and we are able to remove a restrictive global electro-neutrality condition imposed in [10] for uniqueness of steady states. Moreover, we prove exponential stability of steady states which is not given in [10]. The methods applied here are related to [20], where exponential stability of steady states for concentrations is derived in the absence of fluid motion.…”

Electrokinetics and soil decontamination: concepts and overview (Review)

“…In order to describe the transport and reaction processes in a porous medium in electrical field, one-dimensional numerical models have been developed by several authors [60][61][62]. In several studies, Choi and Lui [63][64][65][66] developed a mathematical model for the elctrokinetic remediation of contaminated soils assuming the contaminants are mostly heavy metals, water is in excess, the dissociation-association of water into hydrogen and hydroxyl ions is rapid, and that electro-osmosis is significant when compared to electromigration (field-induced transport of ions in an electrolyte as defined earlier) as a transport mechanism. The analytical steady state solutions of electroplating and transport in binary electrolyte arising from electrochemistry were provided in several articles by several authors [67][68][69][70].…”