Diffusion Nemst theory

The original and simplest form of the diffusion layer theory was developed by Nemst [105] and Brunner [106], who assumed that the mass flux is given by Fick s first law of diffusion. In that case,... 

A comparison of the experimental data with the solution based on the diffusimi layer theory and the numerical solution presented by Coueignoux and Schuhmann [171] was made by Deslouis et al. [177]. Figure 4.19 presents the normalized complex plane plots for ferricyanide obtained at different potentials corresponding to 1/4, 1/2, and 3/4 of the limiting currents. It is obvious that the approximation using the simplified Nemst diffusion layer theory, curve (a), goes above the experimental points while the numerical solution, curve (b), is much better. 

The EMD studies are performed without any external electric field. The applicability of the EMD results to useful situations is based on the validity of the Nemst-Planck equation, Eq. (10). From Eq. (10), the current can be computed from the diffusion coefficient obtained from EMD simulations. It is well known that Eq. (10) is valid only for a dilute concentration of ions, in the absence of significant ion-ion interactions, and a macroscopic theory can apply. Intuitively, the Nemst-Planck theory can be expected to fail when there is a significant confinement effect or ion-wall interaction and at high electric... 

The fundamental theory of electron escape, owing to Onsager (1938), follows Smoluchowski s (1906) equation of Brownian motion in the presence of a field F. Using the Nemst-Einstein relation p = eD/kRT between the mobility and the diffusion coefficient, Onsager writes the diffusion equation as... 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

In the hydrodynamic theory, the diffusion coefficient of a solute molecule A or single particle through a stationary medium B, DAB, is given by the Nemst-Einstein equation ... 

Crystal growth can be considered to be a reverse dissolution process and the diffusion theories of Noyes and Whitney, and of Nemst, consider that matter is deposited continuously on a crystal face at a rate proportional to the difference of concentration between the surface and the bulk solution. So an equation for crystallisation can be proposed in the form... 

A fully microscopic theory of chemical diffusion can be constructed, however, it requires a careful distinction between the motions of the observed species and the underlying host, and is made complicated by the fact that, as defined, the diffusion coefficient relates flux to the concentration gradient while the actual force that drives diffusion is gradient of the chemical potential. An alternative useful observable is the so-called conductivity diffusion coefficient, which is defined for the motion of charged particles by the Nemst-Einstein equation (11.69)... 

Kinetics of ion exchange is usually considered to be controlled by mass transfer in ion exchange particles or in the immediately surrounding liquid phase. The theory used to describe mass transfer in the particle is based on the Nemst-Planck equations developed by Helffericht which accounted for the effect of the electric field generated by ionic diffusion, but excluded convection. 

The theory presented here resolves itself into a generalization of the well-known Nemst-Einstein equation D = 22T/C>) to several components and optional concentration characteristics. The cases of two- and three-component mixtures are treated in detail. The latter case is also shown to be of interest in treating self diffusion in a binary mixture, a system which results from letting two components become diffusionally identical although still distinguishable. 

The use of the macro-d5uiamical method previously in connection with the osmotic theory of force [the diffusion of electrolytes and ionic mobilities by Nemst diffusion and the hydrodynamic (Stokes ) radius of molecules according to W. Sutherland and Einstein] is weU known. An alternative, simple formulation of two-component diffusion, Eq. (10), is possible if another form of the thermod5mamic factor, based upon osmotic pressme is applied ... 

Nemst-Haskell The theory of dilute diffusion of salts is well developed and has been experimentally verified. For dilute solutions of a single salt, the well-known Nernst-Haskell equation (Reid et al.) is applicable ... 

Diffusion in liquid-filled pores occurs by essentially the same mechanism-as in gaseous systems. However, methods of correlation and prediction are less accurate since the fundamental theory of diffusion in the liquid phase is less well developed than the theory of molecular diffusion in the vapor phase. Correlations based on the Stokes-Einstein and Nemst-Einstein equations must be treated with caution. A wide range of empirical and semiempirical correlations is available but it is generally necessary to select the appropriate correlation with care, taking due account of the nature of the components. Predictive methods are at their best for mixtures of two nonpolar species and at their worst for mixtures of a polar and nonpolar species. 

In considering the transport of a species from a fluid in turbulent flow toward a solid surface, for example, an electrochemically active species to an electrode, Nemst assumed that the transport was governed by molecular diffusion through a stagnant film of fluid of thickness 5. This model, although having questionable physical relevance, is quite useful for correlating effects such as the influence of chemical reaction on mass transfer. A few simple examples of the use of film theory to describe mass transfer in the presence of chemical reaction are considered here. 

Reverse osmosis can be used for the separation of ions om an aqueous solution. Neutral membranes are mainly used for such processes and the transport of ions is determined by their solubility and diffusivity in the membrane (as expressed by the solute permeability coefficient, see eq V 162). The driving force for ion transport is the concentration difference, but if charged membranes or ion-exchange membranes are used instead of neutral membranes ion transport is also affected by the presence of the fixed charge. Teoreil [45] and Meyer and Sievers [46] have used a fixed charge theory to describe ionic transport through these type of systems. This theory is based on two principles the Nemst-Planck equation and Dorman equilibrium. 

Theories of mass transport in electrolytes or elec-trolyttic solutions take into account that motion of dissolved species / can be driven by gradients in electric potential O (migration), as well as by gradients in molar concentration c, (diffusion) and by motion of material at the bulk velocity v (convection). The most commonly deployed model for electrolyte transport is the Nemst-Planck theory [1], developed in detail by Levich [2]. Within this theory, one constituent of the solution - typically a neutral species in relative excess - is identified as a solvent . The total molar flux of any remaining solute species i, Ni, is then expressed relative to a stationary coordinate frame as... 

The Nemst-Planck equation is often employed by practitioners because of its similarity to Pick s law and its convenient separation of diffusion and migratiOTi terms. It should be borne in mind, however, that the theory is inconsistent with the basic requirements of irreversible thermodynamics [6, 7]. Nemst-Planck theory uses n + k properties to characterize transport in an isothermal, isobaric n-species system containing... 

Very often, transport in a liquid near the interface is modelled as a purely diffusive process in a stagnant layer of some thickness S. Generally this thickness has different values S/i and 6b in phases A and B. The concept of stagnant layer was introduced by Nemst at the beginning of this century and it constituted the basis of the two-film theory proposed by Whitman [9]. The parameter 6 represents the... 

This model has been successfully used by Chin and Sabde [25] for crevice cathodic protection using numerical analysis based on the dilute solution theory and reduction reaction of dissolved oxygen and Aa+, Cl, and OH ions at the crevice surface. Hence, the Nemst-Plank equation, eq. (4.2), can be generalized as a differentiable and continues scalar diffusion molar flux function... 

An alternative to the Nemst Planck models of charge diffusion is the rate theory model, which views ion permeation through a channel or pump from a statistical thermodynamics perspective. In this approach, one or more energy barriers are assumed to exist at fixed points in the channel and ions permeate... 

Despite such serious approximations and restrictions, multi-component theories provide essential features of polyelectrolyte dynamics, such as coupled diffusion, plasmon modes and Nemst-Hartley diffusion. 

---