Mass transport Nemst model

In addition to this, the three-dimensional mathematical model of heat and mass transfer [3, 4] has been developed. Stephan-Maxwell equation was used for mass transport calculations in gas channels and gas diffusion layers. Proton transport in membrane and electrocatalytic layer was described by Nemst-Planck equation. The diffusion and electroosmosis of water were taken into account for membrane potential distribution. 

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... 

Mass transport or concentration losses. These result from the change in concentration of the reactants at the surface of the electrodes as the fuel is used. We have seen in Chapter 2 that concentration affects voltage, and so this type of irreversibility is sometimes called concentration loss. Because the reduction in concentration is the result of a failure to transport sufficient reactant to the electrode surface, this type of loss is also often called mass transport loss. This type of loss has a third name - Nemstian . This is because of its connections with concentration, and the effects of concentration are modelled by the Nemst equation. 

Modelling is mainly based on the solution of partial differential equations obtained in most cases by numerical methods like Finite Difference Method (FDM), Finite Element Method (FEM) or Boundary Element Method (BEM) describing always a bimetalhc corrosion situation at various scales combining current and potential distribution (Laplace s equation) with the mass transport of reactive species (Nemst-Planck s equation). 

Normal ionic current profiles has been modelled on a galvanic couple using the Laplace s equation as it was proposed by Crowe and Kasper, but without taking into account the effect of mass transport of species in solution. Considering the total current, i.e., migrative and diffusive components, a good fit is obtained between the experimental (Fig. 19a) and simnlated (Fig. 20) profiles verifying the Nemst-Planck s equation (Eq. 13). 

With the aim of reducing computational efforts, a few assumptions can be introduced into the SECCM model. For the sake of simplicity, the convective contribution to mass transport, u, can be ignored since the contribution to the overall transport of chemical species caused by electro-osmotic fluid flow is relatively small and the liquid movement due to pipette oscillations and lateral translation (during imaging) is negligible compared to diffusion and migration. Thus, in the absence of any homogeneous reactions of chemical species, the Nemst-Planck equation reads... 

Transport in OSN membranes occurs by mechanisms similar to those in membranes used for aqueous separations. Most theoretical analyses rely on either irreversible thermodynamics, the pore-flow model and the extended Nemst-Planck equation, or the solution-diffusion model [135]. To account for coupling between solute and solvent transport (i.e., convective mass transfer effects), the Stefan-Maxwell equations commonly are used. The solution-diffusion model appears to provide a better description of mixed-solvent transport and allow prediction of mixture transport rates from pure component measurements [136]. Experimental transport measurements may depend significantly on membrane preconditioning due to strong solvent-membrane interactions that lead to swelling or solvent phase separation in the membrane pore structure [137]. 

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 6. 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 theoiy to describe mass transfer in the presence of chemical reaction are considered here. 

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