Local limiting current density

Using Eqs. (36)-(39), one obtains the following expressions for the local Sherwood number and local limiting current density on the speherical surface... 

The efficacy of porous electrodes depends on two factors The pores allow an external geometric electrode area of 1 cm2 to be increased many times and the meniscus-like structure of the three-phase boundary gently increases the local limiting current density. Assume a model electrode with pores having a uniform... 

It should be mentioned that passive layers are not protective in all environments. In the presence of so-called aggressive anions, passive layers may break down locally, which leads to the formation of corrosion pits. They grow with a high local dissolution current density into the metal substrate with a serious damage of the metal within very short time. In this sense halides and some pseudo halides like SCN are effective. Chloride is of particular interest due to its presence in many environments. Pitting corrosion starts usually above a critical potential, the so-called pitting potential /i]>j. In the presence of inhibitors an upper limit, the inhibition potential Ej is observed for some metals. Both critical potentials define the potential range in which passivity may break down due to localized corrosion as indicated in Fig. 1. 

A rigorous analysis of the current-potential relation and current distribution in a single pore was carried out taking into account all forms of polarization considering a concentration gradient of only the reactant and in the axial direction of the pore (108). The assumption of a unidirectional concentration gradient is valid under the conditions that the local activation-controlled current density is considerably less than the limiting current density due to radial diffusion (i < iJlO). 

Physically, r is proportional to the ratio of mass transfer coefficient of liquid water in membrane to mass transfer coefficient of water vapour in the backing layer. The parameter r thus describes the competition of two opposite water fluxes back diffusion, which wets the anode side of the membrane and leakage through the backing layer to the channel, which facilitates membrane drying. Physically, r controls the local water-limiting current density (see below). 

As discussed above, this solution arises for r < 1 in which case the parameter/-is positive. We see that in the water-limiting regime local current density increases exponentially with z. Physically, in this case there is a plenty of oxygen everywhere, and the local-limiting current is determined by membrane drying. The growth of/with z is then due to accumulation of water in the feed channel, which results in increasing membrane conductivity with z. 

The fraction inside the parentheses can be expressed [32] in terms of the local Hmit current density Jr, that is, the maximum current reachable when the limiting reactant concentration on the electrode surface approaches zero, and further simpHfied to... 

The use of three-dimensional electrodes requires that the microkinetic polarization curve of the main reaction, sketched in Fig. 2, shows a potential range of width Arj within this the current density approaches the limiting current density. Thus, the optimal bed depth in the direction of current flow is introduced as a new important design parameter, for which the whole bed is working under limiting current conditions. This means that at each point the local overpotential lies within the Arj range, and the full limiting current density is realized. 

Physically, the total limiting current density is the average of the local limiting currents (3.3) over z. This can be shown by direct averaging of (3.3) over 2 with... 

The second solution corresponds to the water-limiting regime, when local current is hmited by membrane drying. This solution arises if /r >0 or, equivalently, r < 1. When r > 1 this solution disappears and for aU z we have an oxygen-limiting regime. Physically, at r > 1 insufficient membrane humidification only reduces the cell potential, but does not affect the limiting current density. 

Equation (4.22) is analogous to Eq. (4.3), the equation for the batch reactor, except that overall partial current density is replaced by a local partial current density We shall return to Eq. (4.22) later but for now we assume a mass transfer limited reaction. Under those circumstances Ax n SkLCAxl substituting this quantity in Eq. (4.22) we get, after a slight rearrangement ... 

Mass-Limiting Current Density We previously examined ohmic limiting current density. Now we consider the case of mass transfer hmiting current density U. At the mass transport limiting current density, the rate of mass transport to the reactant surface is insufficient to promote the rate of consumption required for reaction. In this case, the local concentration of reactant will be reduced to zero, which, from Eq. (4.84), must also reduce the cell voltage to zero. Assuming the surface concentration Cr) is zero at the limiting state (//)... 

D Limited by local or environmental safety requirements regarding apparatus and/or earth voltage gradient regulations E Minimum current density to ensure passivation SO Am ... 

L ir in free suspension in moving water, no limit, local effects under high current density may increase wastage rate M May be used in the environment under special circumstances N High consumption rate in this environment... 

Equation (23) implies that the current density is uniformly distributed at all times. In reality, when the entire electrode has reached the limiting condition, the distribution of current is not uniform this distribution will be determined by the relative thickness of the developing concentration boundary layer along the electrode. To apply the superposition theorem to mass transfer at electrodes with a nonuniform limiting-current distribution, the local current density throughout the approach to the limiting current should be known. 

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