Average limiting current density

The primary current distribution is uniform on the hemisphere. Numerical calculations using the potential theory have shown that the current distribution is essentially uniform on the RHSE if the current density is less than 68% of the average limiting current density [47]. 

The average Sherwood number, Shiv, and average limiting current density, iljmjav, can be obtained by integrating Eqs. (40)-(41) over the electrode surface. The results for a hemisphere, whose entire surface is subject to mass transfer are ... 

Table 2. Model predictions of average limiting current density across wafer surface.

Here i Um is an average limiting current density, cj is the average diluate concentration, a is a... 

If an electrode reaction, controlled by mass transport, takes place on an electrode embedded in the wall, a diffusion layer is established. Its thickness increases as one moves downstream, because the concentration change due to the electrochemical reaction affects an ever-increasing volume. The current density on the electrode is therefore not uniform but decreases towards the downstream end of the electrode. Thus, the longer the electrode, the more the average limiting current density becomes smaller. 

A theoretical analysis of the deposition of a metal B on a vertical electrode of length L, in the laminar flow regime, yields the following expression for the average limiting current density [10] ... 

The overall gain of the multiphase mixture model approach above is that the two-phase flow is still considered, but the simulations have only to solve pseudo-one-phase equations. Problems can arise if the equations are not averaged correctly. Also, the pseudo-one-phase treatment may not allow for pore-size distribution and mixed wettability effects to be considered. Furthermore, the multiphase mixture model predicts much lower saturations than those of Natarajan and Nguyen - and Weber and Newman even though the limiting current densities are comparable. However, without good experimental data on relative permeabilities and the like, one cannot say which approach is more valid. 

Figure 6.7 Influence of pulse parameters on deposit morphology for copper deposition from a copper sulfete/sulfuric acid electrolyte [6.102]. p pulse current density ipj limiting pulse current density i average current density jj limiting current density under dc conditions.

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... 

It was found that for the Fe(III) salts electrolytes the current efficiency was very low, 1-2% (the polarization curves for powder deposition (ytot) and for hydrogen evolution (yn) practically overlapped), and it was necessary to deposit powders at least for 2 h to obtain the amount of powder that could be used for the morphology and composition analysis (SEM, EDS). In the case of Fe(II) salt electrolytes, current efficiency at the potentials more negative than the second inflection point ( in Fig. 5.21) varied between 8% and 15% depending on the Ni/Fe ratio, as shown in Fig. 5.22. The average values for the diffusion limiting current densities for alloy powder electrodeposition were ype-Ni = —0.26 A cm for the ratio 1/3 and /pe-Ni = —0.49 A cm for the ratio 9/1. 

We discussed in this chapter about the limitations of the simplified model for determination of limiting current density based on the gas-phase diffusivity. In particular, besides the diffusion media, there is also diffusion resistance in the catalyst layer, which is in series with the gas diffusion layer, and the effects of a thin Nafion or liquid layer on the catalyst. Assume the anode and cathode catalyst layer porosity is 0.5 and thickness is 20 nm. Consider a system with a thin layer of flooding and an ionomer on the catalyst. Consider the cathode only, at a normal operating temperature of 80°C, and a pressure of 15 psig. Assume the average mole fraction of the oxygen in the flow channel 0.12. Develop an expression for, and solve for, the mass... 

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