Diffusion-convection layer current densities

We assume that the concentration distribution within the diffusion—convection layer can be treated in the similar way to that described in Chapter 2, and then the concentration distribution of the oxidant near the electrode surface can be schematically expressed in Figure 5.2. Thus, the diffusion—convection current density (ioc.o) can be expressed in a similar form to those Eqns (2.57) and (2.58) ... 

In order to get the current—potential relationship on the RDE, particularly the expression of limiting current density as the function of the electrode rotating rate and the reactant concentration, Pick s second law has to be used to give the equations of reactant concentration change with time at the steady-state situation of diffusion—convection. When the surface concentration of oxidant reaches zero during the reaction at the steady-state situation, the concentration distribution within the diffusion—convection layer is not changing with time anymore, meaning that the diffusion rate is... 

It can be seen that this thickness of the diffusion—convection layer is not a function of the location on the electrode surface, which is different from that of Eqn (5.1), and therefore, the current density over the entire RDE surface is uniformly distributed. 

The two major causes of uneven current distribution are diffusion and ohmic resistance. Nonuniformity due to diffusion originates from variations in the effective thickness of the diffusion layer 8 over the electrode surface as shown in Figure 10.13. It is seen that 8 is larger at recesses than at peaks. Thus, if the mass-transport process controls the rate of deposition, the current density at peaks ip is larger than that at recesses since the rate of mass transport by convective diffusion is given by... 

The time variation of 8 before the onset of natural convection depends on how the diffusion process is provoked. If a constant current density is switched on at t = 0, then the time variation of the effective diffusion-layer thickness can be obtained from Eqs. (7.179) and (7.202)... 

When forced convection is applied in the cell by means of, for instance, a magnetic stirrer, the flux due to convection increases and may become the dominant constituent of the total flux even after jusl a few ms. This results in a steady-state situation, where the diffusion layer stops growing. (If the convection is laminar, then the solution adjacent to the electrode surface will not move relative to the electrode, and diffusion becomes the only mode of mass transport in this thin layer.) Overall, the eflcct of convection is thus to shrink the thickness of the diffusion layer, resulting in larger concentration gradients in the diffusion layer with much more efficient mass transport of the electroactive species. In other words, the current densities that can be accomplished in stirred solutions are much higher than in unstirred. 

Figure 6.15 Steady state current density, igg, as a function of for Ag OPD in the system Au(100)/0.1 M AgC104 + 0.5 M HCIO4 at T = 298 K [6.161]. The overvoltage 7 is corrected by ohmic drt and diffusion overvoltage assuming Df - = 2 x 10 cm s and a diffusion layer thickness

Of course, the influence of magnetic field appears to be restricted to the diffusion-limited regions. During electrolysis under parallel fields, the Lorentz force induces convective flow of the electrolyte close to electrode surface. A magnetically stimulated convection leads to a decrease of the diffusion layer thickness thus increasing the diffusion-limited current density.39 As a rule, it was adopted that the limiting diffusion current density depends on magnetic field, as z l oo 51/341 Anyway, the increase of the... 

We saw above that the concentration gradient at an electrode will be linear with respect to the spatial coordinate perpendicular to the electrode surface if the anode/cathode cell were operated at a constant current density and if the fluid velocity were zero. In actuality, there will always be some bulk liquid electrolyte stirring during current flow, either an imposed forced convection velocity or a natural convection fluid motion due to changes in the reacting species concentration and fluid density near the electrode surface. In electrochemical systems with fluid flow, the mass transfer and hydrodynamic fluid flow equations are coupled and the solution of the relevant differential equations is often a formidable task, involving complex mathematical and/or numerical solution techniques. The concept of a stagnant diffusion layer or Nemst layer parallel and adjacent to the electrode surface is often used to simplify the analysis of convective mass transfer in... 

The surface electric current is approximately zero since electric currents of the anions and cations are of a convective nature and roughly compensate each other. The electric current density within the diffuse layer of ionic surfactants obeys the equation... 

The surface concentration of the reacting species decreases with increasing current density. For a given current density, it is lower the larger the thickness of the diffusion layer, or in other words, the lower the convection rate. 

This maximum current density is normally called the diffusion-limiting current density. It can be seen that both Eqns (2.55) and (2.56) represent the steady-state situation created by the convection process outside the region of diffusion layer. Due to... 

The hydrogen evolution influences the hydrodynamic conditions inside electrochemical cell [6-8]. The increase in hydrogen evolution rate leads to the decrease of the diffusion layer thickness and hence to the increase of limiting diffusion current density of electrode processes. It was shown [6] that if the rate of gas evolutimi at the electrode is larger than 100 cm /cm min (>5 A cm ), the diffusion layer becomes only a few micrometers thick. A coverage of an electrode surface with gas bubbles can be about 30 % [6]. If the thickness of the diffusion layer in conditions of natural convection is 5 10 cm and in strongly stirred electrolyte 5 10 cm [9], it is clear that gas evolution is the most effective way of the decrease of mass transport limitations for electrochemical processes in mixed activation-diffusion control. 

Taking into account that Sand s equation is valid only as long as the change of concentration occurs within a stagnant layer undisturbed by convection and introducing the Nemst diffusion layer boundary 8 and hydrodynamic layer boundary Ah, the minimum current density that must be applied in the first pulse for electrodeposition of the second layer to take place is given by... 

In theoretical consideration of multilayer electrodeposition of Cu-Ni alloy under the conditions of convective diffusion [63], it was shown that a constant concentration of Cu in the second layer (Cu-Ni alloy) could be established at different thicknesses of the second layer, depending on the value of the current density of a second pulse and the rotation rate. As the value of the current density in the second pulse increases the thickness at which a constant concentration of Cu could be... 

The model presented here is a comprehensive full three-dimensional, non-isothermal, singlephase, steady-state model that resolves coupled transport processes in the membrane, eatalyst layer, gas diffusion eleetrodes and reactant flow channels of a PEM fuel cell. This model accounts for a distributed over potential at the catalyst layer as well as in the membrane and gas diffusion electrodes. The model features an algorithm that allows for a more realistie representation of the loeal activation overpotentials which leads to improved prediction of the local current density distribution. This model also takes into aeeount convection and diffusion of different species in the channels as well as in the porous gas diffusion layer, heat transfer in the solids as well as in the gases, electrochemical reactions and the transport of water through the membrane. 

The thickness of the diffusion layer and therefore the limiting current density vary as a function of convection conditions. There are two forms of convection ... 

T steady-state mass transport regime the concentration profile in the diffusion layer corresponds to that of the steady state and the limiting current density depends exclusively on convection conditions. 

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