Electrolytes convection velocity

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... 

Equation (26.69) (or Equation (26.70) for the case of a supporting electrolyte) was originally derived under the assumption of no convective velocities. These same relationships can be utilized within the effective mass transfer boundary layer when fluid stirring exists. A current density/con-centration equation with fluid stirring can now be generated starting with Equation (26.69) or Equation (26.70). The dCldy term in Equation (26.69) is replaced by AC/8, (where 8, is the effective mass transfer boundary-layer thickness) ... 

As the current density is increased during a metal deposition process (or any electrochemical reaction where the electroactive species in the bulk electrolyte is consumed at the electrode surface) with a constant value of 5 (i.e., for a given forced convection velocity), the surface concentration (CJ decreases since and 5 are constant and independent of the electrode reaction rate. The linear concentration gradient in Equation (26.73) or (26.75) has a maximum value when C = 0. The current density corresponding to this surface concentration condition is known as the limiting current density (1 ) ... 

The convection velocity, u, in the porous electrolyte structure is given either by Darcy s law equation (Equation 6.17) or by Brinkman s equation (Equation 6.18) as discussed in Chapter 6. 

Figure 6. A schematic of the electroosmotic flow of the medium (e.g., an electrolyte) in a capillary caused by the flow of counter ions as a plug, under the influence of the applied electric field, E UL, is the convective liquid velocity from electroosmosis. Adapted from Everett.48...

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

In a real electrochemical system, convection is usually introduced by such means as rotating electrode, stirring, or other forced circulation. In any case, the electrolyte moves relative to electrode surfaces. Due to the mechanical friction between electrolyte solution and electrode surface, a velocity v(x) variation exists. The velocity of solution flow is generally a constant (vqo) in bulk solution (far from the electrode surface and the wall of solution container) and decreases while approaching the solid surfaces [6]. The solution flow velocity v(x) = 0 at solid surface (x = 0). A hydrodynamic (or Prandtl) boundary layer is defined as [6]... 

In the process under study here, where S02 oxidation is the limiting half reaction, the electrolyte flow rates are controlled by volumetric pumps to ensure forced convection. Moreover, both the anode and cathode compartments are provided with a plastic mesh turbulence promoter. The flow is therefore assumed fully turbulent and a uniform velocity profile is assumed at the inlet. However, for simplification, these devices are not represented in the simulation domain. Although the turbulence promoter should actually influence the bubble population, no reference has been found on its effects. 

In a battery, and therefore in a unit cell, if the velocity of the electrolyte is very slow (no-stirring), then the convection term is usually neglected in Eq. (33) resulting in the following molar flux equation ... 

Except when natural convection is considered, the analysis of mass transfer can be determined after the flow field is obtained. Here, we thus assume that fluid velocity fields are known. Since Schmidt numbers in aqueous electrolytes are typically on the order of 1000 and can be much larger, the accurate resolution of concentration fields may require much finer meshes than those for the flow fields. It thus may be advantageous to develop methodologies that permit the use of different grids for the concentration fields. 

In Equations (26.78a,b), the subscripts F and N refer to forced and natural convection stirring. In Equations (26.79a-d), L is a characteristic electtode dimension, D is the diffusion coefficient, v is velocity, g is the gravity acceleration constant, p is viscosity, is bulk solution density, and Ap is the difference in density between the bulk solution and the solution at the electrode surface. Once a Sh or expression has been found/generated, it is combined with Equation (26.70) (or the analogous equation for a supporting electrolyte system) to obtain an / relationship. Examples of mass transfer correlations follow. 

In ECM, the effect of concentration overpotential is reduced due to the movement of electrolyte, which is flowing with high velocity between the electrodes and creates turbulent flow. Due to the electrolyte temperature, ion movement is aided by diffusion and thermal convection. However, in the case of micro-ECM, which prefers stagnant electrolyte, the concentration overpotential factor hampers the anodic dissolution in the microscopic domain and may pose a major challenge that has to be overcome. 

The potential gradient that exists in the elextrolyte contributes negligibly to the movement of minor ionic species their transport is almost entirely by convection and diffusion. Therefore, the equations that are used for neutral species, such as for dissolved molecular oxygen, are also valid for minor ionic species. Convection refers to the macroscopic movement of a fluid under the influence of a mechanical force (forced convection) or of gravity force (free convection). At solid surfaces the velocity of fluids is zero and as a consequence only diffusion contributes to the flux at the electrode-electrolyte interface. This allows us to write the following expression for the flux of a minor ionic species B ... 

Figure 4.31 Velocity profiles near an electrode surface under conditions of free convection. The density of the electrolyte at the surface, p, can be either greater (a) or smaller (b) than that of the bulk, Pb-...

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