Hydrodynamic electrodes: coordinates

Fig. 8.1. Coordinates used for common hydrodynamic electrode geometries.

Velocity (v) — is a vector measure of the rate of change of the position of a point with respect to time. For cartesian space the velocity of a point (x) can be written as v = dx/dt and has units of m s-1 using the SI system. In polar coordinates a two-dimensional velocity can be represented by an angular velocity (to) and the distance to the origin (r), v = cor. Velocity is found widely within electrochemical analysis, for example, within hydrodynamic devices such as the rotating disc electrode where the solution velocity may often be approximated analytically [i, ii], permitting, via further analysis, cur-rent/voltage characteristics to be calculated. 

Third, in the system of coordinates with the origin located at the surface of one of the electrodes, the hydrodynamic velocity field is two dimensional. Therefore, prescribing the distributions of hydrodynamic velocity, gas fraction, temperature, and so forth across the I EG, one can integrate the equations of mass, momentum, and energy transfer with respect to the distance between the electrodes. As a result, it is possible to reduce the problem s dimension by a unit. 

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... 

FIGURE 16.1 Bipolar plate without codes or edges for the flow rate of reactants on carhon paste electrodes. The spatial coordinates are indicated as the flux hydrodynamic directions. 

The origin of the coordinates is taken in the middle of the cell. The boundary effects such as the electrode reactions and the closing of the hydrodynamic loops are negligible in this region. 

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