**9. References**


**19**

*Mexico* 

**Hydrodynamic Analysis**

**of Electrochemical Cells**

(1)

is the rotation speed and *a* is the power such that

*Universidad Autonoma Metropolitana - Azcapotzalco* 

Cesar Augusto Real-Ramirez and Jesus Isidro Gonzalez-Trejo

The systems in which an electrode immersed in a solution causes a chemical reaction have been studied for over a hundred years. It has long been known that the behavior of these systems is determined by two main factors: the rate with which the substance comes into contact with the electrode and the rate of the electrochemical reactions at the electrode. During the first four decades of the twentieth century, many works were devoted to this subject; however, most of them were experimental works. Those works found that the limiting current increases with increasing the rate of stirring (Bircumshaw & Riddiford,

1952). Usually, the results were expressed by means of a power relation of the form:

extremely small and the movement of fluid within it may be neglected.

resulting system of ordinary differential equations.

lim *<sup>a</sup> j* 

The earliest theoretical studies of electrochemical cells with a rotating disk were reported by Nernst (Nernst, 1904; Nernst & Merriam, 1905). In that works, Nernst introduced the concept of diffusion layer. According to Nernst, the thickness of the diffusion layer is

In 1932, Eucken (Eucken, 1932) presented another theoretical study of electrochemical cells. The aim of that work was to provide an exact hydrodynamics theory of the diffusion towards a plane electrode submerged in a solution moving with a relatively high velocity. Following a similar approach to that employed by Eucken, Levich (Levich, 1942) presented a theory describing accurately the hydrodynamics generated by an electrode with the shape of a flat disk of a sufficiently large area, rotating about an axis perpendicular to the plane of the disc with a constant angular velocity. The theory of Levich is restricted to the case of sufficiently small Reynolds numbers, so that the motion of the fluid might be considered as laminar. Levich used the transformation proposed by von Kármán (von Kármán, 1921), which allows writing the Navier-Stokes equations as a system of ordinary differential equations. Levich also used the solution proposed by Cochran (Cochran, 1934) to the

Although the theory developed by Levich was in a good agreement with most experimental results reported previously, at the end of his work Levich pointed out that: "… a precise experimental study of the phenomena of concentration polarization in a wide range of

**1. Introduction** 

0 1 *a* .

where *j*lim is the limiting current,

