**7. Conclusions**

20 Electrochemical Cells

In Figure 9, the weighted mean values of the charge transfer parameters and their 95 % confidence interval, obtained in the IRDE and the RDE reactors, are compared. It can be seen that the confidence intervals of *kox* perfectly overlap, while a small deviation between the confidence intervals is observed for *kred* and *αox*. However, the deviation between the confidence interval is smaller than 1% for *αox* and smaller than 5% for *kred*. The deviation between the confidence intervals is determined by the difference between the maximum and the minimum values of the respective confidence intervals obtained in the RDE and the IRDE configurations, normalized to the mean value of the respective model parameter obtained in the RDE configuration. The values lie sufficiently close that it is reasonable to assume that the mass transfer characteristics of the RDE are also valid for the IRDE. The estimation of the charge transfer parameters does not depend on the hydrodynamics and mass transport within the electrochemical cell, which in its turn demonstrates that the IRDE is a suitable tool for the mechanistic study of the electrochemical reactions. Moreover, the differences between the values of the rate constants estimated for the RDE and the IRDE reactors narrow the window of values reported in literature (Angell & Dickinson, 1972; Beriet & Pletcher, 1993; Bruce et al.,

5.00E−1 1.00E+00 1.50E+00 2.00E+00 5.00E−1

(b) *kred* (m/s)

RDE IRDE

0.80E−09 1.20E−08 1.60E−08 2.00E−08

(c) *kox* (m/s)

Fig. 9. Comparison of the 95 % confidence intervals of the weighted mean of the charge

**6. Towards the identification and quantification of characteristic parameters of**

In general, an accurate and fully statistical founded solution is the aim of all kinetic and mechanistic studies of electrochemical systems. The proposed analytical fitting model is

1994; Jahn & Vielstich, 1962).

RDE IRDE

4.9E−01 5.0E−01 5.1E−01 5.2E−01 5.3E−01 5.4E−01 5.5E−01

(a) *αox*

RDE IRDE

transfer parameters obtained in the IRDE and the RDE configurations.

**complex electrochemical systems**

The strength of the analytical fitting model to quantify the kinetic parameters of an electrochemical reaction is shown. The coupling of statistically founded parameter estimation techniques with LSV/RDE experiments is an important innovative point of the modeling strategy.

The fitting methodology requires the proposition of an appropriate mechanism for the studied reaction and its mathematical translation into an expression that analytically describes the voltammogram. This expression depends on the mass and charge transfer parameters of the reaction (rate constants, transfer coefficients and diffusion coefficients). Powerful parameter estimation algorithms are used in the data fitting tool to adjust the values of the model parameters in order to obtain a good agreement between experimental and modeled data. The values of the model parameters that give rise to the best match, characterize the system quantitatively. Moreover, this method provides error estimates of the obtained parameter values. However, it is only after a statistical evaluation of the obtained results, that it is decided whether the model is able to describe the experiments.

The application of the analytical modeling for the study of the ferri/ferrocyanide reaction with LSV/RDE experiments demonstrate that the modeling methodology is valid to extract the quantitative mechanism of an electrochemical reaction. In the case of the hexaammineruthenium (III)/(II) reaction, however, the results of the analytical modeling point out the importance of a correct formulation of the reaction mechanism.

The IRDE reactor is built to facilitate the study of electrochemical gas evolution reactions. It offers the advantages of the classical RDE set-up, such as well-defined hydrodynamics and mass transport over a wide range of rotation speeds, while the gas bubbles can rise freely and do not shield the electrode surface. It is demonstrated that the IRDE configuration is valid for kinetic and mechanistic investigations of electrochemical reactions.

It has to be emphasized that for the existing fitting procedure the proposed reaction model describing the reactions taking place must be translated into an analytical equation. It is clear that in the presence of, for example, chemical reactions or gas bubbles, an analytical solution does not exist anymore. Therefore, for further modeling studies a fitting tool that makes use of numerical calculation procedures needs to be developed.

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#### **8. Acknowledgments**

The authors thank the Flemish Institute for support of Scientific-Technological Research in Industry (IWT) and Vrije Universiteit Brussel for the financial support.

#### **9. References**


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**8. Acknowledgments**

**9. References**


**3** 

**Electrochemical Probe for Frictional Force** 

**and Innovative Electrochemical Reactors** 

Electrochemistry constitutes an important discipline that involves many phenomena as mass transfer, migration because of the presence of electric field, and hydrodynamic

In fact, electrochemical methods and electrochemical reactors have to be developed in order

For measurement by electrochemical methods, probes have to be developed. For example, knowledge of the magnitude of the frictional forces between the solids and the gas-liquid mixture is very important for design of bioreactors. The growth of biomass on solid surfaces may be sensitive to shear stress. In fluidized bed bioreactors the suspended carriers are used for microbial immobilization or enzyme encapsulation. The knowledge of shear stress is important because some micro-organisms and cells attached to microcarriers are sensitive to excessive friction. The aim is to develop and verify a fast and inexpensive method for

On the other hand the performance of a multiphase reactor – for example, a bubble columndepends on the knowledge the bubble swarm properties as bubble shape, velocity allowing

To establish direct local information and precise bubble dimensions, various probes were used. The electrical resistivity probe was developed to measure the velocity and diameter of a bubble in a conducting liquid medium. In a non-conducting medium, the optical probe is

To ensure easy measurement of bubble sizes in a non transparent conducting medium and to establish direct local information in a reactor, the present work shows the possible use of

to resolve many problems in different area (mining, waste water treatment etc).

measuring the frictional forces in multiphase reactors beds.

to determine the gas liquid mass transfer and liquid solid mass transfer.

**1. Introduction** 

more appropriate.

electrochemical probe.

especially in reactor with large scale.

**for Electrocoagulation/Electroflotation** 

*Ecole Supérieure de Technologie de Casablanca, Oasis, Casablanca* 

**and Bubble Measurements** 

Abdel Hafid Essadki

*Morocco* 

*Hassan II Aïn Chock University* 

**in Gas-Liquid-Solid Contactors** 

