Electrochemical wave propagation

In this model, e is the ratio of the time scales associated with the reactive dynamics of the two variables u and v, while D and are their diffusion coefficients. The parameters a and p characterize the local reactive dynamics. The FHN model was originally constructed as a simple scheme for describing electrochemical wave propagation in excitable nerve or cardiac tissue. The variable u corresponds to the potential while v represents ion currents in the nerve tissue. It has since been used extensively as a generic model that describes so-called excitable behavior of chemically reacting systems. In fact, as we shall show later in this chapter, it is possible to write a chemical reaction scheme whose rate law is of FUN form. ... 

When large areas of the membrane are depolarized in this manner, the electrochemical disturbance propagates in wave-like form down the membrane, generating a nerve impulse. Myelin sheets, formed by Schwann cells, wrap around nerve fibers and provide an electrical insulator that surrounds most of the nerve and greatly speeds up the propagation of the wave (signal) by allowing ions to flow in and out of the membrane... 

In the literature we can now find several papers which establish a widely accepted scenario of the benefits and effects of an ultrasound field in an electrochemical process [13-15]. Most of this work has been focused on low frequency and high power ultrasound fields. Its propagation in a fluid such as water is quite complex, where the acoustic streaming and especially the cavitation are the two most important phenomena. In addition, other effects derived from the cavitation such as microjetting and shock waves have been related with other benefits reported for this coupling. For example, shock waves induced in the liquid cause not only an enhanced convective movement of material but also a possible surface damage. Micro jets of liquid, with speeds of up to 100 ms-1, result from the asymmetric collapse of cavitation bubbles at the solid surface [16] and contribute to the enhancement of the mass transport of material to the solid surface of the electrode. Therefore, depassivation [17], reaction mechanism modification [18], surface activation [19], adsorption phenomena decrease [20] and the mass transport enhancement [21] are effects derived from the presence of an ultrasound field on electrode processes. We have only listed the main phenomena referring to the reader to the specific reviews [22, 23] and reference therein. 

A combination of different techniques can frequently improve yields of final compounds or synthetic conditions, for example a reunion of direct electrochemical synthesis and simultaneous ultrasonic treatment of the reaction system [715]. Reunion of microwave and ultrasonic treatment was an aim to construct an original microwave-ultrasound reactor suitable for organic synthesis (pyrolysis and esterification) (Fig. 3.7) [716], The US system is a cup horn type the emission of ultrasound waves occurs at the bottom of the reactor. The US probe is not in direct contact with the reactive mixture. It is placed a distance from the electromagnetic field in order to avoid interactions and short circuits. The propagation of the US waves into the reactor occurs by means of decalin introduced into the double jacket. This liquid was chosen by the authors of Ref. 716 because of its low viscosity that induces good propagation of ultrasonic waves and inertia towards microwaves. 

Electrochemical cell The limiting current in an electrochemical cell was found to increase substantially when one electrode was a platinum-coated FPW device driven so as to produce either propagating or standing flexural waves [76]. The fractional increase in cell current was proportional to the square of the drive voltage, and hence to the square of the wave amplitude (Figure 3.53, page 138). 

In the electrochemical cell, circulation of the entire fluid (propagating wave) or local circulation (standing wave) stirs the electrolyte near the... 

Apart from the stationary potential patterns just discussed, propagating potential waves under the influence of global (nonlocal) coupling via migration of ions in the electric field are much more readily realized in electrochemical systems [5]. These effects may be most conveniently studied with quasi-one-dimensional systems, that is, ring electrodes where the potential can be recorded at various locations. One example is concerned with the potentiostatic electrochemical oxidation of formic acid on a platinum ring electrode under bistable conditions, as... 

The modified electrodes are electrochemically active and present a pair of sine-shaped waves at pc = 0.92 and fpa = 0.99 V (20 mV s ), whose intensities are directly proportional to the scan rate, as expected for redox species immobilized on the electrode surface . A linear Cottrell plot has been obtained for the chronoamperometry data but with a negative deviation at longer times, where the charge propagation is not diffusion controlled. The estimated charge-... 

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