Electrode vibrating

Vibration of an electrode is an experimentally simple way of producing hydrodynamic modulation. Whilst the advantage is experimental simplicity, the disadvantage is that the hydrodynamic regime is difficult to describe accurately (see Section 10.3.6.3). 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft .f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

The above studies supported the findings of Lindsay [34], who for a 0.5 mm diameter electrode vibrated with 3 mm amplitude, showed a weak linear dependence of mean current on amplitude and frequency, for sufficiently low values of these parameters. The current eventually became independent of a and / at sufficiently high values. The maximum augmentation of the current due to vibration was ca. 15%. With similar electrode dimensions and vibration amplitudes, Pratt and Johnson [57] 

For sufficiently large electrodes with a small vibration amplitude, aid 1, a solution of the hydrodynamic problem is possible [58, 59]. As well as the periodic flow pattern, a steady secondary flow is induced as a consequence of the interaction of viscous and inertial effects in the boundary layer [13] as shown in Fig. 10.10. It is this flow which causes the enhancement of mass-transfer. The theory developed by Schlichting [13] and Jameson [58] applies when the time of oscillation, w l is small in comparison with the time taken for a species to diffuse across the hydrodynamic boundary layer (thickness SH= (v/a )ln diffusion timescale 8h/D), i.e., when v/D t 1. Re needs to be sufficiently high for the calculation to converge but sufficiently low such that the flow does not become turbulent. Experiment shows that, for large diameter wires (radius, r, — 1 cm), the condition is Re 2000. The solution Sh = 0.746Re1/2 Sc1/3(a/r)1/6, where Sh (the Sherwood number) = kmr/D and km is the mass-transfer coefficient, 

The theory was refined by Dumarque and Humeau [59], who gave the expected mean current response for an electrochemical experiment at the limiting current as  

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Fig. IV-6. Vibrating electrode method for measuring surface potentials. (From Ref 1.)...

Rao et al. (R5) and Raju et al. (R2) also investigated mass transfer at vibrating electrodes for low vibration frequencies (higher frequencies would cause cavitation). Mass transfer follows a laminar-type correlation both for a transverse vibration of a vertical cylinder and for a vertical plate vibrating parallel to the face. In the case of the plate, the Reynolds number is based on width, indicating the predominance of form drag. When vibrations take place perpendicular to the thickness, skin friction predominates and the Reynolds number is then preferably based on the equivalent diameter (total surface area divided by transverse perimeter). 

Complications arise, mainly because of secondary flows in cells of restricted volume. Such steady secondary flows occur also by the action of vibrating electrodes, leading to the mass transfer rates correlated in the previous subsection. 

Vibrating Electrode Atomization (VEP) 300-500 Mild steel, Cr-Ni steel, Cu-Ni alloy, W — -0.2 — Spherical, high-purity particles, Simple Low volume productivity... 

Hackerman and Lee (83) have also used the simple vibrating electrode to examine the effect of O2 and other gases on evaporated metal films of Fe, Ni, Cr, Al, and Pb. Employing a Pt plate as a reference electrode, they found that the work function increased when the transition metals were exposed to O2 later it decreased as the chemisorbed O2 was converted to an oxide layer. With Al and Pb, however, the work function steadily decreased... 

Figure 22.2 Scanning vibrating electrode (SVET) measurements of the ionic currents above the surface of the inhibitor-free SiOx ZrOx hybrid film (a) to (c) and of the SiOx ZrOx hybrid film with inhibitor-loaded Si02 nanocontainers (d) to (f). (a, d) at the beginning (b, e) after 42 hours of corrosion (c, f) after 60 hours. Scale units p,A cm 2, spatial resolution 150 pm. Solution 0.1 M NaCl.

Convection terms commonly crop up with the dropping mercury electrode, rotating disk electrodes and in what has become known as hydrodynamic voltammetry, where the electrolyte is made to flow past an electrode in some reproducible way (e.g. the impinging jet, channel and tubular flows, vibrating electrodes, etc). This is discussed in Chap. 13. 

Perturbation imposed upon stationary solution or electrode vibrating electrodes... 

If the oscillation of motion of fluid with respect to an electrode is imposed upon a stationary system and the perturbation is not small with respect to the steady-state then new effects can appear. For example, the flow induced by the motion can have both an oscillating and a steady component (the latter due to the interaction between viscous and inertial effects in the boundary layer) and the oscillating part may have components which are harmonics of the imposed oscillation. In some cases the stationary component of the induced flow can, indeed, dominate the oscillating component. These effects are particularly seen for vibrating electrodes. 

Fe(CN)6- at a static and a vibrating electrode (oscillating parallel to its short axis) are shown in Fig. 10.7. As can be seen, the effect of the vibration is to induce both an increase in the stationary current and a modulation. Typical current waveforms and their Fourier decomposition are shown in Fig. 10.8. 

The velocity in a sinusoidal oscillation is proportional to the amplitude, a, and the frequency, /, of the oscillation. For vibrating electrodes, the simple interpretation relating the instantaneous current to the instan-... 

A rather simple interpretation of the behaviour of vibrating electrodes can be obtained by considering the response to a square-wave motion, to which a sinusoid rather crudely approximates [33]. Here, it is considered that the concentration boundary layer is periodically renewed by the instantaneous rapid motion and that in the intervals between the square-wave steps the solution is at rest. This is a reasonable approximation for most practical purposes because the hydrodynamic boundary layer relaxation time is short, (Section 10.3.3). In this simple model, the waveform would instantaneously rise to a limit during the motion, decaying as a function of t m during the static phase. This decay rate will obviously be dependent on the size and geometry of the electrode wire, microwire, band or microband. If the delay time between steps were r then the mean current would vary as (l/r,)/o f 1/2df, i.e., as t, i/2 or as fm. 

This discussion emphasises a major difference between a vibrating electrode in a stationary solution and a stationary electrode in a steady flow upon which a modulation is imposed. In the former case the signal increases with increasing modulation frequency whereas in the latter case it decreases. This is a consequence of the nonlinear behaviour of the vibrating electrode in quiescent solution. 

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