Electrohydrodynamic impedance

The concept that the response to a modulation of rotation speed O should be seen as a modulation of the square root of fl was naturally supported by the results of the Levich theory in steady-state conditions. However, due to the fact that 

Equation (15.2) shows that the transfer function corresponding to a modulation of the angular velocity is directly proportional to the transfer function corresponding to a modulation of the square root of the angular velocity, eind the coefficient of proportionality is Therefore, after the pioneer works of Bruckenstein et 

223 direct modulation of the angular velocity was considered. With the increasing development of impedance techniques, aided by development of increasingly sophisticated instrumentation, Deslouis and Tribollet promoted the use of impedance concept for this type of perturbation and introduced the electrohydrodynamic (EHD) impedance.  

The EHD impedance is useful for analysis of electrochemical systems that are either partially or completely limited by mass transport. For a rotating disk electrode, the input quantities are, at least, one electrical quantity, e.g., overall current or electrode potential, and one nonelectrical quantity, i.e., the rotation speed of the rotating disk electrode Q. For EHD impedance, the input quantity is the rotation speed. Under galvanostatic regulation, the output quantity is the electrode potential under potentiostatic regulation, the output quantity is the overall current. To analyze this problem, the mass conservation equation must be considered with the normal velocity Vy near the electrode and the concentration of the involved species c, (0) as state quantities. 

A perturbation of the rotation speed O induces a perturbation of the normal velocity Vy, which, in turn, induces a perturbation of the concentration field of the 

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Modulation of the convective flux, originally proposed by Bruckenstein35, leads to the electrohydrodynamic impedance. It has been used for determining kinetic parameters and diffusion parameters in Newtonian and Ostwaldian fluids, and in corrosion. 

Current Rotation speed Potential Electrohydrodynamic impedance... 

Four state variables may be defined, for example, for the rotating disk described in Qiapter 11. These may include the rotation speed, the temperature, the current, and the potential. At a fixed temperature, three variables remain from which a transfer function may be calculated. As shown in Table 7.1, the generalized transfer functions include impedance, admittance (see Chapter 16), and two types of electrohydrodynamic impedance (see Chapter 15). 

The rotating disk electrode, described in Section 11.6, has the advantage that the fluid flow is well defined emd that the system is compact and simple to use. The rotation of the disk imposes a centrifugal flow that in turn causes a radially uniform flow toward the disk. If the reaction on the disk is mass-transfer controlled, the associated current density is imiform, which greatly simplifies the mathematical description. As discussed in sections 5.6.1 and 8.1.3, the current distribution below the mass-transfer-limited current is not uniform. The distribution of current and potential associated with the disk geometry has been demonstrated to cause a frequency dispersion in impedance results. The rotating disk is therefore ideally suited for experiments in which the disk rotation speed is modulated while im-der the mass-transfer limited condition. Such experiments yield another t)q)e of impedance known as the electrohydrodynamic impedance, discussed in Chapter 15. 

Electrohydrodynamic impedance characterization of calcareous deposits showed mainly partially blocked electrode behavior and allowed the estimation of the average size of characteristic sites of the interface. These results have been confirmed by ex-situ SEM images. 

Wi transfer function associated with the electrohydrodynamic impedance for species i, see equation (15.29)... 

C. Deslouis, B. Tribollet, M. Duprat, and F. Moran, "Transient Mass Transfer at a Coated Rotating Disk Electrode Diffusion and Electrohydrodynamical Impedances," Journal of The Electrochemical Society, 134 (1987) 2496-2501. 

C. R. S. Silva, O. E. Barcia, O. R. Mattos, and C. Deslouis, "Partially Blocked Surface Studied by the Electrohydrodynamic Impedance," Journal of Electro-analytical Chemistry, 365 (1994) 133-138. 

Figure 2.11 Electrohydrodynamic impedance spectroscopy of coumarin inhibited nickel deposition. Note at low perturbation frequency the 180° phase shift (0) between the nickel deposition rate and the inhibitor flux to the surface (source Ref. [230]).

Barton, S.C. and West, A.C. (2001) Electrohydrodynamic impedance in the presence of nonuniform transport properties, journal of the Electrochemical Society, 148 (4), A381-A387. 

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