Rotating hydrodynamic modulation

The aforementioned experiments at rotating electrodes concerned merely steady-state conditions so-called transients123 at these electrodes, e.g., with potential or current steps, as well as with hydrodynamic modulation, i.e., variation of co with time, are, as a consequence of their non-steady-state conditions, less important in analysis and therefore will not be treated here. 

All the electrode kinetic methodology described until now has assumed a steady state (or quasi-steady state in the case of the DME). Many techniques at stationary electrodes involve perturbation of the potential or current in combination with forced convection, this offers new possibilities in the evaluation of a wider range of kinetic parameters. Additionally, we have the possibility of modulating the material flux, the technique of hydrodynamic modulation which has been applied at rotating electrodes. Unfortunately, the mathematical solution of the convective-diffusion equation is considerably more complex and usually has to be performed numerically. 

Hydrodynamic modulation has been performed almost exclusively at the rotating disc electrode. It has found use for analytical purposes at rotating and tubular electrodes owing to the fact that non-convectively dependent electrode processes are unaffected by the modulation [236]. 

HMRDE hydrodynamically modulated rotating disc electrode... 

Miller and Bruckenstein [27,28] introduced the hydrodynamically modulated rotating disc electrode (HMRDE) in 1974. The steady-state current density at a rotating disc electrode is well-defined, given by the Levich equation (equation (10.15)) ... 

Another useful technique features the sinusoidal variation of [called sinusoidal hydrodynamic modulation]. Consider an RDE whose rotation rate is varied sinusoidally about a fixed center speed, o)q, at a frequency cr, so that the instantaneous value of is... 

The hydrodynamically modulated rotating disc electrode The idea of this technique [15-17] is to allow the separation of kinetic and mass transport controlled components of a measured current (either in the region of mixed electron transfer/mass transport control or in situations where there are two competing electrode reactions, one mass transport controlled and the other kinetically controlled, (e.g. solvent decomposition) by using a sinusoidal modulation of the rotation rate and employing a phase sensitive detection method to measure the perturbation of the current. Only the mass transport limited component of the current will respond to the modulation. 

Kanzaki, Y., Tokuda, K., and Bruckenstein, S. (2014) Dissociation rates of weak acids using sinusoidal hydrodynamic modulated rotating disk electrode employing Koutecky-Levich equation. /. Electrochem. Soc., 161 (12), H770-H779. 

HMRRDE hydrodynamically modulated rotating-ring-disk electrode... 

Plasmapheresis typically employs a membrane module of similar configuration as a high-flux hemodialyzer. Alternatively, a rotating membrane separation element is used in which the tendency of the blood cells to deposit on the membrane surface is counteracted with hydrodynamic lift forces created by the rotation. The membrane element and the associated plasmapheresis circuitry are shown in Fig. 49. Worldwide, about 6 million plasmapheresis procedures are performed annually using this system, making this one of the largest biomedical membrane applications after hemodialysis. 

Fig. 9. Polarization curve of an Fe-disc Pt-split-ring electrode with hydrodynamic square wave modulation. In 1 M NaOH with anodic and cathodic scan including capacity of the Fe disc (dashed curve), modulation frequency of rotation co = 0.05 Hz (insert), simultaneous detection of Fe(II) and Fe(III) ions at Pt half rings [12].

Hydrodynamic electrodes permit the control of the diffusion layer thickness by imposing convection. This thickess can also be modulated. Implicit functions link the current, potential and convection modulation. For the rotating disc electrode... 

Jaffrin et al. [57] have made a hydrodynamic comparison between the rotating disk and the VSEP system based on the flux achieved under similar maximum shear rates for baker s yeast microfiltration with an 0.2 p,m ME and skim mUk UF at 50 kDa. They found that the flux variation with time in these two modules was nearly identical when they were operated at the same maximum shear rate, suggesting the dominant effect of shear rate on the filtration performance. 

Both qualitative and quantitative insight can be garnered from transient X -i, i-t and r -t measurements in quiescent or stirred solutions, while measurements of steady-state behavior are best performed under well-defined hydrodynamic conditions. Typically, a rotating disc electrode (RDE), or a related method, is used to specify and/or modulate the hydrodynamic boundary layer thickness, 8. With an RDE the boundary layer is specified by... 

Cojocaru, C., Zakrzewska-Trznadel, G., Miskiewicz, A., Removal of cobalt ions from aqueous solutions by polymer assisted ultrafiltration using experimental design approach. Part 2 Optimization of hydrodynamic conditions for a cross-flow ultrafiltration module with rotating part, J. Hazard. Mater. 169, 610, 2009. 

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