Sinusoidal hydrodynamic modulations

This technique was proposed by Bruckenstein and co-workers [280, 281] and is useful in that the current due to the modulation of the fluid flow is essentially free of any electrode surface-controlled contributions in most cases. Thus, it can be used as an analytical tool to increase sensitivity [282]. Step changes were originally considered but this was later extended to sinusoidal hydrodynamic modulation (SHM) in the limiting current region and then to the region of mixed convective-diffusion/kinetic control [283—287]. If the modulation frequency is o, then the modulation, which is small, can be described by... 

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... 

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. 

In the periodically modulated version of this experiment (32), the laser heating is carried out sinusoidally at a frequency of 5 to 20 Hz, and the resulting sinusoidally varying current, is detected with a lock-in amplifier, as in hydrodynamic modulation. The variation of A/q with E is called thermal modulation voltammetry (TMV). Near, A/p shows a peak whose magnitude for a nemstian reaction is a function of the ratio of the en-tropic energy of the electrode reaction divided by the activation energy of the mass transport process. While the method is capable of extracting thermodynamic information about a reaction, both the theory and the experimental set-up is sufficiently complex that it has not yet found widespread use. 

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. 

The hydrodynamically modulated RRDE (HMRRDE) allows the measurement of small currents on a large background (Haupt and Strehblow, 1987b). The modulated current response due to a sinusoidal, square wave, or rectangular variation of the rota-... 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

At frequencies above the dielectric relaxation frequency, another diffraction with a threshold makes its appearance (see Fig. 4). This is the chevron regime, which is not hydrodynamic in origin but depends on interaction between the anisotropic dielectric properties of the fluid and the field. It represents a sinusoidal modulation of the... 

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