Electrodes turbulent tubular

Fig. 35. Turbulent tubular electrode set-up employed by Vielstich and co-workers [115]. The counter, reference, and working electrodes are denoted by C, R, and W. J represents the cooling jacket and E labels the electrical contact to R and W.

Fig. 50. Plot of In ut vs. (E - Ee) for the ferro-ferricyanide redox couple as measured at a turbulent tubular electrode 7pm in length employing a mean solution velocity of 12m s"1. The data are taken from ref. 99.

In the Figure 10 a detector with a so-called "turbulent tubular electrode" is presented[33]. The cell is equipped with a strip Teflon stirrer, whose axis of rotation is parallel to the axis of the... 

Fig, 10, Detector with turbulent tubular electrode. 1 - lead to... 

Mass transport to channel and tubular electrodes under a turbulent flow regime... 

The description of mass transport to channel and tubular electrodes given in Sect. 2 was restricted to laminar conditions. Once Re > 2000, the pattern of flow is no longer smooth and steady fluctuating, irregular (eddying) motions become superimposed on the main stream. Consequently, a complete theoretical description of mass transport, under such a regime, is impossible [149] and, as a result, empirical methods are introduced. In particular, a simplified representation of turbulence is afforded by consider-... 

The fully developed turbulent velocity profile within the tubular electrode cell can satisfactorily be represented by the empirical equation [150, 151]... 

Fig. 46. Comparison of laminar and turbulent (l/7th power) velocity distributions in a tubular electrode cell.

Dreeson and Vielstich [146] solved the problem of turbulent mass transport to a tubular electrode in both the entry and the fully developed regions. The steady-state mass transport equation to be solved may be written as... 

Whilst the kinetic parameters of an electron-transfer reaction can be obtained in an identical fashion under laminar conditions [where u is now given by eqn. (58)] as illustrated by Blaedel [66], it is evident that the dependence of u on the cube root of the solution velocity in the laminar case [eqn. (58)] compared with the -dependence under turbulent conditions [eqn. (166)], implies that faster electron-transfer reactions can be investigated via the latter route. This is best illustrated with a practical example. Using flow rates characterised by Reynolds numbers up to 2 x 105 at a tubular electrode 7 pm in length within a tubular cell of radius 5 mm, Vielstich and co-workers [99] were able to measure a and ke for the ferro-ferricyanide redox couple (at 33.5°C). Their experimental data, in terms of a plot of In ut vs. (E - Ee), is represented in Fig. 50. The slope of both of the linear... 

The characteristics of the fluid velocity depend on the design of the hydrodynamic cell and the flow pattern. The latter is said to be laminar when the solution flows smoothly and constantly in parallel layers such that the predominant velocity is that in the direction of the flow. Laminar flow conditions are desirable since accurate descriptions of the solution hydrodynamics are available. On the other hand, under turbulent flow conditions the solution motion is chaotic and the velocities in the directions perpendicular to that of the flow are significant. The transition between the laminar and turbulent regimes is defined in terms of the dimensionless Re5molds number, Re, that is proportional to the relative movement rate between the electrode and solution, and the electrode size, but inversely proportional to the kinematic viscosity of the solution. Thus, for low Re values the flow pattern is laminar and it transits to turbulent as Re increases. For example, in a tubular channel the laminar regime holds for Re < 2300. 

In the case of pipe flow (tubular flow, also tubular or tube electrode), the electrolyte solution is pumped through a circular tube at a rate (flow rate V"f) low enough to secure laminar flow (for the distinction from turbulent flow, see below). The working electrode is embedded as a ring (annulus) in the wall of the pipe a double ring can be mounted also to enable mechanistic studies like with a ring-disc electrode (see above). 

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