IONIC MASS TRANSFER IN CHANNEL ELECTRODES UNDER LAMINAR FLOW*

-The rate of ionic mass transfer under a Poiseuille profile in channel electrodes involving inert zones has been studied. The electrolysis cell was vertically and horizontally placed, the working electrode8 facing either upwards or downwards. An extension of Levich’s solution for the convective-diffusion equation in a tube comprising an inert zone was applied. The experimental numerical coefficient lies 10% lower than the one theoreticalIy derived.


INTRODUCTION
THE STUDY of ionic mass transfer with electrodes that form the walls of a duct is of particular interest in electrochemistry for two main reasons.Firstly, the design of such a cell is in principle suitable for hydrodynamic voltammetry, and secondly, it can be successfully applied to continuous electrochemical processes.For these reasons theoretical as well as experimental papers have been published concerning ionic mass transfer in electrodes forming ducts.l-' The rate of mass transfer in a channel-type cell is modified both by the entrance length, involving the region where the hydrodynamic profile is being developed, and by the existence of portions of the surface that are inactive from the standpoint of the occurring reaction.Consequently, their influence is reflected in the rate equations derived by assuming certain momentum and mass transfer mechanisms in the zones adjacent to the reacting surface.
The mass-transfer rate equations for the plane plate, annular and channel electrodes under the laminar flow regime, with or without an inert zone, have been solved by Levich.8Equivalent equations for the plane plate were also obtained by Wra@Cn,Q following the method of von Kk-man.l"Lately, Matsudall obtained mass-transfer rate equations for electrodes forming ducts and involving a Poiseuille profile, although inert regions were not considered in the rate equations.
The results obtained with a rectangular duct electrolysis cell comprising an inert zone are reported in the present article.covering the whole range of velocities empIoyed in the experiments.The solution flowed through a screen with holes of U-3 cm diameter to eliminate any turbulence in the electrochemical cell entrance, and was continuously saturated with purified nitrogen.
EIectroIytic nickel was employed for the electrodes.Three sets of seven working electrodes of rectangular shape 1 x O-1 5 cm2 were placed at the centre of one of the large cell walls.The location of each electrode in the rectangular duct is deduced from Fig. 1 and 3.The counter-electrode was also of nickel and located just in front of a working eiectrode.Its area was 75 cm2.The location of these eIectrodes assured a good current distribution.The nickel electrodes were activated prior to the experiments, by making them cathodes in a O-5 N sodium hydroxide solution at a cd of 20 mA/cm2 I h with a nickel anode.
The electrochemical reaction occurring at the working electrodes is represented by Fe(CN),S-+ e ZZ Fe(CN),&.
The diffusion coefficient of the ions involved in the reaction, and the density and viscosity of solutions required in the calculations, are reported in the literature.lsConventional electrolysis and measurement circuitries, as reported in earlier work, were used.15*16The limiting current was read at a constant potential and different flow-rates.Temperatures both at the cell inlet and outlet were simultaneously recorded and a sample of the solution was separated to evaluate its concentration.Experiments with the electroIyte at rest were also made to establish the influence of natural convection.

RESULTS
The limiting cds obtained at different flow rates were processed with the aid of a computer in the usual way.The average mass transfer rate constant, k, was obtained with where 1~ is the limiting current, A the electrode area, C, the bulk concentration of the reacting ion, and z and F have the usual meanings.
A log/log plot of the average rate constant, f;, against the average fluid velocity P, yields a set of straight lines as shown in Figs.4-6, each line corresponding to a particular electrode.From those plots it is concluded that & is proportional to the 113th power of the average velocity for all the electrodes in the different positions.
The usual way of expressing dimensionless correlations for mass transfer in ducts is by means of Sherwood (Sh), Schmidt (SC) and Reynolds (Re) numbers, the latter given in terms of the equivaIent diameter.The dimensionless numbers are defined as *.
'.A theoretical rate equation for ionic mass transfer on electrodes located at a tube wall was derived by Levichs for a laminar flow when no inert zone existed, assuming that the flow is upward and that the hydrodynamic boundary layer is smaller than the diffusion boundary layer.In the region where the hydrodynamic profile is fully developed the following rate equation for the total flux, .J,,=, is obtained, where V,, is the maximum velocity in the x-direction and R is the radius of the tube.When there is an inert zone of length h, the ionic mass transfer rate towards the surface increases, due to the tangential transport of the reacting species, Then, the rate equation for the average flux, j,,, becomes : x.nax =;; 0.67C& (&)""(-g3.Although the effect is small it shows a systematic trend beyond the error of the experimental measurements.
It is interesting to emphasize that the same behaviour has been reported by Tobias and Hickman,s who observed a sim.iIar effect with copper electrodes facing upwards in a channel cell.This aspect of the problem deserves further study.

FIG. 9 . 1 F
FIG. 9. Dependence of the rate constant, k, on the position of the electrode for different fluid velocities.Cell horizonbUy placed with electrodes facing downwards.Equivalent diameter l-5 cm.

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A general theoretical treatment of the ionic mass transfer in ducts under a Poiseuille profile without contribution of inert zone was made by Matsuda.llThe generalAs far as the fluctuations of the rate constants with distance along the flow direction are concerned, no quantitative interpretation can be given, as this effect is not considered in the rate equations.