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Dispersion in electrochemical cells with radial flow between parallel electrodes. I. A dispersive plug flow mathematical model

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Abstract

The conventional relations for dispersion in tubes and ducts are inappropriate for radial flows such as are found in the disc-stack and pump cells. A first-order mathematical model is therefore developed for radial flow between infinite parallel planes. The shapes of the predicted responses to pulses of injected material are shown to be in qualitative agreement with experimental curves, however the form of the mathematical expression is inappropriate for routine data analysis. Nevertheless simple relationships are derived which enable the dispersion coefficient and mean residence time of an electrogenerated species to be determined from the first and second moments of the response and a knowledge of the geometry of the system. In Part II experimental data are analysed in detail with the aid of the model; however, it is clear that an improved model is of a three-phase flow, a slow phase creeping along either plane with a faster ‘core’ flow in between.

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Abbreviations

c :

concentration (mol cm−3)

¯D :

dispersion coefficient (cm2 s−1)

h :

interelectrode gap (cm)

M 1 :

normalized first moment of the response defined by Equation 28

M 2 :

normalized second moment of the response, defined by Equation 29

Q=V/h :

volumetric flow rate per unit height of gap (cm2 s−1)

q= (s/¯D) 1/2 :

(cm)

r :

radius (cm)

s :

Laplace transform parameter (s−1)

t :

time (s)

V :

volumetric flow rate per unit height

x= (r−r i )/2(¯Dt)1/2 :

dimensionless distance

v :

Q/(4π¯D)

λ :

r(s/¯D)1/2

τ = M 1 :

mean residence time of marked material(s)

i:

inner

o:

outer

References

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Authors and Affiliations

  1. Chemistry Department, The University, Southampton, UK

    M. Fleischmann & R. E. W. Jansson

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  1. M. Fleischmann
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  2. R. E. W. Jansson
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Fleischmann, M., Jansson, R.E.W. Dispersion in electrochemical cells with radial flow between parallel electrodes. I. A dispersive plug flow mathematical model. J Appl Electrochem 9, 427–435 (1979). https://doi.org/10.1007/BF00617553

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  • DOI: https://doi.org/10.1007/BF00617553

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