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Calculation of mean current densities in a two rotating disc electrodes system

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Abstract

A theoretical relationship for mass transfer in the laminar flow region of streaming in a rotating electrolyser was derived by the method of similarity of the diffusion layer for electrodes placed sufficiently far from the rotation axis. The obtained relationship was compared with the known equations valid for systems with axial symmetry. The mean current densities were found from the numerical solution of the convective diffusion equation by the finite-element method and were compared with experimental results.

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Abbreviations

a :

constant, exponent

c :

concentration

c 0 :

concentration in the bulk phase

C ij :

matrix coefficient

D :

diffusion coefficient

F :

Faraday constant, 96487 C mol−1

h :

interelectrode distance

j :

current density

\(\bar j\) :

mean current density

J :

mass flux density

L j :

base function

n :

number of transferred electrons in electrode reaction

n r :

outer normal to the boundary

\(\dot n\) :

mass flux

N :

number of nodal points in an element

Q :

volume rate of flow

\(\bar Q\) :

mean volume rate of flow

r :

radial coordinate

r 0 :

inner electrode radius

r l :

outer electrode radius

r v :

radius of inlet orifice

r d :

outer disc radius

v r :

radial velocity component

v z :

normal velocity component

z :

normal coordinate

γ:

thickness of the layer in which the equation of convective diffusion is solved

Γ:

boundary of the integration domain

δ:

thickness of the diffusion layer

δ N :

thickness of the Nernst diffusion layer

v :

kinematic viscosity

ω:

angular velocity

Ω:

surface

Re chan :

channel Reynolds numberQ/hv

Re loc :

local Reynolds number,Q/π⋎(r + r 0)

\(\overline {Re} _{loc} \) :

local Reynolds number at mean electrode radius,Q/πv(r 1 +r 0)

Re rot :

rotation Reynolds number, ωr 2d /v

\(\overline {Re} _{rot} \) :

modified rotation Reynolds number at mean electrode radius, ω(r 1+r 0)2/4v

Ré rot :

modified rotation Reynolds number, ω(r+r 0)2/4v

Sc :

Schmidt number,v/D

Sh Δr :

local Sherwood number,j(r-r 0)/nFDc o

\(\overline {Sh} _{\Delta r} \) :

mean Sherwood number,\(\bar j(r_1 - r_0 )/nFDc_0 \)

Ta :

Taylor number,h(ω/v)1/2

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Authors and Affiliations

  1. Fezko s.p., 386 16, Strakonice, Czechoslovakia

    M. Šimek

  2. Department of Inorganic Technology, Institute of Chemical Technology, 166 28, Prague 6, Czechoslovakia

    I. Roušar

Authors
  1. M. Šimek
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  2. I. Roušar
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Šimek, M., Roušar, I. Calculation of mean current densities in a two rotating disc electrodes system. J Appl Electrochem 21, 111–117 (1991). https://doi.org/10.1007/BF01464290

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  • DOI: https://doi.org/10.1007/BF01464290

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