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A numerical method of calculating secondary current distributions in electrochemical cells

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Abstract

A numerical method is proposed based on the analogy between the potential distribution in an electrolytic solution and the temperature distribution in a heat-conducting medium. Thus the equation of non-steady-state heat conduction which contains a hypothetical temperaturev(x, y, t) is solved numerically with appropriate boundary conditions. In the steady state the distribution ofv(x, y, t) corresponds to the distribution of potentialφ s (x,y) which satisfies Laplace's equation. The method is useful not only for conventional electrochemical cells but also for complicated systems such as a bipolar electrode for which boundary conditions provide neither the potential nor the current density at the electrode surface.

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Abbreviations

a :

length of unit cell (see Fig. 1)

b, c, d :

geometric parameters of rectangular cell (see Fig. 2a)

C m :

heat capacity of metal

E :

average electric field in solution or average temperature gradient in medium

I :

total current in unit cell

I F :

I S :

by-pass current in solution in unit cell

i e :

cathodic limiting current density

j :

current density

n :

normal distance from the electrode surface

r, θ:

polar coordinates

r 0 :

S :

surface area of electrode

t :

time

V :

cell voltage

V 0 :

threshold voltage or theoretical decomposition voltage

v(x, y, t) :

hypothetical temperature which, fort=∞, corresponds toφ s (x,y)

v m(t):

hypothetical temperature which, fort=∞, correspouds toφ m

w :

complex number defined in Fig. 2c

x, y :

Cartesian coordinates

z :

complex number defined in Fig. 2a

α:

thermal diffusivity

ζ:

complex number defined in Fig. 2b

η c :

cathodic overpotential

κ:

electric conductivity of solution or thermal conductivity of medium

φ m :

potential of metal

φ s (x,y):

potential of solution

i, j, k:

ordinal numbers of division ofx, y, t

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Katagiri, A., Miyazaki, Y. A numerical method of calculating secondary current distributions in electrochemical cells. J Appl Electrochem 19, 281–286 (1989). https://doi.org/10.1007/BF01062313