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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- 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 :
faradaic current in unit cell
- I S :
by-pass current in solution in unit cell
- i e :
cathodic limiting current density
- j :
- n :
normal distance from the electrode surface
- r, θ:
- r 0 :
radius of cylindrical electrode
- S :
surface area of electrode
- t :
- V :
- 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 :
- z :
complex number defined in Fig. 2a
complex number defined in Fig. 2b
- η c :
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
- Boundary Condition
- Physical Chemistry
- Steady State
- Temperature Distribution
- Heat Conduction