In the cathodic protection in high-resistance media as in fresh water, anode configuration offers a very subtle problem and affects the performance, since the potential and current distribution in the electrolyte is predominated by the Ohmic drop rather than the electrochemical polarization at interfaces. In this case Laplace equation can be applied for the solution of the potential and current distribution. A complex function
z=
rc(α
ne
nw+1/e
nw+α
n)
1/nis proposed as a fundamental equation that represents the potential and current distribution in the system comprising of a cylindrical cathode and multiple line-anodes. This cofiguration gives a good simulation of cathodically protected fresh-water tanks. In the above equation,
r and α denote cathode radius and anode position, respectively. Complex variables
z and
w denote geometrical co-ordinates and complex potential, respectively. From this conformal transformation function, several equations for the calculation of electrical resistance and current density were derived. Using these equations and figures, optimal number and location of anodes can be estimated, when maximum electrolysis voltage and allowable maximum/minimum ratio of current density are assumed in the system designing, A practical application is also given for the design of the optimal anode configuration in the protection of a fresh-water tank.
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