Popov K.I., Djokic S.S., Grgur B.N. Fundamental Aspects of Electrometallurgy
Подождите немного. Документ загружается.
112
Chapter 4
electrodes and the side walls of the cell is an indicator of the ability of an
electrolyte to distribute the current density uniformly over the entire electrode.
The experiments were carried out in the cell presented in Fig. 4.6
The dependences of the current density on the cell voltage for different
interelectrode distances and different distances between the edge of the
electrode and side wall, for the system at
a temperature of 20° C are shown in Figs. 4.7 – 4.10.
4. The Current Distribution in Electrochemical Cells
113
114
C
hapter 4
From Figs. 4.7-4.10, the change in the shape of the j-U dependencies as
the inter-electrode distance increases can be seen. In the region of lower
current densities, at the shortest interelectrode distance, the system is under
mixed activation-ohmic control. At higher current densities, although a con-
centration overvolatge appears, the control becomes ohmic because the
magnitude of the overvoltages is negligible in comparison to the ohmic
voltage drop in the electrolyte. As the interelectrode distance increases, the
electrolyte resistance in the cell increases too, giving rise to an increase in
the contribution of ohmic control of the system which in turn causes a larger
spreading out of the current lines between the edges of the electrodes and the
side walls. Therefore, the difference between the j-U curves for different
distances between the side wall and the edge of the electrode becomes larger,
meaning a worse current density distribution. At very large current densities,
approaching the limiting current, the contribution of the concentration
overvoltage to the total cell voltage becomes significant and the system is
under mixed diffusion-ohmic control. Finally, in the region of limiting
current densities, the system is entirely under diffusion control. The pola-
risation curves for different distances between the edge of the electrode and
the side wall are very similar indicating a minimal spreading of the current
lines out of the homogeneous electric field.
4. The Current Distribution in Electrochemical Cells
115
4.1.4.3 Determination of the current density distribution
The effect of the geometry of a cell on the ability of the electrolyte to
distribute the current density uniformly can be illustrated by plotting the
ratios of the current density in cells with different interelectrode distance l
(20, 50, 100 and 150 mm) and an electrode edge – cell side wall distance L =
150 mm, and in cells with different electrode edge-side wall distance L
(12.5, 25, 50, 100, 150 mm) and an interelectrode distance l=150 mm to the
current density in a cell with the same l values and L = 0, as a function of
current density in a cell with L = 0, normalized to the limiting diffusion
current density, as shown in Figs. 4.11 and 4.12. It should be noted that the
increase of the limiting diffusion current density in a cells with L>0 over the
value in a cell with L=0 was not taken into account in the derivation of the
curves in Figs. 4.11-4.13.
Obviously, the larger the current density ratio, the lower is the ability of
the electrolyte to distribute homogeneously the current in the cell.
Hence, increasing the interelectrode distance leads to a worsening of the
current density distribution, as does increasing the electrode edges – cell side
wall distance.
116
Chapter 4
4. The Current Distribution in Electrochemical Cells
117
The effects of the supporting electrolyte and the depositing ion concen-
tration, insoluble anode and temperature on the ability of an electrolyte to
distribute homogeneously the current density are illustrated in Fig. 4.13.
All the above facts can be explained by discussing L', the depth of the
current line penetration between the electrode edges and cell side wall for
L'<L. Previously it was shown that:
and
For one and the same current density in a cell, the electrochemical part of
the cell voltage does not depend on the interelectrode distance, but the ohmic
drop in a homogeneous field is strongly dependant on it, which leads to an
increase of L' with increasing l. This produces decrease of the cell voltage at
a fixed current density, because of the decrease of the overall ohmic
resistance. Hence, at a fixed cell voltage, increasing L' will results in an
increase of the current density relative to a cell with L = 0 and, hence, a
worse current density distribution. The same will happen with increasing L
at l = 150 mm if the condition L' < L is not satisfied.
In the similar way, in the cells with the same l = 150 mm and L = 150
mm, L' will depend on the fractional contribution of the ohmic drop to the
cell voltage. At a fixed l, the value of the product increases faster with
increasing j than the electrochemical part of cell voltage. Hence, increasing
the depositing ion concentration and the stirring rate will cause the ability of
the electrolyte to distribute the current density uniformly worsen, as well as a
decreasing of supporting electrolyte concentration. Increasing value of the
Tafel slope and, probably decreasing exchange current densities will
improve the current distribution.
Increasing the temperature also has a significant effect, regardless of the
simultaneous decrease in and increase in j. This means that the decrease in
is more pronounced than the increase in j. In all cases, the increase in the
degree of diffusion control leads to a better current density distribution on a
macroprofile. On the other hand, in such a situation the current density
distribution worsens on a microprofile (see section 3.2).
118
Chapter 4
4.1.5 Quantitative treatment
Using data from Figs. 4.7-4.10, for L = 0 but with different value of l, the
cell voltage – interelectrode distance dependencies for different current
densities can be obtained. The results of these calculations are shown in Fig.
4.14.
Obviously, the intercepts represent the difference of the anodic and the
cathodic overpotentials for selected values of the current density, and the
resistivity of the electrolyte can be determined from corresponding slopes.
The obtained values are given in Table 4.1.
4. The Current Distribution in Electrochemical Cells
119
4.1.5.1
Calculation of the cell voltage-current density distribution
dependences
The diagrams from Figs. 4.7-4.10, can also be presented in the form shown
in Figs. 4.15-4.18.
120
Chapter 4
4. The Current Distribution in Electrochemical Cells
121
It can be seen from Figs. 4.15-4.18 that the change of current with
increasing L virtually ends at L = l/2 for l < 2A, at L = A for l > 2A and that L'
can be successfully calculated using Eqn. 4.27 and the values from Table
4.1. Calculated L’ is marked on the j-L dependences in Figs. 4.15-4.18 by a
thin vertical line.
Hence, the Eq. 4.27 is valid for and L > L
'
. At larger interelectrode
distances for l > 2A
,
L' remains constant and equal A.
Using equations 4.27 and 4.29, together with the and values from
Table 4.1, dependencies like those from Figs. 4.7-4.10. were calculated and
the results are presented in Figs. 4.19 and 4.20.
It can be seen from Figs. 4.19 and 4.20 that the agreement between the
calculated and the measured values is very good. In this way the method for
the calculation of L' is verified, as is the possibility of the calculation of cell
voltage – current density dependences.
Hence, the current density distribution in cells with plane parallel
electrodes can be calculated without experimental measurements by using
the data from simple polarization measurements, or literature data for kinetic
parameters.