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Optimization of the effectiveness of a three-dimensional electrode with respect to its ohmic variables
OPTIMIZATION
OF THE EFFECTIVENESS
OF
A THREE-DIMENSIONAL ELECTRODE WITH RESPECT TO ITS OHMIC VARIABLES YG’AL
VOLKMAN
(Received 26 October 1978)
Abstract - The effectiveness of three-diieusional electrodes is shown to he a function of its equivalent conductivity - the resultant of the elreetive conductivities of the solid matrix and the electrolytic solution. Criteria for optimizing the etfectiveness by maximizing the equivalent conductivity are evaluated. High porosity, good matrix conductivity and high internal surface area are the basic requirements for design of an etT&ive three-dimensional electrode.
2. THE EQUIVALENTCONDUCDVITY
NOTATION 4 i
i ” Y E ; K-l 0
The inguencc of the effective conductivities of both the electrode matrix and the electrolyte on the performance of thmudimensional electrodes can be evaluated from the general equations that control current and potential distribution[4] :
specific internal surface area (crn’cm-‘) superficial current density (A cm-*) interfacial electrochemical reaction rate cd (A cm-‘) tortuosity factor solution to matrix conductivities ratio porosity of the electrode effective conductivity of the solution (&I-’ cm-‘) potential (V) equivalent conductivity of the electrode (Q-‘cm-‘) effective conductivity of the matrix (Q-l cm-‘)
(2)
Vi, + Vi, = 0
(3)
of change : Vi, = aj,
conservation
1. INTRODUCTION Three-dimensional electrodes were devised to increase the space-time yield of electrochemical reactors[l]. However, the achievement of this purpose is limited
due to excessive ohmic voltage losses within the electrode. Because of these ohmic losses, the local electrode-electrolyte potential difference, which is the driving force for the electrochemical reaction, varies along the electrode, resulting in non-uniform reaction rate distribution[2]. Consequently, the utilization of the full internal surface area of the electrode is restricted. Sabacky and Evans[3] showed that the effectiveness of a threedimensional electrode was very sensitive to the conductance of the electrode matrix. They concluded that either very high or very low matrix conductivity (relative to the conductivity of the solution) created a non-uniform reaction rate distribution, thus reducing the effectiveness of the electrode. From a practical point of view, it is desirable to utilize most of the internal surface area of the electrode. Therefore, the ohmic influence on the etfectiveness of the electrode should be minimized. Hereafter, a simple conductivity-porosity corre lation will be used to predict conditions for minimum ohmic effects. The results may serve as guidelines for optimal design of three-dimensional electrodes. 2411 I--*
(1)
i2 = - KVr#rz
:
electroneutrality
Superscriprs and subscripts 0 bulk values 1 matrix 2 solution * values at optimum conditions.
E.A.
ir = -oV&
Ohm’s law:
(4)
where i is the superficial cd, I$ is the local potential, Q and K are, respectively, the effective conductivities of the matrix and of the electrolyte, (I is the specific internal surface area of the electrode and j is the interfacial reaction rate cd. Superscripts 1 and 2 refer to the matrix phase and the solution phase respectively. The reaction-rate cd is controlled by the matrix-solution potential difference (dr-r$J. It is calculated by the appropriate polarization equation which is not discussed here. From (1) and (2) we obtain: V(&-&)= and by differentiation
:
Vr(& -&) The substitution
-;+;,
= - :Vi,
+ iPi,.
(5)
of (3) into (5) yields:
V’(4, -r#+) =
A+ k 6
Vi,,
(6)
aj.
(7)
)
and if (4) is used:
1145
V’(4, -&)
=
d + + (
As j is a function of (dr -&),
)
(7) is the differential
1146
YG'ALVOLKMAN
equation that governs the distribution of polarization (and hence the reaction rate) along the electrode. It is clearly seen that the combined effect of both matrix and solution effective eonductivities can be described by an equivalent conductivity, K,,, which is defined according to the following relationship: 1
11
K=K+IT. 0s The minimization of the Ohmic effect on the reaction rate distribution is achieved by maximizing the equivalent conductivity of the electrode. The effective conductivities of the matrix and the solution within a three-dimensional electrode are related to their bulk conductivities by the porosity of the electrode[4]. TiedemanandNewman[S] used thefollowingequations for expressing these functional relationships: K = K,,E”,
(9)
d = uo(l-EY,
(10)
where K, and no are the bulk conductivities and Eis the porosity. The n is a factor which accounts for tortuosity effects. It varies between I and 3, the commonly used value being 1.5[4]. It was shown experimentally[6] that n tends to I when the porosity is high (a > 0.9). For straight pores (eg electrode constructed of tubes, ribs or blades in parallel to the current direction), a is always equal to 1. The substitution of these functions in the definition of the equivalent conductivity (8) yields: 1 1 -_=--+ K,c” K=,
1
0.2
K
$!
= 8”.
Calculated values of K, are shown graphically in Fig. 1 for a = 1 and n = 1.5. It is concluded that there are optimal conditions at which K, is maximized. 3. EVALUATIONOFOPTlMALCONDITIONS To find out the optimal conditions at which Koq is maximized, (12) is differentiated with respect to a, and the derivative is equated to zero. The optimal porosity, r*, is thus: I F.*=-----. 1 + y;‘“+’ The optimal effective conductivities. tained from (9) and (IO) are:
CT*and K*, ob-
E=[&J
(17)
(11) Therefore
Yo
:
(1.3
K,=F+(l--E)D*
0
Thus (12) relates the equivalent conductivity to the porosity and to the bulk conductivities of the matrix and of the electrolyte phasea of the electrode. With the common assumption that in practice y0 tends to 0 (infinite matrix conductivity), (12) is reduced simply to:
1 ~(1 -s)“’
or:
Ko
where
04
0.6
0.8
(18)
0.2
04
06
08
c- POroSlty
fig. 1. Equivalent conductivity as B function of porosity &. bulk conductivities. Line no. l--y, = 1.0; z-~,, = 10-l; 3-y, = 10-2;4--y, = lo-‘; 5--y, = 0.0. Broken line-maximal equivalent conductivity.
IO
1147
IO
;
u
02
I
10-S
10-q
r, -Bulk
IO-'
100
IO' IO-++ 10-a
conductivities ratm
Fig. 2. Optimal porosity as a function of the bulk conductivitiesratio. By combining(S), (16) and (17) the optimal equivalent conductivity, K&, is :
E&= [I
f&
+
(19) ye,:+l,l,“+t.
Calculated results of the optimal conditions are repre sented in Figs 2-5. 4. DISCUSSION
AND CONCLUSIONS
The mathematical model of electrode conductivity, which was evaluated above, is based on a rough approximation to the functional relationship between effective conductivities and porosity. However, it enables one to draw important conclusions concerning the design of three-dimensional electrodes. The mathematical formulations made above show that the optimal conditions are determined by the bulk conductivities and by the structure ofthe electrode (via E and n), By increasing the porosity, more free space for the
08
10-S r, -Bulk
10-z
10-l
conductivities
100
IO’
ratio
Fig. 4. Optimal effective conductivities ratio us bulk conductiviti= ratio. electrical current flow in the solution also increases.
On the other hand, the volumetric fraction and thus the effective conductivity of the electrode matrix decreases. This argument explains the existence of a peak value of the equivalent conductivity (which is the resultant of these two conductivities) at a certain optimal porosity. This optimal porosity increases as y,, decreases because the higher porosity must compensate for the lower bulk conductivity of the solution (Fig. 2). In order to avoid excessive and unnecessary voltage losses, theelectrode matrix should have a high effective conductivity. This can be done primarily by using a highly conductive material for the matrix. In that case, the conductivity of the electrolytic solution (which is usually much lower), dominates the value of the equivalent conductivity and controls the effectiveness of the electrode. Therefore, it would be a good practice to design the internal packing of the electrode with a
-
:
c ; z 2
06-
‘CI
E 04-
0
E-
---
zi 0
n.1.5
02-
10-4
co-3
10-z
lo-’
100
IO'
10-o
10-S
10-z
10-1
100
y, --Bulk conductivities ratio p-o-Bulk conductlvities ratio
Fig. 3. Optimal coaductivities of the matria and the electrolytic solutioIL
Fig. 5. Optimal equivalent conductivity.
IO'
YG’AL
1148
,‘OLKMAN
maximum porosity, subject to mechanical and constructional constraints. Obviously, sources of electrical resistance o&r than the material of the matrix itself should be avoided. Consequently, good contacts inside the matrix must be assured. The tortuosity has an adverse effect on the equivalent conductivity. It is concluded from Figs 1 and 5, that the hiiest values of K& are obtained when n = 1. This implies either that the electrode must be highly porosive (6 > 0.9) or made up of straight pores. The optimal constructional features of a threedimensional electrode should, therefore, meet the following requirements: (a) high effective conductivity; (b) high porosity; (c) high internal surface area : (d) adequate mechanical strength (this requirement is not treated in this work). Most of the published experimental work on three dimensional electrodes was carried out with restrained beds of particulate packing. Electrodes of this type are characterized by high internal surface area and high conductivity (neglecting the resistance of contacts between the particles). However, their porosity is low, which results in low conductivity of the solution. The reticulate electrode, recently introduced by Tentorio and Casolo-Ginelly[‘l], has high conductivity and high porosity. On the other hand, its internal surface area is somewhat lower than that of the packed-bed electrodes. Fluid&d-bed electrodes may be operated with high porosities but in that case their conductivity is low[3]. When the expansion of the bed is low, the porosity is low too, and this electrode resembles ohmically the restrained bed electrode. Some published data on the different types of threedimensional electrodes are shown in Table 1. No type of packing meets all the requirements for optimum design. However, it seems from these data that the reticular electrode has the proper combination of constructional features to approach the requirements
for optimal effectiveness. Sulzer’s tower packings BX and CY[ll] and Hydronyl’s knitmesh packing[l2], which are included in Table 1, also have similar characteristics. No work has yet been published concerning the use of this kind of packing as electrochemical reactors. 5. SUMMARY Criteria for optimizing the effectiveness of threedimensional electrodes by maximizing its equivalent conductivity have heen evaluated. It was concluded that the porosity is one of the most important factors that control the conductivities of the electrode matrix and the electrolytic solution. High porosity is one of the basic requirements for constructional design of an effective three-dimensional electrode. REFERENCES I.
2. 3. 4. 5. 6.
7. 8.
P. Galione, Achievements and tasks of electroehemieal en&eerin8, Electroehim. Acts 25 913 (1977). 1. S. Newman and C. W. Tobias, Theoretical analysis of current distibutioa in porous electrodes, J. elecrrockm. Sot. 109, 1183 (1962). B. J. Sabaeky and J. W. Evans, The electrical conductivity of fluid&d bed electrodes - its signiieance and some experimental measurements, Metal/. Trans. 8& 5 (1977). J. Newmanand W. Tiedeman, Porous-electrode theory with battery applications, A.I.Ch.E.JI 21, 25 (1975). W. Tiedeman and J. Newman, Maximum effective capacity in an ohmically limited porous electrode, J. electrochem sot. 122, 1482 (1975). R. E. Meredith and C. W. Tobias, Conduction in Heterogeneous Systems, in : Advancesin Electrochemistry and Ekctr&emical Engineering Vol. 2, p. 15 (Edited by C. W. Tobias) (1962). A. Tmtorio and U. Casolo-Ginelly, Characterization of reticulate., tbreedimensional electrodes, J. uppI. Elecno&m. t$ 195 (1978). D. N. Bannion and J. Newman, Electroehemieal removal of copper ions from very dilute solutions, J. uppl. Elechwchem. 2, 113 (1972).
Table 1. Some data on three-dimensional electrodes Type of electrode Packed-bed Packed-bed Packed-bed
Reticular
Fluid&!&bed sulzer tower packing
Hydronyl wire mesh tower packing
Type of packing Carbon granules plus powder (O.l-O.OOlcm) Graphite particles (-100+150 mesh) Stacked copper screens 100 mesh 150 mesh 200 mesh Copper plated polyurethane foam 10 pores in-’ 20 pores in - ’ Copper shots Corrugated strip of wire mesh (various metals) BX CY Corrugated wire mesh (various metals)
Multifill
E
a/cm-’
Reference
0.30
25
C81
0.50
* 12.5
[91
0.61 0.69 0.67
143.0 188.3 245.0
[I] [lOI
0.975 0.968 0.4-0.5
6.9 9.0
[:3
Not specified Not specified
5.0 7.0
0.95
c41
-20
[:r]
[I21
Optimization of the ektiveness 9. G. B. Adams, R. P. Hollandworth and D. N. Bennion, Electrochemical oxidation of ferrous iron in very dilute solutions, .I. electrochem. Sot. 122 1043 (1975). 10. R. Alkiie and P. K. Ng, Studies on flow-by porous electrodes having perpendicular directions ofcurrent and electrolyte flow, J. ekcrrochent. Sot. 124, 1220 (1977).
of a three-dimensional electrode
1149
11. M. Huber and W. M&r, Sulzer columns for Vacuum rectitication and mass transfer, Sulw Tech. Rev. (l/1975), 3 (1975). 12. Tower Packings, Hydronyl Ltd. (London), catalog TP-33.
OF THE EFFECTIVENESS
OF
A THREE-DIMENSIONAL ELECTRODE WITH RESPECT TO ITS OHMIC VARIABLES YG’AL
VOLKMAN
(Received 26 October 1978)
Abstract - The effectiveness of three-diieusional electrodes is shown to he a function of its equivalent conductivity - the resultant of the elreetive conductivities of the solid matrix and the electrolytic solution. Criteria for optimizing the etfectiveness by maximizing the equivalent conductivity are evaluated. High porosity, good matrix conductivity and high internal surface area are the basic requirements for design of an etT&ive three-dimensional electrode.
2. THE EQUIVALENTCONDUCDVITY
NOTATION 4 i
i ” Y E ; K-l 0
The inguencc of the effective conductivities of both the electrode matrix and the electrolyte on the performance of thmudimensional electrodes can be evaluated from the general equations that control current and potential distribution[4] :
specific internal surface area (crn’cm-‘) superficial current density (A cm-*) interfacial electrochemical reaction rate cd (A cm-‘) tortuosity factor solution to matrix conductivities ratio porosity of the electrode effective conductivity of the solution (&I-’ cm-‘) potential (V) equivalent conductivity of the electrode (Q-‘cm-‘) effective conductivity of the matrix (Q-l cm-‘)
(2)
Vi, + Vi, = 0
(3)
of change : Vi, = aj,
conservation
1. INTRODUCTION Three-dimensional electrodes were devised to increase the space-time yield of electrochemical reactors[l]. However, the achievement of this purpose is limited
due to excessive ohmic voltage losses within the electrode. Because of these ohmic losses, the local electrode-electrolyte potential difference, which is the driving force for the electrochemical reaction, varies along the electrode, resulting in non-uniform reaction rate distribution[2]. Consequently, the utilization of the full internal surface area of the electrode is restricted. Sabacky and Evans[3] showed that the effectiveness of a threedimensional electrode was very sensitive to the conductance of the electrode matrix. They concluded that either very high or very low matrix conductivity (relative to the conductivity of the solution) created a non-uniform reaction rate distribution, thus reducing the effectiveness of the electrode. From a practical point of view, it is desirable to utilize most of the internal surface area of the electrode. Therefore, the ohmic influence on the etfectiveness of the electrode should be minimized. Hereafter, a simple conductivity-porosity corre lation will be used to predict conditions for minimum ohmic effects. The results may serve as guidelines for optimal design of three-dimensional electrodes. 2411 I--*
(1)
i2 = - KVr#rz
:
electroneutrality
Superscriprs and subscripts 0 bulk values 1 matrix 2 solution * values at optimum conditions.
E.A.
ir = -oV&
Ohm’s law:
(4)
where i is the superficial cd, I$ is the local potential, Q and K are, respectively, the effective conductivities of the matrix and of the electrolyte, (I is the specific internal surface area of the electrode and j is the interfacial reaction rate cd. Superscripts 1 and 2 refer to the matrix phase and the solution phase respectively. The reaction-rate cd is controlled by the matrix-solution potential difference (dr-r$J. It is calculated by the appropriate polarization equation which is not discussed here. From (1) and (2) we obtain: V(&-&)= and by differentiation
:
Vr(& -&) The substitution
-;+;,
= - :Vi,
+ iPi,.
(5)
of (3) into (5) yields:
V’(4, -r#+) =
A+ k 6
Vi,,
(6)
aj.
(7)
)
and if (4) is used:
1145
V’(4, -&)
=
d + + (
As j is a function of (dr -&),
)
(7) is the differential
1146
YG'ALVOLKMAN
equation that governs the distribution of polarization (and hence the reaction rate) along the electrode. It is clearly seen that the combined effect of both matrix and solution effective eonductivities can be described by an equivalent conductivity, K,,, which is defined according to the following relationship: 1
11
K=K+IT. 0s The minimization of the Ohmic effect on the reaction rate distribution is achieved by maximizing the equivalent conductivity of the electrode. The effective conductivities of the matrix and the solution within a three-dimensional electrode are related to their bulk conductivities by the porosity of the electrode[4]. TiedemanandNewman[S] used thefollowingequations for expressing these functional relationships: K = K,,E”,
(9)
d = uo(l-EY,
(10)
where K, and no are the bulk conductivities and Eis the porosity. The n is a factor which accounts for tortuosity effects. It varies between I and 3, the commonly used value being 1.5[4]. It was shown experimentally[6] that n tends to I when the porosity is high (a > 0.9). For straight pores (eg electrode constructed of tubes, ribs or blades in parallel to the current direction), a is always equal to 1. The substitution of these functions in the definition of the equivalent conductivity (8) yields: 1 1 -_=--+ K,c” K=,
1
0.2
K
$!
= 8”.
Calculated values of K, are shown graphically in Fig. 1 for a = 1 and n = 1.5. It is concluded that there are optimal conditions at which K, is maximized. 3. EVALUATIONOFOPTlMALCONDITIONS To find out the optimal conditions at which Koq is maximized, (12) is differentiated with respect to a, and the derivative is equated to zero. The optimal porosity, r*, is thus: I F.*=-----. 1 + y;‘“+’ The optimal effective conductivities. tained from (9) and (IO) are:
CT*and K*, ob-
E=[&J
(17)
(11) Therefore
Yo
:
(1.3
K,=F+(l--E)D*
0
Thus (12) relates the equivalent conductivity to the porosity and to the bulk conductivities of the matrix and of the electrolyte phasea of the electrode. With the common assumption that in practice y0 tends to 0 (infinite matrix conductivity), (12) is reduced simply to:
1 ~(1 -s)“’
or:
Ko
where
04
0.6
0.8
(18)
0.2
04
06
08
c- POroSlty
fig. 1. Equivalent conductivity as B function of porosity &. bulk conductivities. Line no. l--y, = 1.0; z-~,, = 10-l; 3-y, = 10-2;4--y, = lo-‘; 5--y, = 0.0. Broken line-maximal equivalent conductivity.
IO
1147
IO
;
u
02
I
10-S
10-q
r, -Bulk
IO-'
100
IO' IO-++ 10-a
conductivities ratm
Fig. 2. Optimal porosity as a function of the bulk conductivitiesratio. By combining(S), (16) and (17) the optimal equivalent conductivity, K&, is :
E&= [I
f&
+
(19) ye,:+l,l,“+t.
Calculated results of the optimal conditions are repre sented in Figs 2-5. 4. DISCUSSION
AND CONCLUSIONS
The mathematical model of electrode conductivity, which was evaluated above, is based on a rough approximation to the functional relationship between effective conductivities and porosity. However, it enables one to draw important conclusions concerning the design of three-dimensional electrodes. The mathematical formulations made above show that the optimal conditions are determined by the bulk conductivities and by the structure ofthe electrode (via E and n), By increasing the porosity, more free space for the
08
10-S r, -Bulk
10-z
10-l
conductivities
100
IO’
ratio
Fig. 4. Optimal effective conductivities ratio us bulk conductiviti= ratio. electrical current flow in the solution also increases.
On the other hand, the volumetric fraction and thus the effective conductivity of the electrode matrix decreases. This argument explains the existence of a peak value of the equivalent conductivity (which is the resultant of these two conductivities) at a certain optimal porosity. This optimal porosity increases as y,, decreases because the higher porosity must compensate for the lower bulk conductivity of the solution (Fig. 2). In order to avoid excessive and unnecessary voltage losses, theelectrode matrix should have a high effective conductivity. This can be done primarily by using a highly conductive material for the matrix. In that case, the conductivity of the electrolytic solution (which is usually much lower), dominates the value of the equivalent conductivity and controls the effectiveness of the electrode. Therefore, it would be a good practice to design the internal packing of the electrode with a
-
:
c ; z 2
06-
‘CI
E 04-
0
E-
---
zi 0
n.1.5
02-
10-4
co-3
10-z
lo-’
100
IO'
10-o
10-S
10-z
10-1
100
y, --Bulk conductivities ratio p-o-Bulk conductlvities ratio
Fig. 3. Optimal coaductivities of the matria and the electrolytic solutioIL
Fig. 5. Optimal equivalent conductivity.
IO'
YG’AL
1148
,‘OLKMAN
maximum porosity, subject to mechanical and constructional constraints. Obviously, sources of electrical resistance o&r than the material of the matrix itself should be avoided. Consequently, good contacts inside the matrix must be assured. The tortuosity has an adverse effect on the equivalent conductivity. It is concluded from Figs 1 and 5, that the hiiest values of K& are obtained when n = 1. This implies either that the electrode must be highly porosive (6 > 0.9) or made up of straight pores. The optimal constructional features of a threedimensional electrode should, therefore, meet the following requirements: (a) high effective conductivity; (b) high porosity; (c) high internal surface area : (d) adequate mechanical strength (this requirement is not treated in this work). Most of the published experimental work on three dimensional electrodes was carried out with restrained beds of particulate packing. Electrodes of this type are characterized by high internal surface area and high conductivity (neglecting the resistance of contacts between the particles). However, their porosity is low, which results in low conductivity of the solution. The reticulate electrode, recently introduced by Tentorio and Casolo-Ginelly[‘l], has high conductivity and high porosity. On the other hand, its internal surface area is somewhat lower than that of the packed-bed electrodes. Fluid&d-bed electrodes may be operated with high porosities but in that case their conductivity is low[3]. When the expansion of the bed is low, the porosity is low too, and this electrode resembles ohmically the restrained bed electrode. Some published data on the different types of threedimensional electrodes are shown in Table 1. No type of packing meets all the requirements for optimum design. However, it seems from these data that the reticular electrode has the proper combination of constructional features to approach the requirements
for optimal effectiveness. Sulzer’s tower packings BX and CY[ll] and Hydronyl’s knitmesh packing[l2], which are included in Table 1, also have similar characteristics. No work has yet been published concerning the use of this kind of packing as electrochemical reactors. 5. SUMMARY Criteria for optimizing the effectiveness of threedimensional electrodes by maximizing its equivalent conductivity have heen evaluated. It was concluded that the porosity is one of the most important factors that control the conductivities of the electrode matrix and the electrolytic solution. High porosity is one of the basic requirements for constructional design of an effective three-dimensional electrode. REFERENCES I.
2. 3. 4. 5. 6.
7. 8.
P. Galione, Achievements and tasks of electroehemieal en&eerin8, Electroehim. Acts 25 913 (1977). 1. S. Newman and C. W. Tobias, Theoretical analysis of current distibutioa in porous electrodes, J. elecrrockm. Sot. 109, 1183 (1962). B. J. Sabaeky and J. W. Evans, The electrical conductivity of fluid&d bed electrodes - its signiieance and some experimental measurements, Metal/. Trans. 8& 5 (1977). J. Newmanand W. Tiedeman, Porous-electrode theory with battery applications, A.I.Ch.E.JI 21, 25 (1975). W. Tiedeman and J. Newman, Maximum effective capacity in an ohmically limited porous electrode, J. electrochem sot. 122, 1482 (1975). R. E. Meredith and C. W. Tobias, Conduction in Heterogeneous Systems, in : Advancesin Electrochemistry and Ekctr&emical Engineering Vol. 2, p. 15 (Edited by C. W. Tobias) (1962). A. Tmtorio and U. Casolo-Ginelly, Characterization of reticulate., tbreedimensional electrodes, J. uppI. Elecno&m. t$ 195 (1978). D. N. Bannion and J. Newman, Electroehemieal removal of copper ions from very dilute solutions, J. uppl. Elechwchem. 2, 113 (1972).
Table 1. Some data on three-dimensional electrodes Type of electrode Packed-bed Packed-bed Packed-bed
Reticular
Fluid&!&bed sulzer tower packing
Hydronyl wire mesh tower packing
Type of packing Carbon granules plus powder (O.l-O.OOlcm) Graphite particles (-100+150 mesh) Stacked copper screens 100 mesh 150 mesh 200 mesh Copper plated polyurethane foam 10 pores in-’ 20 pores in - ’ Copper shots Corrugated strip of wire mesh (various metals) BX CY Corrugated wire mesh (various metals)
Multifill
E
a/cm-’
Reference
0.30
25
C81
0.50
* 12.5
[91
0.61 0.69 0.67
143.0 188.3 245.0
[I] [lOI
0.975 0.968 0.4-0.5
6.9 9.0
[:3
Not specified Not specified
5.0 7.0
0.95
c41
-20
[:r]
[I21
Optimization of the ektiveness 9. G. B. Adams, R. P. Hollandworth and D. N. Bennion, Electrochemical oxidation of ferrous iron in very dilute solutions, .I. electrochem. Sot. 122 1043 (1975). 10. R. Alkiie and P. K. Ng, Studies on flow-by porous electrodes having perpendicular directions ofcurrent and electrolyte flow, J. ekcrrochent. Sot. 124, 1220 (1977).
of a three-dimensional electrode
1149
11. M. Huber and W. M&r, Sulzer columns for Vacuum rectitication and mass transfer, Sulw Tech. Rev. (l/1975), 3 (1975). 12. Tower Packings, Hydronyl Ltd. (London), catalog TP-33.