The surfactant-promoted electroreduction of oxygen to hydrogen peroxide reactor engineering aspects

Article abstract of DOI:10.1149/1.1857773

The two-electron reduction of O₂ at pH 3 (1 M Na ₂SO₄ acidified by glacial acetic acid) and 9.6 (mixture of 0.5 M Na₂CO₃ and 0.5 M NaHCO₃) was investigated in flow-by electrochemical reactors with three-dimensional cathodes, consisting of graphite felt (GF) or reticulated vitreous carbon (RVC). The cathode was operated with co-current upward gas/liquid flow and O ₂ pressures in the range of 200-700 kPa. A factorial design with four variables at two levels was employed to investigate the effects of superficial current density, liquid load, O₂ pressure, and cationic surfactant concentration [i.e., trioctylmethylammonium chloride (Aliquat 336, A336)] on H₂O₂ concentration, current efficiency, and reactor voltage. Among the investigated variables A336 exerted the strongest positive main effect on both H₂O₂ concentration and current efficiency. The beneficial effect of A336 was due to suppression of the H ₂O₂ loss by both electroreduction and surface-catalyzed decomposition. However, A336 increased the pressure gradient through GF by up to 100%. The surfactant effect on the pressure gradient was estimated using the Herbolzheimer-Park model for the influence of surfactant on the motion of gas bubbles in liquid-filled capillaries. An O₂ mass-transfer model in both GF and RVC was developed and correlated with the experimental results.

Full text of DOI:10.1149/1.1857773

D42
Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
0013-4651/2005/152͑3͒/D42/12/$7.00 © The Electrochemical Society, Inc.
The Surfactant-Promoted Electroreduction of Oxygen
to Hydrogen Peroxide
Reactor Engineering Aspects
,z
˝
*
*
Elod L. Gyenge and Colin W. Oloman
Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver,
British Colombia V6T 1Z4, Canada
The two-electron reduction of O2 at pH 3 ͑1 M Na2SO4 acidified by glacial acetic acid͒ and 9.6 ͑mixture of 0.5 M Na2CO3 and
0.5 M NaHCO3) was investigated in flow-by electrochemical reactors with three-dimensional cathodes, consisting of graphite felt
͑GF͒ or reticulated vitreous carbon ͑RVC͒. The cathode was operated with co-current upward gas/liquid flow and O2 pressures in
the range of 200-700 kPa. A factorial design with four variables at two levels was employed to investigate the effects of superficial
current density, liquid load, O2 pressure, and cationic surfactant concentration ͓i.e., trioctylmethylammonium chloride ͑Aliquat®
336, A336͔͒ on H2O2 concentration, current efficiency, and reactor voltage. Among the investigated variables A336 exerted the
strongest positive main effect on both H2O2 concentration and current efficiency. The beneficial effect of A336 was due to
suppression of the H2O2 loss by both electroreduction and surface-catalyzed decomposition. However, A336 increased the pres-
sure gradient through GF by up to 100%. The surfactant effect on the pressure gradient was estimated using the Herbolzheimer-
Park model for the influence of surfactant on the motion of gas bubbles in liquid-filled capillaries. An O2 mass-transfer model in
both GF and RVC was developed and correlated with the experimental results.
© 2005 The Electrochemical Society. ͓DOI: 10.1149/1.1857773͔ All rights reserved.
Manuscript submitted March 4, 2004; revised manuscript received August 30, 2004. Available electronically January 28, 2005.
early with the undissociated H2O2 concentration.11 Thus, at pH
The electrosynthesis of H2O2 on an industrial scale is presently
practiced only with limited commercial success in spite of a stable
peroxide demand growth estimated at 4 to 6% per year in North
America, driven mainly by the pulp and paper industry.1 The only
commercial electrochemical technology targeting this market is the
on-site alkaline peroxide generation system developed by H-D Tech.
͑a Dow-Huron joint venture͒, which is based on the electroreduction
of O2 in a ‘‘diaphragm flow control trickle bed’’ reactor. The elec-
trochemical reactor employs a fixed-bed cathode composed of car-
bon black and Teflon-coated graphite chips of 40 to 60 mesh.2-4 This
Ͼ pKa,H O ϭ 11.6 the rate of the secondary reaction decreases
2
2
markedly with an increase of pH, contributing to a high current
efficiency for the 2eϪ O2 reduction.
To improve the H2O2 formation by O2 electroreduction in acidic
electrolytes various approaches have been explored, such as electro-
chemical mediation by surface-adsorbed quinone derivatives,12,13
electrocatalysis by an electrochemically polymerized Co-tetra͑o-
aminophenol͒ porphyrin film,14 and ultrasound-assisted reduction at
boron-doped diamond electrodes.15 None of the above mentioned
techniques were evaluated under industrially relevant conditions and
reactor designs.
technology produces typically a 4 wt % H2O2 solution in 7 wt %
Ϫ1
NaOH with a specific energy consumption of 4 kWh kg
.
H O
2
2
A major drawback of the H-D Tech. process is the high alkalin-
ity, 1.7-1.8 NaOH:H2O2 weight ratio, of the peroxide product solu-
tion. The optimum caustic to peroxide weight ratio for bleaching
depends on pulp consistency and type ͑e.g., chemical, mechanical͒,
bleaching temperature, and retention time. In alkaline peroxide
bleaching of chemical pulp the optimum NaOH:H2O2 weight ratio is
0.3 for 20-30 wt % pulp consistency and 1.2 in the case of 9-12 wt
% consistency, respectively.5 Furthermore, recent developments in
H2O2 pulp bleaching technologies have been aimed at replacing
NaOH by Na2CO3 as the alkali source. The latter compound im-
parted superior brightness stability during peroxide bleaching,6 gave
higher pulp yield, and lowered the chemical oxygen demand ͑COD͒
level of the bleaching effluent as compared to NaOH.7 Moreover,
catalyzed acidic ͑pH 5͒ peroxide bleaching technologies have been
developed and implemented on an industrial scale.8,9
Recently, the present authors have proposed two approaches for
Ͻ
O2 electroreduction to H2O2 at pH
13, the 2-ethyl-9,10-
anthraquinone mediated O2 reduction in a three-phase, aqueous
acidic ͑pH 0.9-3͒/organic/gaseous, system16,17 and cationic surfac-
tant mediation in a two-phase media, containing an aqueous electro-
lyte ͑pH 0.9-11.5͒ and O2 gas.10 The first method, emulsion media-
tion using an anthraquinone derivative, has been investigated in
flow-by three-dimensional electrodes operated with co-current three-
phase flow. Using a graphite felt cathode a superficial current den-
sity as high as 3000 A mϪ2 could be employed with a H2O2 current
efficiency of 84%.17 However, the specific energy consumption of
Ϫ1
the mediated process, was high, i.e., 16-18 kWh kg
.
H O
2
2
Regarding the second method, cationic surfactant mediation in a
two-phase ͑liquid/gas͒ system, it was found that the presence of a
long-chain quaternary ammonium ion i.e., trioctylmethylammonium
chloride CH (C H ) NϩClϪ, trade name Aliquat® 336 abbrevi-
Unfortunately, the electroreduction of O2 for large-scale H2O2
͓
3
8
17 3
Ͻ
production at pH
ϳ13 presently does not meet industrial feasibil-
ated as A336͔ in the aqueous electrolyte, increased the standard
heterogeneous rate constant for the 2eϪ O2 reduction on glassy car-
bon in the pH range 0.9 ͑i.e., 0.1 M H2SO4) to 11.5 ͑i.e., 0.1 M
Na2CO3).10 This effect has been attributed to an increase of the
cathode surface pH in the presence of adsorbed quaternary ammo-
nium ions. Moreover, batch electrolysis using reticulated vitreous
carbon ͑RVC͒ cathodes showed that the presence of A336 at milli-
mol ͑mM͒ levels improved certain figures of merit for H2O2 elec-
trosynthesis, such as the accumulated H2O2 concentration and the
current efficiency for H2O2 generation.10
ity requirements such as current efficiency above 80% at current
densities of 1-5 kA mϪ2, a specific energy less than about 4 kWh
Ϫ1
kg
, and a return of investment greater than approximately 30%
H O
2
2
per year at a H2O2 price of about 0.6 $͑US͒ kgϪ1. Hydrogen perox-
Ͻ
ide electrosynthesis at pH
13 is challenging due mainly to kinetic
aspects related to the sluggishness of O2 electroreduction2,10 and the
enhanced rate of H2O2 electroreduction to H2O. Regarding the lat-
ter, the H2O2 reduction current density was found to increase lin-
Therefore, it was of interest to investigate the effect of A336 on
the two-phase O2 reduction under conditions closer to potential in-
dustrial applications, employing continuous flow reactors. Due to
* Electrochemical Society Active Member.
z E-mail: egyenge@chml.ubc.ca

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
D43
Figure 1. Front view of the cathode compartment.
the multivariable nature of the process, a statistical experimental
design approach has also been employed. This is the first investiga-
tion looking at the effect of a cationic surfactant on the reactor
engineering of O2 electroreduction in flow-by fiber-bed and reticu-
lated electrodes.
Figure 2. SEM images of: ͑A͒ GF and ͑B͒ RVC.
In addition to pulp bleaching, the potential applications of an
specific electronic conductivity of the RVC was 2.7 times higher
than for GF, while the latter had a higher specific surface area, i.e.,
16,000 m2 mϪ3 vs. 6,560 m2 mϪ3 RVC. Figure 2 reveals the open-
cell ͑foam-like͒ structure of RVC as compared to the irregular ar-
rangement of fibers in GF. In addition to structural difference, en-
ergy dispersive X-ray analysis ͑EDX͒, X-ray photoelectron
spectroscopy ͑XPS͒, and Fourier transform infrared spectroscopy
͑FTIR͒ analysis indicated surface composition differences between
the two types of carbons.
The surface of GF had virtually no oxidized carbon, being com-
posed entirely of graphitic carbon. On the other hand the surface of
RVC showed oxidized carbon in the form of hydroxyl, ester, and
carbonyl functional groups. The oxygen content of RVC surface was
determined by XPS analysis as about 8 atom %. Furthermore, FTIR
analysis revealed that GF is composed of graphitic carbon only,
while RVC shows C-H and C-C bonds that are characteristic for
hydrocarbons. The differences in surface-functional groups could
impact the electrocatalytic properties of the carbon electrodes under
investigation.
Ͻ
efficient H2O2 electrosynthesis method at pH
13 are numerous,
including the paired electrosynthesis of benzaldehyde from toluene
mediated by H2O2 and the V5ϩ/V4ϩ redox couple18 or degradation
of organic effluents, such as formaldehyde,19,20 phenol, cresol, cat-
echol, p-benzoquinone, anilin, oxalic acid, and dyes by H2O2 .21,22
Experimental
Figure 1 shows a front view of the cathode compartment in the
flow-by electrochemical reactor equipped with either a graphite fiber
bed ͑GF, referred to also as graphite felt͒ or reticulated vitreous
carbon ͑RVC, ϳ39 ppc ͑pores per centimeter͒, i.e., 100 ppi ͑pores
per inch͔͒. Table I and Fig. 2 show certain physicochemical and
structural characteristics for GF ͑The Carborundum Co., Sanborn,
NY͒ and RVC ͑ERG Materials & Aerospace Co., Oakland, CA͒. The
Table I. Physicochemical characteristics of the three-dimensional
electrodes.
The cathode thickness in the reactor ͑Fig. 1͒ was 4.5 ϫ 10Ϫ3 m,
corresponding in the case of GF to 38% compression ͑uncompressed
thickness 7.25 ϫ 10Ϫ3 m͒. The superficial cathode area in the direc-
tion of current flow was 33 ϫ 10Ϫ4 m2, while the area in the direc-
tion of fluid flow was 1.1 ϫ 10Ϫ4 m2. The cathode was operated in
flow-by arrangement ͑the current and fluid flow directions perpen-
dicular on each other͒ with co-current upward O2 gas-liquid flow.
The two-phase pressure drop along the cathode height was measured
with Bourdon gauges connected at the inlet and outlet ports of the
cathode compartment.
GF
Reference/
source
Property
͑compressed by 38%͒
RVC
Specific surface area,
m2 mϪ3
16,000
23
6,560
17
17
Electronic conductivity,
62
S mϪ1
Porosity
0.92
20
0.95
53
17
Fig. 2
Mean fiber diameter,
ϫ10Ϫ6
m

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Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
The GF three-dimensional electrode was placed on a stainless
steel current feeder plate and fitted into Durabla® gaskets ͑Fig. 1͒.
The reactor with the GF cathode was uniformly compressed using a
torque wrench set to 5 foot-pound. In the case of the reticulated
vitreous carbon cathode, a graphite fiber paper of 3 ϫ 10Ϫ4
m
thickness was inserted between the stainless steel current feeder
plate and RVC to assure good electric contact. The reactor with the
RVC fixed-bed embedded tightly into gaskets was carefully sealed
to avoid compression and crushing of the rigid reticulated structure.
The anode for alkaline conditions was Ni felt (7 ϫ 10Ϫ4 m thick͒,
while for acidic conditions a dimensionally stable O2 anode ͑DSA͒
plate was employed.
The reactor body was made of Plexiglas plates. The entrance and
exit regions of the cathode contained a plastic mesh acting as a fluid
distributor. The cathode and anode compartments were separated by
a cation exchange membrane ͑Nafion 350͒ supported on the anode
side by a plastic mesh. The anolyte was either 1.5 M NaOH or 0.5 M
Na2SO4 at pH 3, both in upward flow. The catholyte was either a
mixture of 0.5 M Na2CO3-0.5 M NaHCO3 at pH 9.6 ͑at 293 K͒ or 1
M Na2SO4 acidified to pH 3 ͑at 293 K͒ with glacial acetic acid. The
absolute O2 pressure in the cathode compartment was varied be-
tween 200 and 700 kPa. The arrangement of reactor components and
the external flow circuit have been described previously.17 The av-
erage temperature in the reactor during electrosynthesis was 300
Ϯ 7 K. After about half-an hour run at each set of operating con-
ditions with single-pass catholyte, the outlet catholyte stream was
sampled and analyzed for H2O2 content by redox titration with
KMnO4 in H2SO4 20 wt %.23 In the present work no peroxide
stabilization agent was added to the catholyte.
The effect of a triple C8-chain quaternary ammonium salt,
CH3(C8H17)3NϩClϪ ͑trioctylmethylammonium chloride, trade
name Aliquat 336, abbreviated as A336, Sigma-Aldrich, Inc.͒ dis-
persed in the catholyte at concentrations up to 3 mM was investi-
gated by both parametric and factorial experiments. The factorial
experimental design and analysis was executed using the Jass 2.1
software ͑Joiner Associates, Madison, WI͒.
Furthermore, the effect of surfactants on the electroreduction of
H2O2 at 298 K was studied in separate-batch electrolysis experi-
ments using a stirred H-cell equipped with an RVC cathode of 1
ϫ 10Ϫ3 m2 effective superficial area. Coulometry experiments were
performed in deoxygenated (N2 purge͒ 0.1 M Na2CO3 and H2SO4
solutions containing initially ca. 1 M H2O2 ͑prepared from 30 wt %
stock solution, Fisher Scientific, Inc.͒. The peroxide solution con-
tained no stabilizing agent. The cathode superficial current density
was kept constant at 300 A mϪ2 and the residual H2O2 concentration
after 15 min of electrolysis was determined. In addition to A336,
Figure 3. Influence of surfactants on the galvanostatic electroreduction of
H2O2 on RVC 12 ppc cathode. Current density: 300 A mϪ2, time 15 min, 298
K. N2 purge. Electrolyte: ͑A͒ 0.1 M H2SO4 , ͑B͒ 0.1 M Na2CO3 . Legend:
͑᭹͒ A336, ͑᭺͒ Triton X-100, ͑᭢͒ SDS.
H2O2 ϩ 2Hϩ ϩ 2eϪ ꢀ 2H2O Eo ϭ ϩ1.77 VSHE ͓2b͔
Afanas’ev et al. reported the inhibiting effect of certain quater-
nary ammonium salts on H2O2 electroreduction in NaCl 3.16 wt %
on a dropping Hg electrode. These authors found that the inhibiting
effect increased with hydrocarbon chain length, e.g., (C4H9)4Nϩ ion
was more effective than the (CH3)4Nϩ ion.24 In the present work
the comparative influence on peroxide electroreduction on RVC of
A336 and representative nonionic and anionic surfactants, i.e., Tri-
ton X-100 and SDS, respectively, has been assessed using a stirred
H cell. The residual peroxide concentration after 15 min of galvano-
static operation at 300 A mϪ2 is shown in Fig. 3. The initial peroxide
concentration was close to 1 M.
a
nonionic and an anionic surfactant were also tested for
potential effect on H2O2 electroreduction, i.e., Triton X-100
C H O͑C H O) , with n ϭ 9-10, Sigma-Aldrich, Inc.͔ and so-
͓
14 22
2
4
n
dium dodecylsulfate ͑SDS, C12H25OSOϪ3 Naϩ, Sigma-Aldrich, Inc.͒.
Results and Discussion
In the absence of additives the residual peroxide concentrations
were 0.91 M in 0.1 M Na2CO3 and 0.96 M in 0.1 M H2SO4 , i.e.,
8.5 and 4.3% peroxide loss in 15 min, respectively. These values
reflect H2O2 losses by three possible mechanisms, intrinsic elec-
troreduction ͑Eq. 1b and 2b͒ and two non-faradaic mechanisms, i.e.,
heterogeneous, surface-catalyzed, decomposition ͑i.e., effect of elec-
trode material and possibly reaction vessel materials͒ and homoge-
neously catalyzed, bulk decomposition, which is pH and electrolyte
composition dependent. Decomposition in the bulk is promoted by
an increase of pH, the presence of transition metal ions ͓e.g., Fe͑II͒,
Mn͑II͒, Cu͑II͔͒ and carbonate ions.25
It is difficult to differentiate among the three potential peroxide
loss mechanisms since synergistic effects are likely to occur, e.g.,
during electroreduction ͑Eq. 1 and 2͒ the surface pH increases which
in turn raises the rate of non-faradaic H2O2 decomposition. In sepa-
rate experiments without current but with the RVC in the cathode
The effect of cationic surfactant (A336) on the electroreduction
of H2O2.—Complementary to the influence of A336 on the 2eϪ O2
electroreduction,10 in the context of H2O2 electrosynthesis it was of
interest to evaluate the effect of the quaternary ammonium ion on
the secondary reaction of H2O2 electroreduction. The thermodynam-
ics of O2 and H2O2 electroreduction are (Eo values at pH 0 and 14,
respectively, from Ref. 11͒
Alkaline O2 ϩ H2O ϩ 2eϪ ꢀ HO2Ϫ ϩ OHϪ
Eo ϭ Ϫ0.065 VSHE
͓1a͔
HOϪ2 ϩ H2O ϩ 2eϪ ꢀ 3OHϪ Eo ϭ ϩ0.88 VSHE ͓1b͔
Acid O2 ϩ 2Hϩ ϩ 2eϪ ꢀ H2O2 Eo ϭ ϩ0.70 VSHE ͓2a͔

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
chamber, it was found that the non-faradaic decomposition in acid
D45
accounted for about 1% loss of H2O2 in 15 min ͑residual concen-
tration of 0.99 M͒, while in carbonate the corresponding loss was
about 5.5% during the same time interval ͑i.e., residual peroxide
concentration about 0.94 M͒. Thus, it can be concluded that with
current ͑i.e., at 300 A mϪ2͒, electroreduction contributed about 3.3
and 3%, respectively, to the total peroxide loss in 0.1 M H2SO4 and
0.1 M Na2CO3 . The latter values are slightly above ͑by about 1%͒
those expected from Faraday’s law assuming 100% current effi-
ciency. This result indicates possible interaction effects ͑such as an
increase of surface pH͒ contributing to peroxide loss by a non-
faradaic route.
It is proposed, therefore, that in acid the electroreduction of per-
oxide is the main pathway for H2O2 loss, while in carbonate both
electroreduction and non-faradaic routes contribute to peroxide loss,
with the latter mechanism being more significant at 300 A mϪ2
.
These findings are corroborated by the study of Kolyagin and Ko-
rnienko who investigated the H2O2 decomposition rates in acidic
and alkaline solutions on gas-diffusion electrodes prepared with hy-
drophobized carbon black and operated at 500 A mϪ2 26
However,
.
considering that the rate of electroreduction is potential-dependent it
is expected that the relative contribution of the electrochemical path-
way to the total peroxide loss will increase with current density.
In 0.1 M H2SO4 ͑Fig. 3A͒ all three surfactants, cationic: A336,
non-ionic: Triton X-100 and anionic: SDS, reduced the loss of
H2O2 . Surfactant concentrations above 3 mM reduced the H2O2
loss to levels corresponding approximately to non-faradaic decom-
position only. In 0.1 M Na2CO3 , on the other hand ͑Fig. 3B͒, the
anionic surfactant SDS was ineffective ͑i.e., the residual H2O2 con-
centration was the same as in the absence of surfactant͒. However,
both A336 and Triton X-100 suppressed the H2O2 loss, while A336
was more effective. Furthermore, A336 was the only additive, which
suppressed both the faradaic and the surface-catalyzed non-faradaic
peroxide loss ͑Fig. 3B͒.
Figure 4. Cathode potentials measured after 1 min of H2O2 electroreduction
under galvanostatic operation at 300 A mϪ2. Cathode: RVC 12 ppc. Condi-
tions identical to Fig. 3. Electrolyte: ͑A͒ 0.1 M H2SO4 , ͑B͒ 0.1 M Na2CO3 .
Legend: ͑᭹͒ A336, ͑᭺͒ Triton X-100, ͑᭢͒ SDS.
Figure 4 shows the cathode potentials at 300 A mϪ2 for H2O2
reduction in the presence and absence of surfactants after 1 min of
electrolysis. In acid, millimole levels of all three surfactants de-
creased the H2O2 cathode reduction potential. The potential shifted
from Ϫ1.05 V vs. Ag/AgCl, KClstd without surfactant to about Ϫ2.2
and Ϫ2.4 V with surfactant present ͑Fig. 4A͒. In carbonate, A336
brought about the largest decrease of cathode potential, i.e., from
Ϫ0.9 to about Ϫ1.7 V, while SDS left the H2O2 reduction potential
unchanged at around Ϫ0.9 V ͑Fig. 4B͒. These data suggest clearly
that the effectiveness of surfactants in repressing the H2O2 loss is
related to changes occurring on the electrode surface, induced most
likely by surfactant adsorption ͑both electrostatic and specific͒. In
alkaline media the electrosorption of both SDS ͑anionic͒ and Triton
X-100 ͑non-ionic͒ is less favored as compared to the cationic sur-
factant A336. Thus, the former are not effective suppressors of H2O2
electroreduction. In acid ͑pH 0.9͒ on the other hand, both SDS and
Triton X-100 undergo protonation, canceling out to some extent the
electrostatic repulsion encountered at the cathode surface. Thereby,
they are almost as effective as A336 in lowering the H2O2 electrore-
duction rate.
load of 4.5 kg mϪ2 sϪ1. The liquid-to-gas load ratio ensured a surg-
ing flow regime.27 The absolute outlet pressure was 350 kPa for
alkaline and 425 kPa for acidic conditions, respectively.
Comparing Fig. 5 and 6 reveals that in the alkaline solution ͑pH
9.6͒, regardless of the surfactant presence, the peroxide concentra-
tions generated per single pass are higher for GF than for RVC at
superficial current densities above 500 A mϪ2. The GF cathode,
could be operated at current densities as high as 4000 A mϪ2 with a
current efficiency close to 70% with 3 mM A336 in the electrolyte
͑Fig. 5, inset͒. In the case of RVC in the presence of A336, a current
efficiency of about 70% was obtained at a superficial current density
of only 700 A mϪ2
.
The difference in performance between RVC and GF at superfi-
cial current densities above about 500 A mϪ2 can be explained by a
mass-transfer model that estimates the superficial mass-transfer lim-
iting current density for O2 reduction and the corresponding maxi-
mum electroactive bed thickness ͑Appendix A͒.
In the case of the alkaline electrolyte, for the employed liquid
and gas loads, the mass-transfer limiting superficial current densities
in the absence of surfactant were about 370 A mϪ2 for RVC and
1520 A mϪ2 for GF, respectively ͑Appendix A, Table A-I͒. Figure 5
and 6 show for both three-dimensional electrodes at superficial cur-
rent densities below the respective mass-transfer limiting values,
oxygen was reduced to H2O2 , with current efficiencies above 75%
regardless of A336 presence. The corresponding maximum electro-
active thickness was only 0.6 mm for GF and 2.5 mm for RVC,
compared to the geometric bed thickness of 4.5 mm. Thus, due to
the nonlinear potential and current distribution across the three-
dimensional electrode only a fraction of the bed thickness is capable
In addition to the inhibiting effect of A336 on H2O2 electrore-
duction investigated here, it has been previously found, as indicated
in the introduction, that A336 improved the two-electron O2 reduc-
tion kinetics.10 Therefore, the cationic surfactant, trioctylmethylam-
monium chloride ͑A336͒, has been retained as an additive for O2
electroreduction to H2O2 in flow-by reactors.
Comparative investigation of graphite felt and reticulated
vitreous carbon cathodes in flow-by reactors.—Graphite felt and
reticulated vitreous carbon 39 ppc were tested as cathodes for O2
reduction in both alkaline ͑pH 9.6͒ and acidic ͑pH 3͒ solutions, in
the presence and absence of the cationic surfactant A336 ͑Experi-
mental section͒. The flow-by reactor was operated with co-current
upward gas/liquid flow, O2 gas load of 0.16 kg mϪ2 sϪ1, and liquid

D46
Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
Figure 5. Electroreduction of O2 in 0.5 M Na2CO3-0.5 M NaHCO3 ͑pH 9.6͒
in a flow-by reactor with GF cathode operated with two-phase upward
G/L flow. Temperature: 300 K, liquid load: 4.5 kg mϪ2 Ϫ1. Gas load:
s
0.16 kg mϪ2 Ϫ1, pressure 350 kPa. Legend: ͑᭹͒ 3 mM A336 and ͑᭞͒
s
without surfactant. Inset: current efficiency for H2O2 .
of working at the limiting current density without significant side
reactions.
The calculated limiting current density for RVC ͑i.e., 370 A mϪ2
͒
is corroborated by the experimental data of Davison et al. that
showed current efficiencies for H2O2 generation on RVC above 80%
only for superficial current densities below 500 A mϪ2 (O2 reduction
in 2 M NaOH at 1725 kPa absolute pressure͒.28
The presence of A336 influences the polarization curve of O2
reduction10 and the overpotential of H2O2 electroreduction ͑Fig. 4͒.
Thus, A336 will affect the maximum allowable potential drop
⌬⌽max,I that can be tolerated without significant secondary reaction
in the three-dimensional electrode. Consequently, A336 will have an
effect on both the maximum electroactive bed thickness and the
Figure 7. Electroreduction of O2 in 1 M Na2SO4 ͑pH 3 acidified with gla-
cial acetic acid͒. Comparison between GF and RVC 39 ppc cathodes.
Flow-by reactor with two-phase upward G/L flow. Temperature: 300 K, liq-
uid load: 4.5 kg mϪ2 sϪ1. Gas load: 0.16 kg mϪ2 sϪ1, pressure: 425 kPa. ͑A͒
H2O2 concentration per pass; ͑B͒ current efficiency. Legend: ͑᭹͒ RVC, 1
mM A336, ͑᭺͒ RVC, without surfactant, ͑᭢͒ GF, 1 mM A336, ͑᭞͒ GF,
without surfactant.
superficial limiting current density for O2 reduction, as shown in
Appendix A. With surfactant present, it is estimated that the maxi-
mum electroactive thickness increased to 0.9 mm for GF and 4.1
mm for RVC ͑i.e., almost equal to the geometric thickness of RVC͒
͑Table A-I, Appendix A͒. The corresponding superficial limiting cur-
rent densities were higher, therefore, than without A336 present, i.e.,
2760 and 680 A mϪ2 for GF and RVC, respectively.
For GF ͑Fig. 5͒ the current efficiency corresponding to the O2
mass-transfer limited superficial current density was about 75%. At
current densities higher than 2760 A mϪ2 the H2O2 accumulation
rate diminished and the current efficiency dropped below 75%.
Correlating the O2 mass-transfer limited superficial current den-
sity with the experimental results in the case of RVC ͑Fig. 6͒, it is
observed that with surfactant the H2O2 concentration increased with
current density up to the mass-transfer limited value of 680 A mϪ2
where the current efficiency was close to 70%. At current densities
above 680 A mϪ2 both the H2O2 concentration and current effi-
ciency dropped, as expected, due to the increased significance of the
secondary reaction ͑i.e., H2O2 electroreduction͒.
In the case of the acidic solution on the other hand ͑Fig. 7͒, using
either GF or RVC cathode current efficiencies for H2O2 generation
of and above 75% were obtained only at superficial current densities
below 500 A mϪ2. This observation is consistent with the electrode
kinetic limitation of O2 reduction in acidic media. The presence of 1
Figure 6. Electroreduction of O2 in 0.5 M Na2CO3-0.5 M NaHCO3 ͑pH 9.6͒
in a flow-by reactor with RVC 39 ppc cathode and two-phase upward
G/L flow. Temperature: 300 K, liquid load: 4.5 kg mϪ2 Ϫ1. Gas load:
s
0.16 kg mϪ2
s
Ϫ1, pressure: 350 kPa. Legend: ͑᭹͒ 1 mM A336 and ͑᭞͒
without surfactant. Inset: current efficiency for H2O2 .

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
D47
Table II. Variables and their levels for the 24 ¿ 1 factorial runs
in 0.5 M Na2CO3-0.5 M NaHCO3 „pH 9.6…. Cathode: GF, tem-
Table III. Design matrix and responses „in random order… for the
factorial runs in 0.5 M Na2CO3-0.5 M NaHCO3 „pH 9.6….
perature: 300 K, O2 gas load: 0.27 kg mÀ2 sÀ1
.
H2O2
Current
Reactor
voltagec
͑V͒
Variable levels
concentrationa efficiencyb
Levels
Center ͑0͒
2780
Variables
͑Symbols, units͒
i
L
P
S
No.
͑mM͒
͑%͒
No.
1
Low ͑Ϫ͒
High ͑ϩ͒
1
2
3
4
5
6
7
8
9
Ϫ
ϩ
Ϫ
Ϫ
ϩ
ϩ
ϩ
0
ϩ
Ϫ
Ϫ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
ϩ
ϩ
Ϫ
Ϫ
ϩ
Ϫ
0
Ϫ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
Ϫ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
0
ϩ
Ϫ
Ϫ
Ϫ
ϩ
ϩ
ϩ
ϩ
ϩ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
Ϫ
ϩ
0
ϩ
ϩ
ϩ
Ϫ
ϩ
Ϫ
ϩ
Ϫ
Ϫ
78
62
18
82
59
85
85
63 Ϯ 3
68
84 Ϯ 2
83 Ϯ 2
74 Ϯ 3
97
88
47 Ϯ 2
77
2.85
6.30
2.60
Current density; i
927
4650
͑A mϪ2
͒
2
3
4
Catholyte load; L
1.7
200
0
5.3
350
1
7.8
475
3
80
2.55
͑kg mϪ2 sϪ1
͒
301 Ϯ 13
72
400 Ϯ 9
77 Ϯ 2
350 Ϯ 7
20.5
83
50 Ϯ 2
81
5.50 Ϯ 0.07
5.60
5.22 Ϯ 0.24
4.50
5.50 Ϯ 0.33
2.85
Pressure; Pa
͑kPa͒
A336 conc.; S
͑mM͒
a Absolute outlet reactor pressure.
10
11
12
13
14
15
16
17
2.60
5.80
5.70
2.50
2.50
2.45
5.20
78
21
20
82
100
95
77 Ϯ 1
mM A336 was beneficial for H2O2 electrosynthesis using both elec-
trodes. In the case of GF operated at 750 A mϪ2, the surfactant
raised the current efficiency from 42 to 60%. Using RVC at 300 A
mϪ2 in the absence of surfactant the current efficiency was only
about 30%, while with 1 mM A336 the H2O2 current efficiency
improved to 75% ͑Fig. 7͒.
The calculated limiting superficial current densities and the
maximum electroactive bed thickness were lower at pH 3 compared
to pH 9.6 ͑Table A-I, Appendix A͒, due to the decrease of ⌬⌽max,I
͑Appendix A͒ as a consequence of the enhanced rate of H2O2 re-
duction in acid.11 The cationic surfactant had a positive effect on
both H2O2 concentration and current efficiency ͑Fig. 7͒. In the case
of RVC, A336 increased the limiting superficial current density from
260 A mϪ2 ͑without͒ to 470 A mϪ2 ͑with A336͒ ͑Appendix A͒.
Consequently, for the latter current density value ͑Fig. 7͒, the H2O2
current efficiency was about 70% with A336 and only 27% in its
absence.
364 Ϯ 5
a Average response: 128 mM. Pooled standard deviation: Ϯ8.3 mM.
b Average response: 79%. Pooled standard deviation: Ϯ2.4%.
c Average response: 4.13 V. Pooled standard deviation: Ϯ0.24 V.
sponses can be expressed as a regression model.29 The three figures
of merit considered here, i.e., H2O2 concentration CH O ͑mM͒, cur-
2
2
rent efficiency CE ͑%͒, and reactor voltage, Ereactor ͑V͒, could be
described by the following regression equations ͑statistically insig-
nificant effects were neglected͒
CH O mM͒ ϭ 128 ϩ 80.1X Ϫ 87.2X ϩ 7.7XS Ϫ 56.9XIXL
͑
I
L
2
2
ϩ 6.2XIXS Ϫ 7.45XPXS Ϫ 6.95XIXPXS
ϩ 7XLXPXS
To evaluate and quantify the main and synergistic effects of four
process variables, superficial current density, liquid-to-gas load ra-
tio, pressure, and A336 concentration, factorial experiments were
carried out. Graphite felt was retained as the cathode of choice.
͓3͔
CE %͒ ϭ 79 Ϫ 10.3X ϩ 2.95X ϩ 3.6X Ϫ 5.45X X
I L
͑
I
P
S
Alkaline electrolyte pH 9.6: factorial experiments.—With a
catholyte composed of 0.5 M Na2CO3 and 0.5 M NaHCO3 factorial
experiments were performed using four variables at two levels and
one centerpoint ͑i.e., 24 ϩ 1 design, Table II͒. The superficial cur-
rent densities used in the factorial design were chosen such that the
low value of 927 A mϪ2 is below while the high value of 4650 A
mϪ2 is above the mass-limiting superficial current density for O2
reduction under the conditions employed in the factorial design. The
liquid flow rates were 1.67 ϫ 10Ϫ7 m3 sϪ1 and 7.5 ϫ 10Ϫ7 m3 sϪ1
at the low and high load level ͑Table II͒, respectively. The corre-
sponding calculated average residence times in the cathode compart-
ϩ 2.45XIXP ϩ 3.55XLXP Ϫ 2.3XPXS
Ereactor ͑V) ϭ 4.13 ϩ 1.49XI ,
͓4͔
͓5͔
where the coded variables are defined as XI ϭ (i Ϫ 2788.5)/
1861.5, XP ϭ (P Ϫ 337.5)/137.5, XS ϭ (S Ϫ 1.5)/1.5, and XL
ϭ (L Ϫ 4.75)/3.05, with i the superficial current density ͑A mϪ2͒,
L liquid load ͑kg mϪ2 sϪ1͒, P absolute pressure ͑kPa͒, and S the
A336 concentration ͑mM͒.
Equation 3-5 show that in the factorial experiments the average
H2O2 concentration per pass and current efficiency were 128
Ϯ 8.3 mM and 79 Ϯ 2.4%, respectively, associated with an aver-
age reactor voltage of 4.13 Ϯ 0.24 V. The regression equations for
H2O2 concentration and current efficiency can be represented as
contour plots. Figure 8 depicts the interaction between the superfi-
cial current density ͑i.e., given as coded variable XI) and liquid load
͑i.e., XL) corresponding to XS ϭ 1 and XP ϭ Ϫ1 ͑i.e., high concen-
tration of A336 and low pressure͒. For the employed reactor design
the contour plot shows ͑Fig. 8͒ that a H2O2 concentration per pass of
350 mM ͑or higher͒ is achievable with a current efficiency of 75-
80% as long as XI is in the range of 0.8 to 1.0 while XL is between
Ϫ0.8 and Ϫ1.0. The corresponding reactor voltage is expected to be
in the range of 5.3-5.6 V. On the other hand, current efficiencies
greater than 90% can only be obtained for XI р Ϫ0.6. Under the
latter condition, the expected H2O2 concentration per pass is р150
mM depending on XL . Thus, there is an obvious trade-off between
current efficiency and H2O2 concentration.
ment were 20 and 90 s. The gas load was constant 0.27 kg mϪ2 sϪ1
.
Increasing the liquid load from low to high changed the flow regime
from pulsing to surging flow.27 The outlet absolute pressure ranged
between 200 and 475 kPa.
Table III shows the complete set of the seventeen factorial runs,
as designed with the aid of the Jass 2.1 software, and the figures of
merit ͑i.e., H2O2 concentration, current efficiency, and reactor volt-
age͒. The outlet pH varied between 9.7 ͑for high flow rate coupled
with low current density͒ and 12.5 ͑low flow rate-high current den-
sity combination͒. The operating temperature was 300 Ϯ 7 K.
Table III shows that H2O2 concentrations higher than 300 mM
could be obtained with current efficiencies above 60% for combina-
tions of low liquid load and high current density levels ͑e.g., runs
no. 5, 7, 9, and 17, in Table III͒.
Based on the factorial experimental design results the main and
interaction effects were calculated with the Jass 2.1 software. Fur-
thermore, using the main and interaction effects the factorial re-

D48
Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
words, increasing the operating pressure from low to high when
A336 is at the high ͑i.e., 3 mM͒ level was not beneficial ͑especially
in the case of high current density level, e.g., compare runs no. 7 and
9, Table III͒.
To explain the pressure-surfactant interaction, one has to con-
sider the flow conditions in the graphite felt electrode in the pres-
ence of surfactant. At high pressure ͑475 kPa͒ the radii of the O2
bubbles decreases, therefore, the specific gas-liquid ͑G/L͒ interfacial
area increases under the same conditions. For trickle-bed reactors it
was found that the specific G/L interfacial area increased with gas
pressure for superficial gas velocities exceeding 0.02-0.03 m sϪ1
͑for a review see Ref. 30͒. For the present case the superficial O2
velocity was 0.2 m sϪ1 at STP ͑or 0.045 m sϪ1 at 475 kPa, 307 K͒,
therefore, it is likely that the G/L interfacial area increased with
pressure from low ͑200 kPa͒ to high ͑475 kPa͒. A sample calculation
is presented at the end of the present section.
The increase of the G/L interfacial area causes a local decrease of
surfactant excess concentration at the G/L interface, hence, a local
increase of surface tension. In order to counteract the local increase
of surface tension, mass transfer of surfactant occurs from the bulk
liquid to the G/L interface.31,32 The surfactant mass transfer to the
G/L interface could decrease the surfactant concentration at the
solid-liquid interface. Consequently, the ability of A336 to adsorb
and form surface structures on the electrode that are effective in
suppressing H2O2 electroreduction and/or decomposition, is dimin-
ished. It is hypothesized, therefore, that the negative interaction be-
tween surfactant and pressure is related to G/L surface tension gra-
dients generated at high operating pressures ͑e.g., 475 kPa͒.
One way to test experimentally the discussed hypothesis based
on surface tension gradients is to compare the pressure drop through
the graphite felt with and without the presence of A336. There is
experimental evidence indicating that the pressure drop associated
with the movement of gas bubbles in liquid-filled capillaries, in-
creases in the presence of surfactants.31 A 50 to 100 times higher
two-phase pressure drop was reported for co-current upward G/L
flow through graphite felt in the presence of the foaming agent Ter-
gitol ͑at 0.1% volume ratio of surfactant to liquid͒.33 The theoretical
explanation put forward by Herbolzheimer ͑1988, quoted by
Probstein,31a͒ and Park ͑1992,31b͒, relies on the fact that the pressure
drop increase with surfactant is due to an increase of the Laplace
pressure difference between the front and rear of the gas bubble as a
result of surfactant accumulation at the rear. In other words, a sur-
face tension difference develops between the front and rear menisci
Figure 8. Contour plot of the factorial regression model for electroreduction
of O2 in 0.5 M Na2CO3-0.5 M NaHCO3 ͑pH 9.6͒ on GF. XS ϭ 1 and XP
ϭ Ϫ1. ͑A͒ H2O2 concentration, ͑B͒ current efficiency.
Ͼ
of the bubble, with ⌬␥ ϭ ␥front Ϫ ␥rear
0. Thus, the drag force
acting on the bubble in the rigid liquid film region increases in the
presence of surfactant.31
As shown by Eq. 4, with respect to current efficiency the surfac-
tant concentration had the second most significant effect after cur-
rent density. Interestingly, the surfactant main effect was higher than
the main effect of pressure, as indicated by the respective coeffi-
cients in the regression Eq. 4. At a high level of current density, low
liquid load and pressure, with 3 mM A336 present in the electrolyte
the peroxide concentration increased by about 33%, i.e., from 300 to
400 mM ͑compare runs no. 5 and 7, Table III, current efficiency of
63 and 84%, respectively͒.
In the present work the two-phase liquid-gas ͑L/G͒ pressure gra-
dient has been measured with and without 3 mM A336 in the elec-
trolyte, i.e., ⌬pLG,A336 and ⌬pLG , respectively. Table IV shows the
two pressure gradients as a function of liquid load at an operating
pressure of 475 kPa. The measured two-phase pressure gradient in
the absence of surfactant ⌬pLG , at a liquid load of 1.7 kg mϪ2 sϪ1
matched fairly well ͑standard deviation about 10%͒ the value pre-
dicted for fiber beds by the Hodgson and Oloman correlation.34
At 475 kPa͑abs͒ operating pressure the presence of 3 mM A336
increased the two-phase pressure gradient by 70 to 100% ͑Table IV͒.
For a liquid load of 1.7 kg mϪ2 sϪ1 the pressure gradient doubled
Furthermore, the surfactant and pressure had a negative two-
factor interaction and the three-factor interaction including the su-
perficial current density was negative as well ͑Eq. 3 and 4͒. In other
Table IV. The effect of surfactant concentration „A336… on the pressure gradient in the graphite fiber bed with co-current upward two-phase
„gas-liquid… flow. Gas „O2… load 0.27 kg mÀ2 sÀ1, pressure 475 kPa „abs…. For calculations see Appendix B.
Without surfactant
A336 concentration ϭ 3 mM
5
⌬pL ϫ 105
⌬pLG ϫ 105
⌬pG ϫ 105
⌬pG ϫ 10
⌬pLG,A336 ϫ 105
⌬pG,A336 ϫ 105
⌬pG,␥ ϫ 105
*
*
Liquid load L
͑kg mϪ2 sϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
͑Pa mϪ1
͒
1.7
7.8
0.11
0.49
1.72
3.45
0.29
0.21
0.27
0.21
3.45
5.86
0.88
0.77
0.88
0.78

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
D49
Table V. Variables and their levels for the 24 ¿ 1 factorial runs
Table VI. Design matrix and responses „in random order… for the
factorial runs in 1 M Na2SO4 „pH 3….
in 1 M Na2SO4 „pH 3 acidified with glacial acetic acid…. Cathode:
GF, temperature: 300 K and O2 gas load 0.47 kg mÀ2 sÀ1
.
H2O2
Current
Reactor
Variable levels
concentration efficiency
voltage
Levels
a
b
c
Variables
i
L
P
S
No.
͑mM͒
͑%͒
͑V͒
No.
1
͑Symbols, units͒
Low ͑Ϫ͒
Center ͑0͒
High ͑ϩ͒
1274
1
2
3
4
5
6
7
8
9
0
0
0
0
30 Ϯ 1
22
17
20
46
15
16 Ϯ 1
28
34 Ϯ 0.6
23
37
36
30
12
45 Ϯ 1
43
32
53 Ϯ 2
80
60
40
35
31
58 Ϯ 4
38
46 Ϯ 1.7
49
49
28
62
44
35 Ϯ 1
57
25
7.55 Ϯ 0.18
6.05
Current density; i
729
1000
Ϫ
Ϫ
ϩ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
Ϫ
ϩ
ϩ
ϩ
ϩ
Ϫ
ϩ
ϩ
Ϫ
Ϫ
ϩ
Ϫ
Ϫ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
ϩ
Ϫ
ϩ
ϩ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
Ϫ
Ϫ
ϩ
Ϫ
ϩ
Ϫ
ϩ
ϩ
Ϫ
͑A mϪ2
͒
6.60
8.70
8.75
10.60
6.05
6.40
6.50
8.20
6.70
2
3
4
Catholyte load; L
1.6
425
0
2.9
525
4.3
͑kg mϪ2 sϪ1
͒
Pressure; P a
͑kPa͒
700
1
A336 conc.; S
͑mM͒
0.66
10
a Absolute outlet reactor pressure.
11
12
13
14
15
16
17
8.40
7.97 Ϯ 0.17
5.20
8.50 Ϯ 0.10
6.50
from ⌬pLG ϭ 1.72 ϫ 105 Pa mϪ1 ͑without A336͒ to ⌬pLG,A336
ϭ 3.45 ϫ 105 Pa mϪ1 ͑with A336͒.
Furthermore, the pressure gradient associated with the movement
of O2 gas bubbles in liquid-filled capillaries with surfactant present
8.45
a Average factorial response: 29 mM. Pooled standard deviation: Ϯ0.8
*
⌬pG,␥ , has been estimated using the Herbolzheimer-Park model
mM.
͑for details, see Appendix B͒. It was found ͑Table IV͒ that the model
b Average factorial response: 46.5%. Pooled standard deviation:
*
calculation pressure gradient ⌬pG,␥ matched the gas-phase pressure
Ϯ1.8%.
c Average factorial response: 7.47 V. Pooled standard deviation: Ϯ0.15
gradient obtained from experimental data in the presence of A336,
⌬pG,A336 ͑for calculation details see Appendix B͒. Therefore, it
is plausible to assume that in the presence of A336 at high ͑i.e.,
475 kPa͒ operating pressure, surface tension gradients arise at
the G/L interface, increasing the pressure gradient and furthermore,
diminishing the surface excess concentration of A336 at the solid
͓i.e., electrode-liquid ͑S/L͔͒ interface. The latter effects are less
significant at low pressure ͑i.e., 200 kPa͒ where only a 20-30%
increase of two-phase pressure gradient has been observed in the
presence of A336. These considerations could explain the negative
two-factor interaction between surfactant and pressure with respect
to both H2O2 concentrations and current efficiency, Eq. 3 and 4,
respectively.
V.
formed. The experiments and the results obtained are summarized in
Table VI. The outlet pH of the electrolyte varied between 3.8 and
5.0.
Under the employed conditions the highest H2O2 concentration
per pass was about 45 mM obtained at low liquid load combined
with high superficial current density ͑runs no. 5 and 15, Table VI͒.
The highest current efficiency on the other hand, i.e., 80% ͑run no.
2͒, has been obtained under opposite conditions, of low current den-
sity and high liquid load.
A decrease of A336 S/L surface excess with increasing pressure
is supported by a surfactant mass balance that accounts for the equi-
librium distribution of A336 between the G/L and S/L interfaces and
depends on the A336 feed concentration, the respective adsorption
isotherms, the gas bubble diameter, the liquid hold-up, and the spe-
cific surface area of the electrodes. The A336 surface excess con-
centration at complete monolayer coverage is 3.25 ϫ 10Ϫ6 mol
Neglecting the statistically insignificant effects, the three figures
of merit in the case of the acidic media are described by the follow-
ing regression model
CH O mM͒ ϭ 29 ϩ 2.35X Ϫ 9.15XL ϩ 2.6XP ϩ 4XS
͑
I
2
2
ϩ 0.75XLXP Ϫ 1.15XLXS ϩ 1.15XIXLXP
mϪ2 10
.
Assuming no micelles, Langmuir adsorption, monolayer at
͓6͔
͓7͔
the G/L, and bilayer at the S/L interface,10 and a liquid hold-up of
50%, the ideal gas law predicts an increase of the specific surface
area from 2.0 ϫ 105 to 2.7 ϫ 105 m2 mϪ3 as the pressure is raised
from 200 to 475 kPa and the bubble diameter decreases from 13.5 to
10 ␮m, resulting in a 2% decrease in the S/L surface excess of
A336. This change in A336 S/L surface excess is sensitive to the
liquid hold-up such that if the liquid hold-up drops to 30% the
predicted S/L surface excess drops by about 37% compared to its
value at 50% liquid hold-up at 200 kPa. Since it is known that liquid
hold-up in trickle beds is smaller for foaming vs. nonfoaming liquids
͑i.e., due to an increase of the Weber number͒,30 there is a good
possibility that the combined effect of pressure and A336 on the
peroxide efficiency is caused by the corresponding redistribution of
the surfactant between the G/L and S/L surfaces, as outlined above.
CE %͒ ϭ 46.5 ϩ 6.9X Ϫ 7.95XI ϩ 5.7XP ϩ 6.3XS
͑
L
ϩ 3.45XLXP
Ereactor V͒ ϭ 7.47 ϩ 1.23X Ϫ 0.21X ϩ 0.23X XL Ϫ 0.23XIXP
͑
I
P
I
Ϫ 0.22XIXS Ϫ 0.23XIXLXS
͓8͔
where the coded variables are given by
i Ϫ 1001.5
P Ϫ 562.5
XI ϭ
XS ϭ
,
XP ϭ
,
272.5
137.5
S Ϫ 0.5
L Ϫ 2.95
,
and XL ϭ
0.5
1.35
Factorial experimental design: acid electrolyte pH 3.—Em-
ploying the GF cathode a factorial experimental design of O2 elec-
troreduction to H2O2 in 1 M Na2SO4 ͑pH 3 acidified by glacial
acetic acid͒ was carried out, using four variables at two levels and a
centerpoint ͑i.e., 24 ϩ 1 design͒. The variables and their levels are
given in Table V. According to the 24 ϩ 1 experimental design
created with the Jass 2.1 software seventeen experiments were per-
As shown by Eq. 6-8, the average values of the three figures of
merit were: H2O2 concentration 29 Ϯ 0.8 mM, current efficiency
for H2O2 46.5 Ϯ 1.8%, and reactor voltage 7.47 Ϯ 0.15 V. These
values indicate a poorer overall reactor performance as compared to
the alkaline electrolyte ͑section on Alkaline electrolyte pH 9.6; fac-
torial experiments͒.

D50
Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
Conclusions
The effect of four process variables, superficial current density,
liquid load, pressure, and cationic surfactant concentration ͑i.e., trio-
ctylmethylammonium chloride, A336͒ on the O2 electroreduction to
H2O2 was investigated using three-dimensional fixed-bed cathodes
of GF and RVC.
The cathode was operated with co-current upward gas-liquid
flow in either surging or pulsing regimes. The O2 pressure was be-
tween 200 and 700 kPa͑abs͒ ͑abs, absolute pressure͒. Two different
electrolyte compositions were employed, with pH of 9.6 and 3, re-
spectively. The higher O2 mass-transfer capacity of GF compared
to RVC under all the conditions explored here, allows the GF
to operate with current efficiency above 70% ͑with A336͒ up
to about 700 A mϪ2 ͑pH 3͒ and 2,700 A mϪ2 ͑pH 9.6͒ while with the
same efficiency RVC operates only up to about 470 A mϪ2 ͑pH 3͒
and 680 A mϪ2 ͑pH 9.6͒.
A complete factorial experimental design with four variables at
two levels and one centerpoint, revealed a positive main effect for
A336 in both alkaline and acidic electrolytes with regard to current
efficiency and peroxide concentration. The surfactant effect was at-
tributed to lowering the rate of both H2O2 electroreduction and
surface-catalyzed non-faradaic H2O2 decomposition. Using RVC
operated at 300 A mϪ2, it was found that in acidic conditions, elec-
troreduction is the major route of peroxide loss, while in alkaline
conditions both the faradaic and non-faradaic peroxide losses must
be taken into account. Future studies should also look at the impact
of carbon surface chemistry on both the H2O2 electroreduction and
surface-catalyzed decomposition.
Additionally, the enhancement of the 2eϪ O2 reduction rate in-
duced by A336 surface film formation, as previously proposed by
the present authors, should be taken into account.10 The surfactant
effect on O2 reduction is probably more relevant in the acidic elec-
trolyte where the O2 electroreduction kinetics is sluggish.
In the 0.5 M Na2CO3-0.5 M NaHCO3 mixture ͑pH 9.6͒, a H2O2
concentration per single pass of 400 mM was obtained with a
current efficiency of 84%, at 4650 A mϪ2 with 3 mM A336 in
the electrolyte, 200 kPa pressure, 1.7 kg mϪ2 sϪ1 liquid, and
0.27 kg mϪ2 sϪ1 O2 load, respectively. Under identical conditions
but without A336, the current efficiency was 63%, corresponding to
an H2O2 concentration of 300 mM.
Figure 9. Contour plot of the factorial regression model for electroreduction
of O2 in 1 M Na2SO4 ͑pH 3 acidified with glacial acetic acid͒ on GF. XS
ϭ 1 and XP ϭ Ϫ1. ͑A͒ H2O2 concentration, ͑B͒ current efficiency.
Furthermore, in alkali a negative interaction effect was found
between the A336 concentration and operating pressure. The
Herbolzheimer-Park model of the gas-phase pressure gradient due to
surface tension differences acting along the length of gas bubbles
gave a good agreement with the experimentally measured data. The
measured two-phase flow pressure gradient in the fiber bed in-
creased in the presence of cationic surfactant by up to 100%. It is
proposed that the negative interaction effect between surfactant and
operating pressure is due to diminished A336 surface excess con-
centration at the solid͑electrode͒-liquid interface, as a result of sur-
factant mass transfer to the gas-liquid interface to counteract the
surface tension gradients created at high operating pressure.
The long-term stability of the figures of merit is an important
aspect for the scale-up of the O2 electroreduction process. All ex-
periments in the factorial design were completed with the same elec-
trodes and this amounted to a total of about 50 h of reactor opera-
tion. During this time the reproducibility of the experiments was
satisfactory, as indicated in the statistically designed experimental
analysis. Furthermore, collateral in-house data showed that during
continuous operation of a similar peroxide electrosynthesis reactor
using a graphite felt cathode and commercial grade NaOH over a 30
day period the current efficiency fell by about 0.3% per day. The
drop in current efficiency was due to decomposition of peroxide by
the accumulated transition metal ions from the feed liquid. In that
collateral work the current efficiency was restored by washing the
reactor with dilute HNO3 or alternatively the drop in current effi-
ciency was suppressed by the presence of chelating agents in the
feed solution.43
The cationic surfactant had a significant positive main effect on
both H2O2 concentration and current efficiency, as indicated by
Eq. 6 and 7, respectively. Similarly to the alkaline media, the main
effect of A336 was larger than the one due to pressure. However,
the pressures main effect was higher in acidic than in alkali condi-
tions ͑compare Eq. 7 and 4͒. The main effect of A336 is very well
illustrated by a comparison between runs no. 2 and 7 in Table VI. At
729 A mϪ2 the current efficiency was 58% without A336, while the
corresponding current efficiency with A336 was 80%.
The two-factor pressure-surfactant interaction effect was overall
statistically insignificant in acidic solution, suggesting that interfa-
cial mechanisms similar to the one described for the alkaline elec-
trolyte case, might be operative in offsetting the beneficial effect of
high pressure in the presence of surfactant ͑e.g., compare runs no. 5
and 15, Table VI͒.
Equation 6 and 7 have been plotted as contour plots as a function
of both XI and XL for XS ϭ 1 and XP ϭ Ϫ 1 ͑Fig. 9͒. To obtain
current efficiencies Ͼ50%, the liquid load and superficial current
density must satisfy the following condition: XL у 0 and XI р
Ϫ0.6. The expected H2O2 concentration, on the other hand, would
be less than 30 mM ͑Fig. 9͒.

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
D51
The liquid hold-up ␤L in the graphite fiber bed is given by the Hodgson-Oloman
correlation34
Future work should look at optimizing the process variables in
conjunction with scale-up of the three-dimensional electrodes with
various configurations ͑e.g., bipolar stack͒. Moreover, in addition to
A336, other cationic surfactants could be evaluated for potentially
improved performance especially in acidic conditions.
␤
ϭ 1 Ϫ 0.907LϪ0.362G0.301
,
0 Ͻ G Ͻ 0.35 kg mϪ2 sϪ1
and 1.53 Ͻ L Ͻ 7.62 kg mϪ2 sϪ1
where L and G are the liquid and gas load, respectively ͑kg mϪ2 sϪ1͒.
,
L
͓A-8͔
Acknowledgments
In Eq. A-4 the maximum tolerable ͑theoretical͒ electrode potential difference
⌬⌽max,1 across the bed thickness with negligible secondary reaction ͑i.e., H2O2 elec-
troreduction͒ was evaluated as the width of the O2 reduction limiting current plateau.38
Employing polarization curves published in the literature ⌬⌽max,1 was assumed equal to
0.1 V in alkaline10,11,28 and 0.03 V in the acidic electrolyte,10,19 respectively.
The presence of the cationic surfactant A336 had a profound influence on the O2
polarization behavior, shifting the O2 reduction wave and peak potential to positive
values. At the A336 concentration of the present work the magnitude of the peak
potential shift was about 0.3 V in carbonate and about 0.09 V in acid.10 Therefore, it
was assumed that in the presence of the cationic surfactant, ⌬⌽max,1 is about 0.3 V in
the alkaline and 0.09 V in the acidic electrolyte.
The authors gratefully acknowledge financial support from the
Network of Centers of Excellence ͑Mechanical Wood Pulps͒ of the
Government of Canada and the Natural Sciences and Engineering
Research Council of Canada, as well as from the University of Brit-
ish Columbia New Faculty Start-Up Fund ͑E.G.͒.
The University of British Columbia assisted in meeting the publication
costs of this article.
The overall O2 mass-transfer capacity Kmc,O for two-phase co-current upward flow
Appendix A
2
in GF could be estimated using the correlation presented by Hodgson and Oloman34
Modeling of O2 reduction to H2O2 in GF and RVC electrodes under mass-transfer
limiting conditions: The effect of cationic surfactant A336.—For both three-dimensional
electrodes ͑i.e., GF and RVC͒ the mass-transfer limiting superficial current density for
Kmc,O ,GF ϭ 5.9L0.372G0.232
͓A-9͔
2
O2 reduction iml,O ͑A mϪ2͒, is expressed as
2
For reticulated vitreous carbon electrodes on the other hand, there has been no compre-
hensive study of the two-phase gas-liquid mass transfer.
iml,O ϭ nFKmc,O ␶1CO
2
͓A-1͔
2
2
Therefore, the two-phase O2 mass-transfer coefficient in RVC was estimated as the
contribution of three mechanisms, i.e., single liquid-phase convective flow mass transfer
in the RVC K0 , boundary-layer disturbance effect due to gas bubbles induced local
turbulence Kd , and penetration mechanism where the gas bubbles have the role of
injecting O2 very near to the electrode surface, ͑i.e., virtually gas-solid mass transfer͒
where CO is the O2 concentration in the electrolyte ͑mol mϪ3͒, F is the faraday
constant, ͑C molϪ1͒, Kmc,O is the overall O2 mass-transfer capacity ͑sϪ1͒, n, the no. of
2
2
electrons transferred ͑ϭ2͒, and ␶ is the maximum electroactive bed thickness in the
I
direction of current flow operating at the limiting current density ͑m͒.
The O2 concentration in the employed electrolyte solutions ͑i.e., either a mixture of
0.5 M Na2CO3-0.5 M NaHCO3 or 1 M Na2SO4) can be estimated from a modified
Sechenov equation35,36
Kp
.
The mass-transfer coefficient due to boundary-layer disturbance mechanism Kd in
the RVC electrode could be assessed using the correlation reported by Sedahmed et al.
for inert gas-sparged fixed-be electrodes composed of vertical screen stacks40
Ϫ0.28
CO
,0
␶
2
m
log
ϭ
ks,jCsalt,j
͓A-2͔
St ϭ 0.2͑ReGFrG
͒
Ϫ0.26ScϪ0.66
͓A-10͔
͓A-11͔
ͩ
ͪ
ͩ ͪ
͚
CO
d
j
2
where CO ,0 is the O2 concentration in pure water at a given pressure and temperature,37
Csalt,j is the concentration of salt j, ͑mol mϪ3͒ and ks,j is the Sechenov constant for salt
j ͑m3 molϪ1͒, given by
where
2
uG2
Kd
uG
uGd
vL
St ϭ
,
ReG ϭ
,
Sc ϭ
,
and FrG ϭ
vL
DO
d • g
2
ks,j
ϭ
͑hi ϩ hO ͒zi
͓A-3͔
͚
2
with d the vitreous carbon filament diameter (5.3 ϫ 10Ϫ5 m for RVC 39 ppc, Table I͒,
i
DO diffusion coefficient of O2 in the electrolyte solution ͑i.e., 5 ϫ 10Ϫ10 m2 Ϫ1 at 298
s
2
with hO gas-specific parameter ͑for O2 is equal to zero35͒, hi ion-specific parameter for
K2͒, g acceleration due to gravity ͑m2 sϪ1͒, uG superficial gas velocity ͑m sϪ1͒, vL
2
salt j ͑m3 molϪ1͒ ͑i.e., for Naϩ:1.079 ϫ 10Ϫ4, SO42Ϫ :1.164 ϫ 10Ϫ4, CO23Ϫ :1.158
kinematic electrolyte viscosity ͑m2 sϪ1͒, and ␶ geometric thickness of the RVC elec-
m
Ϫ
ϫ 10Ϫ4, and HCO3 :1.019 ϫ 10Ϫ4 ͒, and zi is the number of ions i in the composi-
35
trode ͑m͒.
The liquid-phase convective mass-transfer coefficient in RVC K0 is given by the
tion of salt j.
Fenton-Alkire correlation41
Furthermore, the presence of A336 increases the solubility of O2 in the electrolytes
under consideration by a factor of about 1.1.10
The expression of the maximum electroactive thickness in Eq. A-I ␶ is dependent
Sh ϭ 11Re0L.3
͓A-12͔
I
on the relationship between the effective specific conductivity of the electrolyte ␬
L,eff
and the effective electronic conductivity of the solid matrix ͑GF or RVC͒ ␴ ͑see Table
where
I͒.38 Thus
1/2
K0␧
uL
aLS
effvL
eff
2␬L,eff⌬⌽max,1
Sh ϭ
and ReL ϭ
͓A-13͔
for ␬L,eff Ͻ ␴;
␶
ϭ
ϭ
͓A-4͔
͓A-5͔
͓A-6͔
1
1
ͩ
ͩ
ͪ
ͪ
aLSDO
␧
nFKmc,O CO
2
2
2
while
with aLS the specific surface area available for liquid-solid mass transfer ͑m2 mϪ3͒ and
uL, the superficial liquid velocity ͑m sϪ1͒.
Last, the penetration mechanism mass-transfer coefficient Kp was obtained by ex-
trapolating the data reported by Takahashi and Alkire42 to the ReL and ReG values
employed in the present work. It was found that
1/2
4␬L,eff⌬⌽max,1
nFKmc,O CO
for ␬L,eff Х ␴;
␶
2
2
In Eq. A-4 and A-5 ␬
can be estimated by39
L,eff
Kp Х 2Kd
͓A-14͔
2␬ ␧
L
eff
␬
L,eff ϭ
The overall O2 mass-transfer capacity in RVC Kmc,O ,RVC , was expressed as
2
3 Ϫ ␧
eff
where ␧ is the effective porosity of the bed with respect to the liquid phase ͑Eq. A-7
eff
Kmc,O ,RVC ϭ aLS͑K0 ϩ Kd͒ ϩ aGSKp
͓A-15͔
2
and A-8͒, while the specific ionic conductivities ␬L of the electrolytes under study have
been experimentally measured. For both electrolyte compositions ͑i.e., alkaline and
with
acidic͒ ␬ was 8 S mϪ1. Therefore, the assumption of ␬L,eff Ͻ ␴ has been made ͑see
L
also Table I͒ and Eq. A-4 has been used to estimate ␶
I
a
LS ϭ ␤Lam and aGS ϭ ͑1 Ϫ ␤L͒am
͓A-16͔
␧
eff ϭ ␤L • ␧
͓A-7͔
where aGS , aLS , are the specific surface area available to gas-solid and liquid-solid
mass transfer, respectively, while am is the specific surface area of the RVC matrix
͑Table I͒ and ␤L was estimated by Eq. A-8.
where ␤L is liquid hold-up and ␧ is the porosity of the three-dimensional matrix
͑Table I͒.

D52
Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
Table A-I. Mass-transfer capacity, maximum electroactive bed thickness and superficial limiting current density for O2 reduction on GF and
RVC electrodes. Conditions corresponding to Fig. 5 and 6 „pH 9.6… and Fig. 7 „pH 3…, respectively.
a
Kmc,O
im1,O
2
͑A mϪ2
͒
⌬⌽max,1
͑V͒
␶
1
͑m͒
2
3D electrode
GF
Electrolyte
͑sϪ1
͒
6.0 ϫ 10Ϫ4
Mixture of:
0.5 M Na2CO3
0.5 M NaHCO3
͑pH 9.6͒
1 M Na2SO4
͑acidified to pH 3͒
0.1
(A336 ϭ 0)
0.3
(A336 ϭ 3 mM͒
0.03
(A336 ϭ 0)
0.09
(A336 ϭ 1 mM͒
0.1
(A336 ϭ 0)
0.3
(A336 ϭ 1 mM͒
0.03
(A336 ϭ 0)
0.09
1520
9.0 ϫ 10Ϫ4
3.0 ϫ 10Ϫ4
4.0 ϫ 10Ϫ4
2.5 ϫ 10Ϫ3
4.1 ϫ 10Ϫ3
1.1 ϫ 10Ϫ3
1.8 ϫ 10Ϫ3
6.7
2760
1040
1890
370
RVC
Mixture of:
0.5 M Na2CO3
0.5 M NaHCO3
͑pH 9.6͒
1 M Na2SO4
͑acidified to pH 3͒
0.38
680
260
470
(A336 ϭ 1 mM͒
a Reflects the estimated effect of the cationic surfactant ͑A336͒ on the polarization curves for O2 and H2O2 reduction. The presence of A336 increases
⌬⌽max,1
.
Equations A-2 to A-16, have been applied to calculate the O2 mass-transfer limiting
To estimate ⌬pG,A336 and ⌬pG from the experimentally measured two-phase data,
the following approach has been adopted. For graphite fiber beds similar to the one used
here, Hodgson and Oloman have shown that the two-phase pressure gradient is best
described by the Sato correlation where the respective single-phase values are expressed
by the Ingmanson equation ͑for a critical review of various correlations and applicabil-
ity to fiber-beds see Ref. 34͒.
superficial current density iml,O expressed by Eq. A-1. Table A-I summarizes the mass-
2
transfer capacity, maximum electroactive thickness, and limiting current density for the
experimental conditions relevant to Fig. 5-7.
Appendix B
Effect of surfactant on the gas-phase pressure gradient in the graphite fiber
bed.—The pressure gradient required to drive a gas bubble through a liquid-filled
capillary in the presence of surfactant can be estimated using the Herbolzheimer-Park
model31
⌬pLG
⌬pL͑1 ϩ 1/Y2͒
0.7
log
ϭ
͓B-5͔
ͫ
ͬ
2
͓log͑Y/1.2͔͒ ϩ 1
where Y ϭ (⌬pL /⌬pG)1/2 is the Lockart-Martinelli parameter, whilst ⌬pLG , ⌬pG
,
and ⌬pL are the pressure gradients ͑Pa mϪ1͒ for the two-phase, gas and liquid single-
phases, respectively.
*
⌬PG,␥
lb
ϭ 0.942␥Ca1/.3
͓B-1͔
*
⌬pG,␥
ϭ
Hc • r2b
Hc
The liquid-phase pressure gradient in fiber beds is34
where ⌬PG,␥ and ⌬pG,␥ are the pressure drop ͑Pa͒ and pressure gradient ͑Pa mϪ1͒,
respectively, associated with the movement of the bubble in the liquid-filled capillary
with surfactant present, Hc is the effective height of the 3D cathode ͑m͒ ͑Fig. 1͒, lb and
rb are the length and menisci radius of the bubble, respectively ͑m͒, ␥ is surface tension
͑N mϪ1͒, and Ca is the dimensionless capillary number defined as
*
*
2
k͑1 Ϫ ␧ ͒
⌬pL ϭ 10Ϫ11
␮
• uL • a2
͓B-6͔
L
f
3
␧
where af is the specific area of the fiber ͓ϭ4/df , df fiber diameter ͑m͔͒, k is the Kozeny
constant for fibrous beds given by Eq. B-7, and uL is the liquid superficial velocity
͑m sϪ1
͒
␮Lub,eff
Ca ϭ
͓B-2͔
␥
3
␧
3
k ϭ 3.6
͓1 ϩ 57͑1 Ϫ ␧͒ ͔
͓B-7͔
with ub,eff effective gas bubble velocity in the capillary filled with liquid ͑m sϪ1͒ and ␮
the liquid dynamic viscosity ͑Pa s͒. The effective gas bubble velocity in the liquid-filled
1/2
L
͑1 Ϫ ␧͒
portion of the bed can be estimated as
Using the experimentally measured ⌬pLG and ⌬pLG,A336 together with ⌬pL calcu-
lated from Eq. B-6-B-7, the gas-phase pressure gradients for the two scenarios,
⌬pG,A336 and ⌬pG , were obtained from Eq. B-5.
Table IV summarizes both the experimentally determined and calculated pressure
gradients, ⌬pLG , ⌬pLG,A336 , ⌬pG , ⌬pG,A336 together with the gas-phase pressure
uG
u
b,eff ϭ
͓B-3͔
␧␤L
*
*
where uG is the superficial gas velocity ͑m sϪ1͒, ␤L is liquid hold-up ͑Eq. A-8͒ and ␧ is
the porosity of the 3D matrix ͑Table I͒.
gradients obtained from the Herbozheimer-Park and Bretherton models ⌬pG,␥ and ⌬pG
for the cases with and without surfactant present, respectively.
In Eq. B-1 and B-2 it was assumed that ␥ ϭ 30 ϫ 10Ϫ3 N mϪ1 in the presence
of 3 mM A336, and a typical O2 gas bubble dimension in the graphite felt electrode
͑Fig. 2A͒ was considered to be lb ϭ 8 ϫ 10Ϫ5 m and rb ϭ 5 ϫ 10Ϫ6 m, respectively.
In the absence of surfactant the pressure gradient associated with the movement of
a bubble in a capillary filled with liquid is expressed by the Bretherton equation ͑for a
review, see Ref. 31͒.
List of Symbols
a
d
C
specific surface area ͑m2 mϪ3
fiber diameter ͑m͒
͒
concentration ͑mol mϪ3 or mM͒
Ca capillary number
D
diffusion coefficient ͑m2 sϪ1
͒
*
⌬PG
␥
Eo standard electrode potential ͑V vs. SHE͒
Ereactor reactor voltage ͑V͒
ϭ 9.4Ca20/.3
͓B-4͔
*
⌬pG
ϭ
Hc
Hc •0rb
F
Faraday’s constant ͑ϭ96,485.3 C molϪ1
͒
where ␥0 is the surfactant-free surface tension of the electrolyte (ϳ70 ϫ 10Ϫ3 N mϪ1͒,
Ca0 is the capillary number corresponding to the surfactant-free case.
Fr Froude number
g
G
i
gravitational acceleration ͑m2 sϪ1
gas load ͑kg mϪ2 sϪ1
superficial current density ͑A mϪ2
ion and gas specific parameter in the modified Sechenov equation ͑m3 molϪ1
͒
Using the experimentally measured two-phase pressure gradient data ⌬pLG and
⌬pLG,A336 ͑i.e., in the absence and presence of A33͒, the gas-phase pressure gradients
⌬pG,A336 and ⌬pG with and without surfactant present were calculated and compared to
͒
͒
h
͒
*
the gas-phase pressure gradients obtained from the Herbolzheimer-Park Eq. B-1 ⌬pG,␥
,
Hc height of the 3D cathode ͑m͒
Kozeny constant ͑dimensionless͒
*
and Bretherton equation, B-4 ⌬pG , respectively ͑Table IV͒.
k

Journal of The Electrochemical Society, 152 ͑3͒ D42-D53 ͑2005͒
D53
ks Sechenov constant ͑m3 molϪ1
͒
3. C. Oloman, Electrochemical Processing for the Pulp and Paper Industry, p. 143,
The Electrochemical Consultancy, Romsey, U.K. ͑1996͒.
4. M. Nozaki, Kami Pa Gikyoshi, 52, 616 ͑1998͒.
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Heimburger, J. Pulp Paper Sci., 19, J47 ͑1993͒.
K
Kmc
l
O2 mass-transfer coefficient ͑m sϪ1
͒
O2 mass transfer capacity ͑sϪ1
length ͑m͒
͒
L
liquid load ͑kg mϪ2 sϪ1
͒
n
total nr. of electrons exchanged in the primary reaction ͑ϭ2͒
⌬p pressure gradient ͑i.e. pressure drop per cathode length͒ ͑Pa mϪ1
͒
P
pressure ͑Pa or kPa absolute͒
⌬P pressure drop ͑Pa͒
radius ͑m͒
Re Reynolds number
cationic surfactant ͑A336͒ concentration ͑mM͒
7. G. X. Pan, S. Vichnevsky, and G. J. Leary, in 1998 Pulping Conference, Tappi
Proceedings, 637 ͑1998͒.
8. T. Koshitsuka, Kami Pa Gikyoshi, 52, 623 ͑1998͒.
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10. E. L. Gyenge and C. W. Oloman, J. Appl. Electrochem., 31, 233 ͑2001͒.
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pp. 632, 639-641, Academic Press, New York ͑1967͒; ͑b͒ D. T. Sawyer, Oxygen
Chemistry, p. 21, Oxford University Press, New York ͑1991͒.
r
S
Sc Schmidt number
Sh Sherwood number
St Stanton number
u
X
fluid superficial velocity ͑m sϪ1
͒
coded variable in the factorial design ͑dimensionless͒ X ϭ y Ϫ (y
ϩ y‘low’/2)͔/͓(y‘high’ Ϫ y‘low’)/2͔, where yϪ is the variable in the factorial
design͔
12. M. S. Wrighton, Science, 231, 32 ͑1986͒.
13. C. Degrand, J. Electroanal. Chem., 169, 259 ͑1984͒.
͓ ͓
‘high’
14. O. El Mouahid, C. Coutanceau, E. M. Belgsir, P. Crouigneau, J. M. Leger, and C.
Lamy, J. Electroanal. Chem., 426, 117 ͑1997͒.
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Scarsbrook, R. S. Sussmann, and A. J. Whitehead, Chem. Commun. (Cambridge),
1998, 1961.
Y
Lockart-Martinelli parameter ͑dimensionless͒
zj no. of ions i in the composition of the electrolyte
Greek
16. E. L. Gyenge and C. W. Oloman, J. Appl. Electrochem., 33, 655 ͑2003͒.
17. E. L. Gyenge and C. W. Oloman, J. Appl. Electrochem., 33, 665 ͑2003͒.
18. Y. Qingfeng, L. Xiaoping, and Z. Xiuling, J. Appl. Electrochem., 33, 273 ͑2003͒.
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20. C. Ponce de Leon and D. Pletcher, J. Appl. Electrochem., 25, 307 ͑1995͒.
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23. W. Wagner and C. J. Hull, Inorganic Titrimetric Analysis, p. 130, Marcel Dekker,
New York ͑1971͒.
␤
liquid hold-up ͑dimensionless͒
L
␧
porosity of the 3D electrode matrix ͑dimensionless͒
␥
surface tension ͑N mϪ1
͒
⌬⌽max,1 maximum tolerable potential drop without significant side reaction ͑V͒
␬
␮
␯
␴
␶
specific ionic conductivity ͑S mϪ1
dynamic viscosity ͑Pa s͒
͒
kinematic viscosity ͑m2 sϪ1
͒
electronic conductivity ͑S mϪ1
thickness of the 3D electrode ͑m͒
͒
24. ͑a͒ B. N. Afanas’ev, Yu. P. Akulova, and L. V. Bykova, Russ. J. Electrochem., 28,
1524 ͑1992͒; ͑b͒ B. N. Afanas’ev, Yu. P. Skobochkina, and L. V. Bykova, Russ. J.
Electrochem., 27, 454 ͑1991͒; English translation.
Subscripts
´
´
25. ͑a͒ Z. M. Galbacs and L. Csanyi, J. Chem. Soc. Dalton Trans., 79, 417 ͑1983͒; ͑b͒
0
1
single-phase convection or pure phase
related to the primary reaction of 2eϪ O2 reduction
ˇ
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A336 in the presence of cationic surfactant A336
b
d
gas bubble
disturbance mechanism
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eff effective
f
G
L
fiber
gas phase
liquid phase
3D electrode matrix
m
ml mass-transfer limited
O2 oxygen index
p
penetration mechanism
solid phase ͑i.e., electrode surface͒
S
wt indicates weight percentage
related to surface tension difference
␥
Superscript
33. A. Mohandes, Ph.D. Thesis, The University of British Columbia, Vancouver,
Canada ͑1994͒.
*
given by a model for gas bubble movement in a liquid-filled capillary
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Abbreviations
abs absolute pressure
CMC critical micelle concentration
GF graphite felt
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RVC reticulated vitreous carbon
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