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Chemical Engineering Journal 179 (2012) 253– 261

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Journal

j ourna l ho mepage: www.elsev ier .com/ locate /ce j

rimary potential and current density distribution analysis: A first approach foresigning electrocoagulation reactors

rmando Vázquez, Israel Rodríguez, Isabel Lázaro ∗

acultad de Ingeniería-Instituto de Metalurgia, Universidad Autónoma de San Luis Potosí, Av. Sierra Leona 550, Lomas, 78210 San Luis Potosi, Mexico

r t i c l e i n f o

rticle history:eceived 12 May 2011eceived in revised form6 September 2011ccepted 24 October 2011

a b s t r a c t

In this work, the importance of potential and current distribution analysis is highlighted as a key factorin the design of energy efficient electrocoagulation (EC) reactors. Although there are three types of dis-tribution of current and potential (primary, secondary and tertiary), only primary potential and currentdensity distributions were analyzed as a first approach. This approach simplifies the analysis by con-sidering only cell geometry. This study included modeling of potential and current distribution and its

eywords:otential distributionurrent distributioneactor designlectrocoagulationluminum anodes

impact on EC performance. The analysis showed the effect of cell geometry and electrode configurationon the distribution of potential in the cell, the current distribution on the anodes and the modification of anon-uniform distribution by changes to electrode configuration. The experimental evaluation of differentelectrode configurations showed that EC performance is enhanced when uniform potential and currentdensity is achieved, and kinetics of anode (in this case aluminum) dissolution can be improved withouthaving to change the applied current density.

. Introduction

Several papers report the advantages of using electrocoagu-ation (EC) technology [1–8] for the treatment of wastewater.

astewater of various types, such as saline wastewater [9], tarand and oil shale wastewater [10], urban wastewater [11], andextile wastewater [12], can be treated by EC technology. Electro-oagulation does not yet seem to be an established technology, evenhough industrial EC trials have been reported since the beginningf the past century [13]. According to those reports [5,13], trialsf the EC technology were abandoned due to operating costs thatid not allow EC to compete against the more established chemicaloagulation process [2]. Energy consumption is the operating costith the highest impact when the use of EC is evaluated. Due to

nergy considerations, current efficiency as well as cell voltage isery important. These variables are affected by cell reactor designarameters, such as the type of electrical connection, interelec-rodic distance and electrode arrangement [5]. However, there iso discussion in any of the EC studies found in the literature of theriteria used for the design of the EC reactors employed in thosetudies.

Some of the extensive reviews [5–7], on fundamental aspectsf the EC process point to studies that are less specific on treat-ng a particular pollutant and more focused on quantifying key

∗ Corresponding author. Tel.: +52 4448254326; fax: +52 4448253574.E-mail address: ilazaro@uaslp.mx (I. Lázaro).

385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cej.2011.10.078

© 2011 Elsevier B.V. All rights reserved.

interactions and relationships between the three “foundation tech-nologies”: electrochemistry, coagulation and flotation [5]. The factthat these processes are difficult to investigate separately in anoperational reactor offers a possible explanation for the lack of adetailed technical literature on EC technology [7].

The electrochemistry of the EC process involves parameters suchas potential and current distributions, which are influenced byaspects of cell geometry, electrode distance, electrolyte conductiv-ity, electrode arrangement, charge overpotential and concentrationoverpotential (defined for processes under mass transfer control).An improvement in the use of cell energy could be achieved by ananalysis of potential and current distribution. Of the three typesof distribution of current and potential (primary, secondary andtertiary), the use of primary distribution simplifies the analysis byassuming that overpotential is not an issue and that the effect isproduced only by the cell geometry [14].

In this paper, a methodology is presented for the analysis ofprimary potential and current distribution in an EC reactor consid-ering only the cell geometry. The results of the distribution analysiswere compared with experimental tests of the EC process. For thesetests, wastewater from the tissue paper industry was used as thetest sample.

2. Experimental details

2.1. Test sample

Based on a previous study [15], wastewater samples comingfrom a tissue paper factory were chosen for EC experiments. These

254 A. Vázquez et al. / Chemical Engineerin

Nomenclature

ji electrode current density (i = a or c) (A m−2)jave average current density (A m−2)L electrode width (cm)Ua potential at the terminal anode (V)Uc potential at the terminal cathode (V)x axial coordinatey axial coordinatew cell width (cm)l cell length (cm)Qv solution flow (L min−1)

Greek characters� electrolyte conductivity (�−1 m−1)

ss

2

r(vt1EmaFdssstaol

An analysis of the current density required for EC tests was

Fa

� potential in the solution phase (V)

amples were taken at the exit of a KROFTA® system used for solidseparation and then stored at 4 ◦C.

.2. Description of the EC cell

EC tests were conducted in an open cell similar to the oneeported in previous work [15]. The cell dimensions were: lengthl) 39 cm, width (w) 15 cm and height (h) 14 cm, with a totalolume capacity of 8.19 L and a total area of 291.5 cm2 per elec-rode. Aluminum plates were used as electrodes with a gap of

cm between anode and cathode to decrease the cell potential.leven plates were used (5 anodes and 6 cathodes) with an arrange-ent (geometry and placement) that allowed the formation of

single channel. This single channel is shown more clearly inig. 1 by a cross-sectional view from the bottom of the cell. Therawing shows three sections (A, B and C) denoted by a greyhade. A distinction among these sections is made because theections A and C have different distances between the anodeurface and the cell wall in the “x” direction and therefore con-ain a different amount of confined electrolyte. The section B is

lso different because the anode surface is between two cath-des. These differences affect the current distribution as shownater.

1 cm

Section BSection A

Inlet solution

ly

x

ig. 1. Drawing of a cross-sectional view from the bottom of the EC cell. The arrows shownd potential distributions were studied.

g Journal 179 (2012) 253– 261

2.3. Physicochemical analysis

All solutions employed were prepared using analytical gradereagents and deionized water of Millipore quality (18.2 M� cm−1).A Varian Model AA2200 atomic absorption spectrometer was usedto measure the concentration of metals in solution, and measure-ments of pH, turbidity and conductivity were made by means of aThermo Orion 420A pH meter, a portable HACH 2100P turbidimeterand a Thermo Orion 3 Star conductimeter, respectively. Measure-ments of chemical oxygen demand (COD) and biochemical oxygendemand (BOD) were performed following standard methods [16].

2.4. Mathematical study of current and potential primarydistribution analysis

Previous to the construction of the cell, an analysis of poten-tial distribution throughout the cell reactor and an analysis ofthree different zones (as shown in Fig. 1) for current distributionwere conducted. To evaluate the proposed electrode configura-tion, four cases were considered; the details are illustrated inFig. 2. In all cases, a gap of 2 cm between the edge of the elec-trodes and the cell wall was considered adequate to allow theflow of the solution through the cell. By insulating the edgesof the anode, the modification of the isopotential surfaces wasevaluated.

The theoretical analysis of primary distribution of current andpotential for the geometries sketched in Fig. 2 was performed bymeans of an approximation of the Laplace equation (see AppendixA) using the software COMSOL Multiphysics® 3.5 and a personalcomputer Dell® Optiplex 745 model with an Intel® CoreTM 2processor at 1.86 GHz and 2.99 GB of RAM memory. For this anal-ysis, a mesh was constructed that considered the geometry ofthe electrodes and included an approximate number of 9 × 104

elements.

∇2� = 0 (1)

2.5. Electrocoagulation experiments

performed, following a procedure similar to previous work [15].A monopolar arrangement with eleven aluminum plates (6 cath-odes and 5 anodes) connected in parallel was used, and all the

Section C

Anode

Cathode

Outlet solution

w

the direction of the solution flow. The grey shade shows the zones where current

A. Vázquez et al. / Chemical Engineering Journal 179 (2012) 253– 261 255

L= 13 cm

2 cm

Cell wall

Gap

h= 1

4 cm

Electrodea b

dc

L= 13 cm

2 cm

Cell wall

Gap

h = 1

4 cm

Electrode

1 cm in sulat ing

L= 13 cm

2 cm

Cell wall

Gap

h= 1

4 cm

Electrode

2 cm in sulating

L= 13 cm

2 cm

Cell wall

Gap

h = 1

4 cm

Electrode

1 cm insulating

Fig. 2. Electrode configurations to be evaluated (a) 2.0 cm gap, (b) 2.0 cm gap + 1.0 cm of insulation on the right edge of the anode, (c) 2.0 cm gap + 2.0 cm of insulation on theright edge of the anode, and (d) 2 cm gap + 1 cm of insulation on the right and left edges of the anode.

em

stwfltr

cwtloabfldttcoc

lectrodes were powered employing a Sorensen power supplierodel SGI60X83C.Due to the problems observed in a batch system because of

tagnant solutions, a continuous flow system was considered. Forhis system, changes in the electrode configurations and geometryere necessary to allow the flow of the solution (Fig. 1). A solutionow (Qv) of 1.6 L min−1 was chosen for all experiments becausehis flow allowed a constant solution volume to be kept in the celleactor.

The effect of potential and current distribution on the EC pro-ess was analyzed by turbidity, COD and BOD removal. The testsere performed following the conditions established in each of

he cases illustrated in Fig. 2. The edges of the anodes were insu-ated with plastic tape. To obtain measurements for the amountf aluminum produced, the electrodes were weighed before andfter the EC experiments. As Holt et al. [7] indicate, there shoulde an analysis not only of electrochemical aspects, but also ofotation characteristics, such as bubble density and bubble sizeistribution involved in the system. The bubble density relates tohe rate of generation of hydrogen bubbles in the cathode, and

he bubble size distribution relates to the hydrodynamics in theell. However, for the present time, only the efficiency of usef the energy applied and its effect on EC performance will beonsidered.

3. Experimental results

3.1. Analysis of potential distribution in an EC cell

For this analysis, calculations were made based on a schematicrepresentation of the geometric model for the section B of the ECcell (Fig. 1) and different electrode configurations (Fig. 2). Thus, foran electrode configuration in which there is a gap of 2 cm betweenthe edge of the anode and the cell wall (Fig. 2a), the graphs of poten-tial show that the distribution along the anode is uniform, but thereis an increase of the intensity of the electric field at the edges of theelectrode due to an excess of electrolyte in these zones (Fig. 3a).The accumulation of energy could result in an undesired evolutionof oxygen and, therefore, a decrease in the amount of aluminumproduced, as Canizares et al. [17] have shown experimentally. Toprevent an increase of the intensity of the electric field an insula-tion of one of the anode edges was made as proposed in Fig. 2band c. According to Fig. 3b and c, the isopotential surfaces on theanode edge without insulation did not show changes, while theisopotential surfaces on the insulated edge expanded to occupy

the interelectrodic space between the anode and cathode surfaces.This distribution did not depend on the extent of insulation used inboth cases (1 or 2 cm), it however will change the anode area avail-able for the EC process and therefore this change should also be

256 A. Vázquez et al. / Chemical Engineering Journal 179 (2012) 253– 261

e confi

etcpi

eiiatsaTnF

3

wtaodaa

c

(

(

Fig. 3. Primary distribution of potential throughout the EC cell for the electrod

valuated in terms of how to maximize the use of the energy onhe EC process. Also, the cathode’s edges that are adjacent to theell wall show changes on the isopotential surfaces, which wouldrovoke a low polarized zone and therefore an important decrease

n the current density.Finally, the effect of insulating both edges of the anode was

valuated (Fig. 2d). Fig. 3d shows, that in a similar fashion, thesopotential surfaces around the area where the second insulat-ng tape was placed (edge adjacent to the cell wall), are rearrangedlong the conductive section of the anodes, however an effect onhe cathode isopotential surfaces is also observed. The isopotentialurfaces around the edges of the cathodes decrease significantlynd shift direction towards the conductive section of the anodes.he isopotential surfaces around the insulated anode edges that areot adjacent to the cell wall show the same behavior described forig. 3b and c.

.2. Current distribution analysis

The analysis of the current distribution on the anode surfaceas made following the procedure described in Appendix A, and

he results are presented as the ratio of the current density and theverage current density on the anode (j/jave), which is a functionf the distance along the anode (y/L). It should be noted that theistance L, varies as function of the insulating section, thus to allow

comparative analysis y/L is presented as a fraction. Further detailsbout this are described in Appendix A.

The effect of placement of electrodes within the cell, on theurrent distribution for the four electrode configurations of Fig. 2

gurations illustrated in Fig. 2. The black shade represents the insulated edges.

was analyzed. According to Fig. 4, except when no insulation of theedges is made (Fig. 4a), the current distribution profile is indepen-dent of the position of the electrodes within the cell. These resultsindicate that the rate of dissolution of the anodes would be thesame in all zones of the cell. Given that sections A and C repre-sent the electrodes at the inlet and outlet of the cell, respectively;and section B represents mainly the rest of the electrodes, this lastwas chosen for the current distribution analysis that herein will bediscussed.

Fig. 5 shows the results of current distribution profiles for theelectrode configurations studied. It is important to highlight thatwhen no insulation of the edges of the anodes is made (Fig. 5a),three zones are distinguished:

a) a zone where current density distribution is uniform (centralzone);

b) a zone where the localized current density (j/jav) decreases upto 80%, corresponding to the zone where the electrode edge isnext to the cell wall (left zone); and

(c) a zone where the localized current density (j/jav) increases up to270%, corresponding to the zone where the edge of the electrodeis 2 cm from the cell wall (right zone).

This current distribution behavior is considerably modified

when the edges of the anodes are insulated, as illustrated inFig. 5b.

Hence it is shown that the current density distribution pro-file on the right zone of the anode (y/L > 0.95) is practically the

A. Vázquez et al. / Chemical Engineering Journal 179 (2012) 253– 261 257

0

0.5

1

1.5

2

2.5

3a b

c d

10.80.60.40.20

j/jav

e

y/L

Section ASection BSection C

0

2.5

5

7.5

10

12.5

10.80.60.40.20

j/jav

e

y/L

Section ASection BSection C

0

2.5

5

7.5

10

12.5

10.80.60.40.20

j/ jav

e

Section ASection BSection C

0

2.5

5

7.5

10

10.80.60.40.20

j/ jav

e

Section ASection BSection C

ensity

stusaeosiep

y/L

Fig. 4. Effect of placement of the electrodes within the cell on the current d

ame for the three configurations in agreement with the poten-ial distribution analysis (Fig. 3). In the central zone there still is aniform current distribution but the localized current decreaseslightly for the three configurations although is more notice-ble when both edges are insulated. For the left zone, when thedges are not insulated a decrease of the localized current isbserved; however, when this edge is insulated the electrode

hows a wider zone (y/L) of constant current (Fig. 5b) and anncrease in the localized current. This last, would imply that thenergy being applied could be more efficiently used on the ECrocess.

0

0.5

1

1.5

2

2.5

3

10.80.60.40.20

j/j av

e

y/L

a

Fig. 5. Effect of insulating the edges of the anodes on the current densit

y/L

distribution profiles for all the electrode configurations evaluated (Fig. 2).

3.3. Voltammetric analysis

Zaied and Bellakhal [18] reported that the rate of removal ofcontaminants is proportional to the current density applied. Sev-eral authors [3,6,17,19] have pointed out the importance of wateroxidation as a competing reaction, and Canizares et al. [17] haveshown experimental evidence of this process. Thus, using alu-

minum anodes, Canizares et al. [17] observed that applying currentdensities higher than 10 A m−2 affected the efficiency of the processdue to competition with parallel reactions, such as the oxidation ofwater.

-4

-2

0

2

4

6

8b

10.80.60.40.20

j/jav

e

y/L

1 cm2 cmBoth edges insulated

y distribution profiles, (a) without insulation (b) with insulation.

258 A. Vázquez et al. / Chemical Engineering Journal 179 (2012) 253– 261

-2

-1

0

1

2

3

4

5

1.510.50-0.5-1-1.5

j (A

m-2

)

E (V/SHE)

Fig. 6. Cyclic voltammogram obtained with an aluminum disc electrode in a syn-tis

mcittttbtmdtzaboroaloolso

TP

0

100

200

300

400

500

600

700

2402101801501209060300

Tur

budi

ty (N

TU

)

t (min)

100 A/m2

80 A/m2

40 A/m2

20 A/m2

10 A/m2

100 A m-2

80 A m-2

40 A m-2

20 A m-2

10 A m-2

hetic solution containing 800 mg L−1 of chloride ions and 3000 mg L−1 of sulfateons. A scan rate of 5 mV s−1 was used. The arrows indicate the direction of theweep potential.

Following the methodology of previous studies [20], the voltam-etric response of an aluminum electrode in a synthetic solution

ontaining 800 mg L−1 of chloride ions and 3000 mg L−1 of sulfateons was measured (Fig. 6). The voltammogram was initiated fromhe open circuit potential (−1.04 V/SHE) towards positive poten-ials at a scan rate of 5 mV s−1. The voltammetric response showedhat the dissolution of aluminum is slightly limited in the poten-ial region of −0.8 to −0.5 V, as depicted by the current plateau,ut at potentials above this region, the current density increases ashe potential increases. This diagram shows that the extent of alu-

inum dissolution is a function of either the potential or currentensity applied. Furthermore, according to the current density dis-ribution results, the extent of this reaction would depend on theone of the anode. For instance, if a potential of −0.266 V/SHE ispplied to this cell design, a current density of 0.8 A m−2 woulde expected if the distribution was uniform, as shown by resultsf the central zone of the anode (Fig. 5a). Conversely, the left andight zones of the anode show a decrease and increase, respectively,f the expected current density. On the left zone, for y/L < 0.2 thenode surface loses up to 80% of the applied current density. Thisoss of applied current density could result either in the formationf a passive layer (as depicted by the plateau on the voltammogram)

r in a decrease in the rate of aluminum dissolution because of aower energy supply. Meanwhile, the increase in local current den-ity in the right zone (y/L > 0.92) of the anode surface could favorxygen evolution and, therefore, produce a decrease in the amount

able 1hysicochemical analysis of the wastewater used in EC tests.

Parameters Units Waste water sample

Chemical oxygen demand (COD) mg L−1 1012Biochemical oxygen demand (BOD) mg L−1 300–450Turbidity NTU 500–600Total solids (TS) mg L−1 4400Suspended solids (SS) mg L−1 30Total dissolved solids (TDS) mg L−1 4360Conductivity mS cm−1 4.89pH – 7.2–7.7Cadmium mg L−1 <0.03Copper mg L−1 <0.07Nickel mg L−1 <0.16Lead mg L−1 <0.19Zinc mg L−1 0.57Sulfate mg L−1 3000Chloride mg L−1 880

Fig. 7. Effect of current density on the removal of turbidity from wastewater comingfrom a tissue paper factory.

of aluminum produced for coagulation [17]. The results in Fig. 5 sug-gest that an electrode configuration, such as that in Fig. 2a, wouldpresent a lower level of aluminum dissolution on 21% of the anodesurface.

3.4. Physicochemical analysis of the wastewater sample

Table 1 shows all the parameters that were analyzed to deter-mine the quality of the effluents that will be used to test theperformance of the EC process. According to these measurements,the pH of the effluents is normally neutral and there is a low con-centration of metal ions, decreasing the possibility of reactionsassociated with reduction of metals.

3.5. Electrocoagulation tests

The performance of the EC treatment of wastewater comingfrom the tissue paper industry was evaluated by means of turbiditymeasurements. Experiments using five different current densitieswere conducted to establish the optimal current density for clari-fication of the wastewater sample (Fig. 7).

The results of these experiments show that when a current den-sity of 10 A m−2 is used, 3 h are necessary to achieve 95% turbidityremoval. The process of turbidity removal involves three stages: (i)lag stage where turbidity either increases or keeps constant, (ii)reactive stage where turbidity removal starts and (iii) stabiliza-tion stage where turbidity removal reaches a constant value [4].For a current density of 10 A m−2, the lag stage lasts 60 min, a dura-tion unsuitable for application of the EC process. When the currentdensity is doubled (20 A m−2), the lag stage is reduced to 15 minand a turbidity removal of 96% is achieved in 90 min. When a cur-

−2

rent density of 40 A m is applied, the lag stage disappears and97% turbidity removal requires only 1 h. The use of higher currentdensities improves the kinetics of the EC process as expected, butthis improvement is particularly associated with reduction of the

Table 2Effect of current density on COD and BOD removal.

j (A m−2) % Removal COD % Removal BOD

100 27.48 20.8680 30.46 17.3940 28.53 17.3920 24.26 19.2310 27.03 17.85

A. Vázquez et al. / Chemical Engineering Journal 179 (2012) 253– 261 259

Table 3Effect of current density and potential distribution on the EC performance.

Anode configuration % RemovalCOD

% RemovalBOD

% RemovalTurbidity

Al produced(g L−1)

Al in solution(g L−1)

Energy consumption(kWh m−3)

No insulation 26.96 13.79 99 0.66 0.014 1.599 0.68 0.015 1.399 0.72 0.013 1.209 0.78 0.01 1.02

dt

A

A

A

atipfAoottr

Boscoc4a

op1vwe

epsr(attTrc

tneodta

0

100

200

300

400

500

600

120100806040200T

urbi

dity

(NT

U)

t (min)

Without insulator

1 cm insulator

2 cm insulator

Both edges insulated

1 cm of insulation on right edge 28.53 17.39 92 cm insulation on right edge 28.22 16.0 91 cm insulation on both edges 26.88 15.0 9

uration of the lag phase. Once the Al3+ is produced at the anode,he hydrolysis path and products can be summarized as:

l3+(aq) + H2O(l) → AlOH2+

(aq) + H+(aq) (2)

lOH2+(aq) + H2O(l) → Al(OH)2

+(aq) + H+

(aq) (3)

l(OH)2+

(aq) + H2O(l) → Al(OH)3(s) + H+(aq) (4)

According to Terrazas et al. [15], the monomeric species (AlOH2+

nd Al(OH)2+) are formed initially, and as the aluminum concen-

ration increases, the formation of Al(OH)3 is favored. At pH 7 (thenitial pH of the wastewater sample), the main mechanism forollutant removal is the adsorption of pollutants on the Al(OH)3ormed [21]. When the rate of aluminum ion formation is increased,l(OH)3 will be formed in a shorter time, and therefore, the durationf the lag phase will be reduced. Measurements of the conductivityf the medium show a reduction of this value lower than 10% fromhe original value (Table 1), thus this allows to be near to the condi-ion of constant conductivity that the mathematical model appliedequires (Appendix A).

On the other hand, Table 2 shows that the removal of COD andOD was not affected by current density, with a maximum removalf 30% for COD and 20% for BOD. Because the current density did noteem to affect the extent of COD and BOD removal, colloidal parti-les have a minor contribution to these removal values and solublerganic matter plays a more significant role. A further increase inurrent did not produce better COD and BOD removal results, and0 A m−2 was therefore chosen as the optimal current density forll the EC tests.

To determine whether the current density could have an effectn soluble organic matter when it is free of coagulates, tests wereerformed using filtered solutions from the EC experiments at00 A m−2. The results (not shown) revealed that the COD and BODalues did not change and that the potential achieved on the anodesas not sufficient to oxidize the soluble organic matter in the efflu-

nt.To evaluate the effect of current distribution on the EC process,

xperiments were performed using the electrode configurationsroposed in Fig. 2 and applying a current density of 40 A m−2. Fig. 8hows that insulation of the anodes produced an increase in theate of turbidity removal, although maximum turbidity removal99%) was achieved at the same time in all experiments. Results ofnalysis of current density distribution showed that insulation ofhe edges of the anodes produced a more uniform distribution onhe anode surface (Fig. 5) and therefore a better EC performance.he efficient use of energy favored the EC process due to a higherate of formation of aluminum ions, which increased the rate ofolloidal matter removal.

Results of measurements of COD and BOD removal for theseests showed that a more uniform current density distribution doesot affect these parameters, as the values were similar for all thelectrode configurations evaluated (Table 3). These results show

nce again that COD and BOD removal from this type of wastewatero not seem to be affected by the aluminum ions available andherefore EC should be used in conjunction with a technique ofdvanced oxidation [22].

Fig. 8. Effect on the EC performance of insulation of the anode edge for all theelectrode configurations shown in Fig. 2, j = 40 A m−2.

Thus, it is shown that an efficient use of the energy beingapplied to the EC cell, derived from a more uniform distribution ofcurrent, leads to a higher production of aluminum available forthe EC process, however, it is noticeable that the turbidity removalachieved in all cases is the same. We attribute this behavior to thefact that extending the EC time favors the chemical dissolution pro-cess of aluminum, since it is shown that the higher production ofaluminum is achieved with the lower energy consumption (whenboth edges of the anode are insulated), and therefore this aluminumcould not be totally produced by a faradaic process. This last impliesthat an improvement has to be made to prevent an unnecessary dis-solution of aluminum. Finally, it is evident that Al(OH)3 formationis favored given that the final concentration in solution is the samein all cases.

4. Conclusions

The present study showed that current and potential are notdistributed uniformly in a conventional cell and that there is anincrease of the intensity of the electric field density at the edges ofthe electrodes. This accumulation of energy can produce localizedzones of higher and lower current density than the current beingapplied. Placing an insulating material on the anode edges helped torearrange the isopotential surfaces towards the interelectrodic gapbetween cathode and anode, resulting in a more uniform currentdensity distribution with a higher localized current (j/jave > 1) onmost of the anode surface.

Theoretical analysis of distribution of primary current andpotential is a valuable tool that allows achievement of an adequatepreliminary electrocoagulation reactor design. The theoreticalanalysis predicts the effect of changing different parameters (such

as coagulant formation) on EC performance. In our study, the ECexperimental results showed that by improving current densitydistribution a more efficient use of the energy is achieved, and

260 A. Vázquez et al. / Chemical Engineerin

tc

A

umi

For a better illustration of the boundary conditions of the system,

Fig. A1. Scheme of section B showing boundary conditions.

herefore in this way one of the major concerns for EC development,ould be better addressed.

cknowledgements

The authors are grateful for the financial support of CONACyTnder grant SEP-CONACyT-61871 and the scholarship 217508 for

aster studies of A. Vázquez. The support of C. Hernández for chem-

cal analysis is also acknowledged.

Fig. A2. Illustration of metal dissolution when t

g Journal 179 (2012) 253– 261

Appendix A.

When the ion concentration is low, the ionic current in an elec-trochemical system can be described by the flux equation [14],provided that: (a) there is no accumulation of charge through-out the cell reactor, (b) the electrolyte concentration gradient isnegligible, (c) the electrolyte presents a uniform conductivity, and(d) there is a uniform current density along the aluminum anode.Under these conditions, the general flux equation can be simplifiedto:

∂2�

∂x2+ ∂2�

∂y2= 0 (A.1)

where � represents the solution potential. Assuming that themetallic phase of the electrodes is isopotential and the overpoten-tials at the interface are negligible, the primary current distributioncan be calculated under the following boundary conditions:

at the anode,

� = Ua (A.2)

at the terminal cathode,

� = Uc (A.3)

at the insulating walls

∂�(x, y)∂x

= 0 at x = 0 and x = l (A.4)

and

∂�(x, y)∂y

= 0 at y = 0 and y = w (A.5)

Fig. A1 shows a schematic representation of the geometric modelfor the section B, used to calculate the potential distribution in thecell.

here is non-uniform current distribution.

ineerin

rbt

ott

tw

j

1tcs

tttrw

ntjwsod

R

[

[

[

[

[

[

[

[

[

[

[

A. Vázquez et al. / Chemical Eng

After calculating the potential distribution in the cell, the theo-etical current density (ji) on the electrode surface can be calculatedy means of Eq. (A.6), using the data for the potential values nearhe electrode (�s).

∂�s

∂x= − ji

�with i = a or c at x = 0

and x = l for 0 < y < 0.86w (A.6)

According to Eq. (A.6) the value of ji is proportional to the valuef �s. If there is an increment in the intensity of the electric field,he current density in that zone will be higher than in zones wherehe intensity of the electric field is lower.

To represent the current distribution on the electrode surfacehe ratio of j/jave is used, with jave obtained by means of Eq. (A.7),here n represents the number of local current data points,

ave = 1n

n∑

k=1

jk = j1 + j2 + ... + jnn

(A.7)

In the case of non-insulating anodes (L = 13 cm), n is equal to20 points. As the edge(s) are insulated, L decreases and thereforehe number of points. Thus to make a comparative analysis of theurrent distribution results for the various cases considered in thistudy, the local current (jk) is plotted as a fraction of L.

When the ratio j/jave is equal to 1, the current density distribu-ion is considered uniform, and therefore, all local currents (jk) arehe same on the electrode surface. The current density correspondso the current being applied to most of the electrode surface. If theatio j/jave is lower than 1, there are spots on the electrode surfacehere the current density is lower than the current being applied.

Fig. A2 illustrates an example of the effects that can arise from aon-uniform current density distribution when an aluminum elec-rode is subjected to electrodissolution. Fluctuations in the ratio/jave are an indication of different local (y/L) current density values

ith respect to the average value. These different local current den-ity values produce a non-uniform surface dissolution. The analysisf this ratio is therefore very important, as it allows predicting theistribution of energy on the electrodes for a given cell design.

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