Chemical Engineering Science 57 (2002) 2449–2455www.elsevier.com/locate/ces

Investigation on the electrolysis voltage of electrocoagulationXueming Chen, Guohua Chen ∗, Po Lock Yue

Department of Chemical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received 29 August 2001; accepted 27 February 2002

Abstract

The relation between electrolysis voltage and the other variables of an electrocoagulation process was analyzed. Theoretical modelsdescribing such a relation were established. Experiments were conducted to con4rm the theoretical analysis and to determine the constantsin the models. Both the theoretical analysis and experiments demonstrated that water pH and 7ow rate had little e8ects on the electrolysisvoltage within a large range. The electrolysis voltage depends primarily on the inter-electrode distance, conductivity, current density andthe electrode surface state. The models obtained can be used to calculate the total required electrolysis voltage for an electrocoagulationprocess. ? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Model; Overpotential; Aluminum electrode; Water; Wastewater

1. Introduction

Electrocoagulation is an e8ective process to destabilize4nely dispersed particles for water and wastewater treat-ment. It has been successfully used to treat potable water(Vik, Carlson, Eikum, & Gjessing, 1984), urban wastew-ater (Pouet & Grasmick, 1995) and a variety of industrialwastewaters (Dobolyi, 1978; Pazenko, Khalturina, Kolova,& Rubailo, 1985; Balmer & Foulds, 1986; Demmin &Uhrich, 1988; Renk, 1988; Do & Chen, 1994; McClung& Lemley, 1994; Lin & Peng, 1996; Chen, Chen, & Yue,2000a, b).

Usually, aluminum or iron plates are used as electrodesin the electrocoagulation process. When a DC voltage isapplied, the anodes sacri4ce themselves to produce Al3+

or Fe2+ ions. These electrochemically generated metallicions are good coagulants. They can hydrolyze near theanodes to produce a series of activated intermediates thatare able to destabilize the 4nely dispersed particles presentin the water=wastewater to treat. The destabilized particlesthen aggregate to form 7ocs. At the meantime, the tinyhydrogen bubbles produced at the cathode can 7oat most7ocs formed, reaching e8ective separation of particles fromwater=wastewater. Compared with conventional coagula-tion, electrocoagulation has many advantages. Firstly, itis more e8ective in destabilizing small colloidal particles.

∗ Corresponding author. Tel.: +852-2358-7138; fax: +852-2358-0054.E-mail address: kechengh@ust.hk (Guohua Chen).

Secondly, it is able to ful4ll simultaneous coagulation and7otation, with less sludge produced. Thirdly, the electroco-agulation equipment is very compact and thus suitable forinstallation where the available space is rather limited. Fur-thermore, the convenience of dosing control only by adjust-ing current makes automation quite easy.

Although electrocoagulation has been available for morethan a century, nowadays the design of an industrial electro-coagulation unit is still mainly based on empirical knowl-edge due to the lack of available models. The electrolysisvoltage is one of the most important variables. It is stronglydependent on the current density, the conductivity of thewater=wastewater to treat, the inter-electrode distance, andthe surface state of electrodes. A model involving termsof activation overpotential, concentration overpotential andohmic drop of the solution resistance has been proposedby Vik et al. (1984). However, that model cannot directlypredict the electrolysis voltage because it still contains un-known terms including the activation overpotential and theconcentration overpotential. In fact, these unknown overpo-tentials can be related to other simple variables accordingto the Tafel equation and Nernst equation. Therefore, it ispossible to obtain simpli4ed models for the estimation ofelectrolysis voltage.

The objectives of the present study are to establish the the-oretical models regarding the electrolysis voltage requiredin the electrocoagulation process and to verify them experi-mentally. Since the dispersed particles in water=wastewaterdo not take part in the electrochemical reactions during elec-trocoagulation, the electrochemical behavior performed in

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S 0009 -2509(02)00147 -1

2450 X. Chen et al. / Chemical Engineering Science 57 (2002) 2449–2455

real water=wastewater should be similar to that carried outin aqueous solutions. Therefore, in this work, all experi-ments were conducted in the synthesized Na2SO4 solutionsfor the purpose of easy control of conductivity. In addition,aluminum electrodes were used because they are the mostcommon electrodes found in industrial applications.

2. Theoretical analysis

When current passes through an electrochemical reactor,it must overcome the equilibrium potential di8erence, an-ode overpotential, cathode overpotential and ohmic poten-tial drop of the solution (Scott, 1995). The anode overpo-tential includes the activation overpotential and concentra-tion overpotential, as well as the possible passive overpo-tential resulted from the passive 4lm at the anode surface,while the cathode overpotential is principally composed ofthe activation overpotential and concentration overpotential.Therefore,

U0 = Eeq + �a;a + �a;c + �a;p + |�c;a| + |�c;c| + dj: (1)

When aluminum is used as electrode material, there arethree major reactions in the electrochemical reactor as fol-lows:(i) The oxidation reaction at the anode,

Al − 3e = Al3+;

’Al3+=Al = ’oAl3+=Al +

RT3F

lnC∗Al3+ :

(ii) The reduction reaction at the cathode,

2H+ + 2e = H2;

’H+=H2 = ’oH+=H2

+RT2F

lnC∗2

H+

PH2

:

(iii) The hydrolysis reaction,

Al3+ + 3H2O = Al(OH)3 + 3H+;

Kh =C∗3

H+

C∗Al3+

(2)

The equilibrium potential di8erence between the anodeand the cathode is

Eeq = ’Al3+=Al − ’H+=H2 ;

i.e.

Eeq = ’oAl3+=Al − ’o

H+=H2+

RT3F

ln(pH2)

3=2

Kh: (3)

Eq. (3) suggests that Eeq is not a8ected by pH. The acti-vation overpotential can be calculated from Tafel equationwhen the current density is relatively large as is the case formost industrial installations

�a;a = aa + ba ln j; (4)

|�c;a| = ac + bc ln j: (5)

0

Anode surface

Diffusion layer

H+

OH_

Al3+

x

Fig. 1. Concentration variation of Al3+, H+ and OH− near the anode.

In an electrochemical reaction, the mass transport includesdi8usion, convection and electric migration, and can be cal-culated by Nernst–Plank equation (Bard & Faulkner, 1980)

Jj(x) = −Dj@Cj(x)@x

− zjFDjCj(x)RT

@�(x)@x

+ Cj(x)v(x)

or

Jj(x) = −Dj@Cj(x)@x

+ ujCj(x)@�(x)@x

+ Cj(x)v(x):

The total current is contributed by all ions present in thewater=wastewater

j = F�zjJj

= F�zj

[−Dj

@Cj(x)@x

+ ujCj(x)@�(x)@x

+ Cj(x)v(x)]

or

j = �{zjF

[−Dj

@Cj(x)@x

+ Cj(x)v(x)]

+ tjj}:

Near the electrode surface, the convective 7ux term iseliminated (Scott, 1995). Moreover, within the di8usionlayer adjacent to the anode surface, except for electrochem-ically and chemically reactive ions including Al3+, H+ andOH−, non-reactive ions such as Na+, SO2+

4 , and so on, canproduce a gradient of concentration and thus cause a dif-fusion current which is equal but opposite to the migra-tion current at steady state. Consequently, the net trans-port and the net current of ions except for Al3+, H+, OH−

through the anode di8usion layer is zero. Fig. 1 illustratesthe concentration variation of Al3+, H+ and OH− near the

X. Chen et al. / Chemical Engineering Science 57 (2002) 2449–2455 2451

anode. In the practical application, although the original pHof water=wastewater may be low or high, the in7uent pH isusually controlled in a mediate range as the best electroco-agulation eMciency is commonly achieved in that pH range.Because of this, concentrations of H+ and OH− near theanode are relatively low and can be neglected. The total cur-rent in the circuit is then composed primarily of the currentfrom migration and di8usion of Al3+, that is

j = −3FDAl3+@CAl3+ |x=0

@x+ tAl3+j:

Suppose that Al3+ concentration varies linearly across thewhole di8usion layer, that is

@CAl3+ |x=0

@x=

CAl3+ |x=0 − C∗Al3+

a;

then

j = 3FDAl3+

CAl3+ |x=0 − C∗Al3+

a+ tAl3+j:

Usually, C∗Al3+�CAl3+ |x=0.

Thus,

CAl3+ |x=0 =(1 − tAl3+)j a

3FDAl3+:

a depends on the turbulence of water or wastewater 7ow.In the electrocoagulation process, the turbulence is causedmainly from the agitation of the hydrogen gas generated atthe cathode because the 7ow rate through an electrochemicalreactor is slow. The larger the current density, the more thegenerated hydrogen gas and thus the thinner the a. Supposea power-law relationship exists between a and j, that is

a = k1j−p;

then

CAl3+ |x=0 =k1(1 − tAl3+)j1−p

3FDAl3+: (6)

C∗Al3+ can be calculated from Eq. (2) as

C∗Al3+ =

C∗3H+

Kh: (7)

Therefore,

�a;c =RT3F

lnCAl3+ |x=0

C∗Al3+

=RT3F

lnk1Kh(1 − tAl3+)j1−p

3FDAl3+C∗3H+

: (8)

Similarly, the net transport and thus the net current of ionsexcept for H+, OH− through the cathode di8usion layer iszero. Fig. 2 illustrates the concentration variation of H+ andOH− near the cathode. Because H+ is reduced to producehydrogen gas, pH near the cathode is alkaline even if bulkpH is acidic but not extremely strong. In other words, theconcentration of OH− near the cathode is much higher thanthat of H+ and hence the current there comes predominantly

x0

Cathode surface

OH_

Diffusion layer

H+

Fig. 2. Concentration variation of H+ and OH− near the cathode.

from the di8usion and migration of OH−

j = −FDOH−@COH− |x=0

@x+ tOH−j:

An analogous approximation is to assume a linear varia-tion of OH− concentration across the whole di8usion layer,which is valid when bulk pH is not far away from neutral.Then

@COH− |x=0

@x=

C∗OH− − COH− |x=0

c:

Thus,

j = −FDOH−C∗

OH− − COH− |x=0

c+ tOH−j:

Usually, C∗OH−�COH− |x=0, thus

COH− |x=0 =(1 − tOH−)j c

FDOH−:

Similarly, suppose c = k2j−q, then

COH− |x=0 =k2(1 − tOH−)j1−q

FDOH−:

The corresponding concentration of H+at the cathode sur-face can be calculated according to the ion product of water

CH+ |x=0 =Kw

COH− |x=0

or

CH+ |x=0 =KwFDOH−

k2(1 − tOH−)j1−q : (9)

2452 X. Chen et al. / Chemical Engineering Science 57 (2002) 2449–2455

Thus,

|�c;c|= RTF

lnC∗

H+

CH+ |x=0

=RTF

lnk2(1 − tOH−)j1−qC∗

H+

KwFDOH−: (10)

Combining Eqs. (3)–(5), (8) and (10), Eq. (1) can berewritten as

U0 =’oAl3+=Al − ’o

H+=H2+

RT3F

ln(pH2)

3=2

Kh+ aa + ac

+RT3F

lnk1Kh(1 − tAl3+)

3FDAl3+

+RTF

lnk2(1 − tOH−)KwFDOH−

+ �a;p +dj

+[ba + bc +

RT (1 − p)3F

+RT (1 − q)

F

]ln j: (11)

Let

A=’oAl3+=Al − ’o

H+=H2+

RT3F

ln(pH2)

3=2

Kh+ aa + ac

+RT3F

lnk1Kh(1 − tAl3+)

3FDAl3++

RTF

lnk2(1 − tOH−)KwFDOH−

and

K1 = ba + bc +RT (1 − p)

3F+

RT (1 − q)F

;

then Eq. (11) becomes

U0 = A + �a;p +dj + K1 ln j: (12)

It should be noted that the passive overpotential highlydepends on the electrode surface state. For the newnon-passivated aluminum electrodes, the passive overpo-tential can be neglected and Eq. (12) simpli4es to

U0 = A +dj + K1 ln j: (13)

For the old passivated aluminum electrodes, the passiveoverpotential is usually signi4cant. It is related to many fac-tors including pH, conductivity and current density. How-ever, taking into account the fact that pH close to the anodeis always acidic as long as bulk pH is not overly alkaline,it can be generally believed that �a;p depends mainly onthe conductivity and current density. Usually, �a;p increaseswith the current density and decreases with the conductivity.Assuming a power-law relation of �a;p with j and , then

�a;p =K2j n

m :

Therefore, for old passivated aluminum electrodes

U0 = A +dj + K1 ln j +

K2j n

m : (14)

On the right-hand side of Eqs. (13) and (14), both K1

and K2 are constants. Although A is related to tAl3+ and

tOH− , it approaches constant when is large. This is becausetAl3+ and tOH− approach zero at large . Eqs. (13) and (14)indicate that U0 is independent on pH. The values of A, K1,K2, m, n, need to be determined experimentally.

3. Experimental veri�cation

To con4rm the theoretical analysis, a series of experi-ments was conducted at di8erent pH, 7ow rate, current den-sity, conductivity and anode surface state. The experimentalsetup is schematically shown in Fig. 3. It consists of an elec-trocoagulation system, a DC power supply (PD 110 −5 AD,Kenwood TMI Corporation, Japan), a feed tank and a micro-processor pump (Model 7518-12, Master7ex, Cole-ParmerInstrument Co., USA). The electrocoagulation system hasan electrochemical reactor of 0:30 L and a separator of 1:2 l.The electrochemical reactor contains 4ve aluminum elec-trodes connected in a bipolar mode. The original dimensionof each electrode is 140 mm×44 mm×3 mm. Water 7owsthrough the electrochemical reactor upward, perpendicularto the electric current. Deionized water was used in all theexperimental runs. The conductivity and pH were adjustedby adding Na2SO4 (100 g=L) solution and H2SO4 (0:1 M)or NaOH (0:1 M) solution. Water pH and conductivity weremeasured using pH meter (Model 420A, Orion Research Inc,USA) and conductivity meter (Checkmate 90, Corning In-corporated Scienti4c Products Division, USA), respectively.

1 2

34

5

6

Sludge

Effluent

Influent

+_

1. Tank 2. Microprocessor Pump 3. Electrocoagulation System4. Electrochemical Reactor 5. Separator 6. D.C. Power Supply

Fig. 3. Schematic diagram of experimental setup.

X. Chen et al. / Chemical Engineering Science 57 (2002) 2449–2455 2453

The experiments were carried out in two stages. The 4rststage experiments were conducted after the electrodes hadbeen used for about a month. At this stage, the anode surfacelooked still relatively smooth, thus could be considered asnot passivated. The second stage experiments were doneafter the electrodes had been used for more than 3 months.At this stage, the anode surface was full of pits and coveredwith metal oxide, i.e. the anodes have been passivated.

4. Results and discussion

4.1. E.ect of pH

The theoretical analysis has demonstrated that the elec-trolysis voltage between electrodes is independent of pH aslong as water is not far away from neutral. In order to con-4rm it, electrolysis voltages were measured at di8erent pHvalues. It was found that the e8ect of pH on U0 was reallyinsigni4cant for both new and passivated electrodes. For thenew electrodes, an increase in pH from 3.75 to 10.41 re-sulted in only an increase in U0 from 13.2 to 13:8 V evenat a current density as high as 137 A=m2. For the passivatedelectrodes, when pH varied from 3.38 to 10.79, the maxi-mum di8erence of U0 measured at a constant current den-sity was only 7.7%. Therefore, both results from new andpassivated electrodes support the theoretical analysis well.

4.2. E.ect of water /ow rate

In the theoretical analysis, the water 7ow rate was as-sumed not to a8ect the electrolysis voltage signi4cantly.This needs to be veri4ed experimentally. Although a slightdecrease in U0 was found as 7ow rate increased from 3 L=hto 15 L=h using new electrodes, the extent of such a de-crease was always less than 10%. In contrast, when the cur-rent density varied from 20 to 100 A=m2, almost 4vefold in-crease in electrolysis voltage was measured. For passivatedelectrodes, it was found that the electrolysis voltage was al-most the same within the investigated water 7ow rate rangeof 1.8–21:6 L=h. This phenomenon is expected because therough surface of passivated electrodes makes the e8ect of7ow rate on turbulence insigni4cant. Such results supportthe assumption made earlier regarding the e8ect of 7ow rate.

4.3. Dependence of U0 on j and

Fig. 4 demonstrates the electrolysis voltage between elec-trodes as a function of the conductivity and current densityfor non-passivated electrodes. Through nonlinear regressionof the data in Fig. 4, the constant and coeMcient in Eq. (13)were obtained as A = −0:76, K1 = 0:20. Hence

U0 = −0:76 +dj + 0:20 ln j: (15)

Current density/A m−2

0

U0/V

0

5

10

15

20

25

κ = 355 µs/cm

κ = 578 µs/cm

κ = 908 µs/cm

κ = 1210 µs/cm

κ = 2090 µs/cm

10 20 30 40 50 60 70 80 90 100 120 130 140110

Fig. 4. Dependence of electrolysis voltage on conductivity and currentdensity for non-passivated electrodes. Inter-electrode distance 6:4 mm, pH7.20–7.37, temperature 22.5–23:8

◦C, 7ow rate 6 l=h.

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

U0/V

Current density/A m−2

κ = 445 µs/cm

κ = 849 µs/cm

κ = 1390 µs/cm

κ = 2120 µs/cm

κ = 3130 µs/cm

Fig. 5. Dependence of electrolysis voltage on conductivity and currentdensity for passivated electrodes. Inter-electrode distance 7:0 mm, pH6.95, temperature 21.9–22:8

◦C, 7ow rate 6 l=h.

It shows in Fig. 4 that good agreement exists betweenthe measured and predicted U0 for large solution. This isexpected because A is a constant only when is large. Al-though there is considerable di8erence in for di8erent in-dustrial operation, it is usually within the range investigatedin this study. Thus, the present model can be applied withoutmuch error. The constant A has a negative value, which isattributed to the large but negative standard electrode poten-tial di8erence between the anode and the cathode, −1:706 Vat 25◦C.

Better prediction was obtained for passivated electrodesas shown in Fig. 5. This may be because the power-lawterm with regard to j accommodates partially the variationof A with . Again the constants in Eq. (14) were obtained

2454 X. Chen et al. / Chemical Engineering Science 57 (2002) 2449–2455

through nonlinear regression, and the equation became

U0 = −0:43 +0:0160:47 j0:75 +

dj + 0:20 ln j: (16)

WithU0 obtained, the total required electrolysis voltageUof an electrocoagulation process can be calculated easily. Ingeneral, there are two basic electrode connection modes: themonopolar mode and the bipolar mode. For the monopolarmode, the total required electrolysis voltage is the same asthe electrolysis voltage between electrodes, that is

U = U0: (17)

For the bipolar mode, the total required electrolysis volt-age is U0 times the number of total cell which is the numberof electrodes minus one. Thus

U = (N − 1)U0: (18)

5. Conclusions

Theoretical analysis and experiments demonstrated thatwater pH and 7ow rate had little e8ects on the electroly-sis voltage of electrocoagulation process. Two mathematicalmodels, one applicable to non-passivated aluminum elec-trodes and the other to passivated aluminum electrodes wereestablished and veri4ed. With these models the total requiredelectrolysis voltage of an electrocoagulation process can becalculated.

Notation

aa constant of Tafel equation at the anode, Vac constant of Tafel equation at the cathode, Vba coeMcient of Tafel equation at the anode, Vbc coeMcient of Tafel equation at the cathode, VC∗j bulk concentration of species j, mol=l

Cj(x) concentration of species j at distance x, mol=lCj|x=0 concentration of species j at the electrode surface,

mol=ld net distance between electrodes, mDj di8usion coeMcient of species j, m2=sEeq equilibrium potential di8erence between an anode

and a cathode, VF Faraday constant, C=molj current density, A=m2

Jj(x) 7ux of species j at distance x, mol=m2 sKh hydrolysis constantKw ion product of waterm constantn constantN total electrode number of an electrocoagulation unitp constantq constant

pH2 fractional pressure of hydrogen at the cathode, atmR gas constant, J=mol KT absolute temperature, Ktj transport number of species jU total required electrolysis voltage of an electroco-

agulation process, Vuj mobility of species j, m2=V sU0 electrolysis voltage between electrodes, Vv(x) convective velocity of water 7ow in the current

direction at distance x, m=szj charge number of species j

Greek letters

a di8usion layer thickness near an anode, m c di8usion layer thickness near an cathode, m�a;a anode activation overpotential, V�a;c anode concentration overpotential, V�a;p anode passive overpotential, V�c;a cathode activation overpotential, V�c;c cathode concentration overpotential, V conductivity of water=wastewater treated, mho=m�(x) potential at distance x, V

Acknowledgements

The authors wish to acknowledge the Environment andConservation Fund=WooWheelock Green Fund for the 4-nancial support of this project.

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