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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol. 15 n. 4 São Paulo Dec. 1998 



Universidade Estadual de Campinas, Fac. Engenharia Mecânica, Departamento de Engenharia de Materiais, Caixa Postal 6122, 13083-970, Campinas, SP, Brazil.


(Received: August 2, 1998; Accepted: October 20, 1998)


Abstract - The removal of lead from an acid borate-nitrate solution containing Pb(II) was used to characterize the mass transport properties of an electrolytic reactor with reticulated vitreous carbon cathodes, operated in the flow-through mode. Current potential curves recorded at a rotating vitreous carbon disc electrode were used to determine the diffusion coefficient for Pb(II) under the conditions of the experiments. The performance and figures of merit of the electrolytic reactor were investigated by using different flowrates and cathode porosities. Dimensionless Sherwood and Reynolds numbers were correlated to characterize the mass transport properties of the reactor, and they were fitted to the equation Sh=24Re0.32Sc0.33.
Keywords: Porous eletrodes, electrolytic treatment of wastewater, electrolytic reactors.




The environmental sciences have experienced enormous progress in the last several years. The necessity of planning the rational use of energy and water resources has provided a challenge to the applied sciences and engineering to develop new technologies, new processes and new materials for pollution prevention and control. This is also a consequence of the increasing legal pressures that are forcing industry to accept responsibility for waste treatment or storage in an attempt to minimize pollution. The permanent responsibility to care for waste materials "from cradle-to grave" is encouraging not only a move towards zero-effluent discharge but also towards the adoption of solutions at the source of effluents rather than at the end of the industrial process.

Aqueous effluents containing metallic ions are conventionally treated on the basis of chemical precipitation of insoluble salts and hydroxides. For some metals, conventional treatment efficiently complies with the legislation on final discharge. The major drawback of precipitation treatment is the sludge that remains after the separation of the solid phase. Sludge storage or disposal is the responsibility of the industries that are forced by legal restriction to care for the waste. Electrochemical technology offers an efficient means of controlling pollution as it provides removal of transition and heavy metals via redox reactions without the disadvantages of conventional treatment. Indeed, electrons are the only reactant added to the treatment process that produces absolutely no by-products. The literature on electrolytic metal ion removal from aqueous solutions using porous electrode cells is extensive (Alkire and Ng, 1977; Tentorio and Casolo-Ginelli, 1978; Sioda and Piotrowska, 1980; Simonssom,1984; Carta et al., 1991; Pletcher et al., 1991a; Pletcher et al., 1991b; Wang and Dewald, 1983; Abda et al., 1991; Oren and Soffer, 1983; Matlosz and Newman, 1986; Langlois et al., 1989; Bockris et al., 1994). By flowing simulated effluents containing metal ions through three-dimensional porous cathodes, it is possible to achieve both high mass transfer rates and large surface areas for the electrochemical reaction. Metals in such solutions are reduced at the inner surface of the porous electrodes as the electrolyte is percolated through the cell. In the past, an investigation reported the results obtained for the removal of Pb(II) from different pH 2 aqueous media (Ponce de Leon and Pletcher, 1996). The experiments were conducted in a flow-by cell with a reticulated vitreous carbon (RVC) electrode. More recently, a flow-through cell with an RVC cathode was designed for lead removal, and optimization studies have been carried out using solutions with characteristics closer to those presented by a real aqueous waste from the electroplating industry (Widner et al., 1998). Drag-out from lead plating bath to the rinsing water tank results in a borate/nitrate solution of Pb(II) with a pH ranging from 4 to 6. Lead also enters waterways via effluent discharges from the explosive producing and battery manufacturing industries.

In this paper we continue the study presented earlier (Widner et al., 1998) and present the figures of merit of the flow-through electrolytic cell with a porous cathode of RVC. The mass transfer performance of the electrolytic reactor is presented using dimensionless numbers of Re, Sh and Sc. A mathematical relationship between them, which maximizes the rate of mass transport to the cathode surface, is investigated.



The development of the electrolytic cell for Pb(II) removal was carried out in two stages. Initially, a voltammetric study of the Pb(II) reduction reaction on a glassy carbon rotating disc electrode was performed in order to determine the range of potentials over which this reaction is controlled by mass transfer. Subsequently, a potential value within this interval was selected and applied to a flow-through electrolytic cell containing a reticulated vitreous carbon cathode. Electrolyte flow rate and cathode porosity were varied in order to establish the best conditions for lead removal.

All electrochemical experiments were performed using a Model 273 A potentiostat/galvanostat system controlled by the Electrochemical 270/250 software (both from EG&G Princeton Applied Research Corporation). At both stages, three-electrode cells were used, as described below. A Model 3110 Perkin Elmer spectrometer was employed to determine the Pb(II) concentration, using an air/acetylene flame. All reagents were of analytical grade and none underwent further purification. Distilled and deionized water was used to prepare all solutions. The solution was prepared from Pb(NO3)2 in such a way that the Pb(II) concentration was 50 mg dm-3, using boric acid (0.5 M) and sodium nitrate (0.05 M) as the supporting electrolyte. The resulting solution presented a pH of 4.8.

The hydrodynamic voltammetric experiments were carried out in a conventional three-electrode cell. A glassy carbon rotating disc electrode (GCRDE) Model 616 (PARC) was used as the working electrode. A platinum counter electrode, and a saturated calomel reference electrode (SCE) within a Luggin capillary were also used. The glassy carbon electrode was polished to a mirror-like surface, using 0.04 m m alumina slurries on polishing cloth. The complete procedure used to obtain the current-voltage curves for lead reduction reaction is summarized elsewhere (Widner et al., 1998).

The dual continuous-flow cell design is described in detail elsewhere (Widner et al., 1998; Bertazzoli et al., 1997). The electrochemical cell shown in Figure 1 was made from five Nylon® plates (13 x 30 x 1.25 cm) mounted in the form of a "sandwich." The cell was divided into one cathodic and two interlinked anodic compartments, separated by a Nafion® 450 membrane. The cathodic compartment consisted of a rectangular frame in which a block of reticulated vitreous carbon (5.0 x 15.0 x 1.25 cm) was fixed. Two stainless steel sheets (5.0 x 15.0 x 0.05 cm) comprised the anodes. A saturated calomel reference electrode within a Teflon® Luggin capillary entered the catholyte compartment through a hole drilled in the upper side of the RVC cathode-containing frame. The cell had two electrolyte entrances and two electrolyte exits. In this system, the electrolytes flow separately and simultaneously in a closed circuit through the catholyte and anolyte compartments. The anolyte composition was the same as that of the catholyte, but without Pb(II). The flowrates of both electrolytes were adjusted to the same value (60 dm3 h-1, 120 dm3 h-1 or 240 dm3 h-1). Then a constant potential of -0.8 V vs. SCE was applied to the cell. At predetermined time intervals, the solution leaving the cathodic compartment was sampled and the remaining Pb(II) concentration was quantified by atomic absorption spectrometry. The above procedure was also used to examine the efficiency of RVC cathodes of different porosities (20, 45, 60 and 80 ppi).


Figure 1: Expanded view of the electrolytic reactor with a three-dimensional porous cathode of vitreous carbon, used for lead removal.



In a simple batch electrolytic reactor, with a constant volume of electrolyte VT, the reactant will decay from initial concentration C(0) to a value C(t) at time t. The rate of change of the reactant concentration is (Rajesshwar and Ibañez, 1997)


if we assume that the reaction displays first-order kinetics with respect to the reactant. A mass balance in the reactor may be written by relating dC(t)/dt to the cell current as follows:


where i(t) is the instantaneous current at time t and, under mass transport control and by definition of mass transport coefficient, km (Pletcher et al., 1991a),


with n, A and F being the number of electrons changed, the area of the electrode and the Faraday constant, respectively, and im, the limiting current. Substitution of equation (3) into equation (2) and integration gives


where k = (kmA)/VT

Equation (4) describes the reactant concentration as a function of time of electrolysis, and it may be applicable to the case of a single-pass reactor since t is considered as the residence time and is expressed as t = VT/ Q where Q is the flowrate. Therefore, equation (4) may be rewritten as


In this study the electrolytic cell was operated in recycle mode, in a closed flow circuit, where the solution was pumped from the catholyte reservoir to the cell, as described previously (Widner et al., 1998; Bertazzoli et al., 1997). The volume of the reservoir (VT) was much greater than that of the cell inner volume (VC), such that VT/VC=37. If one considers that cell volume VT passes through the reactor n times as a cascade of reactors, the term in exponential equation (5) is multiplied by n that is equal to Qt/VT . Replacing n in equation (5), it becomes equation (4) again. This shows that the present system may be modelled very satisfactorily as a simple batch reactor and there is no need to use a batch-recycle model. As the electrolytic reactor designed for this study uses a three-dimensional porous cathode, the total area of the electrode is considered to be (Langlois and Coeuret, 1989)


where Ae is the specific surface area, or the active area per unit volume of the cathode, and Ve is the volume of the electrode, such that equation (4) becomes


Mass transport data were correlated using the following dimensionless relationship valid for a great variety of electrolytic reactor designs (Rajesshwar and Ibanez, 1997):


where the Sherwood, Reynolds and Schmidt numbers are defined by






u , r , m and D are the linear flowrate, fluid density, fluid viscosity and diffusion coefficient, respectively. The characteristic length, or hydraulic diameter, L, was based on the channel dimensions, being calculated as


where W and T are the width and thickness of the channel that are also the dimensions of the cathode. Equations (8), (9), (10) and (12) show that physical parameters can be changed for optimisation of the removal rate.



As stated earlier, this investigation was accomplished in two phases. In order to determine the appropriate reduction potential for the removal of Pb(II) ions from the chosen medium, where reduction reaction takes place under mass transfer control, a preliminary hydrodynamic voltammetric study was carried out. Subsequently, this potential was applied to the electrolytic cell under several combinations of electrolyte flow rate and RVC cathode porosity.

Voltammetric Experiments

Figure 2 shows a series of voltammograms obtained in the hydrodynamic mode for the solution containing 50 mg dm-3 of lead in the supporting electrolyte, as described in the experimental section. The potential was scanned on a glassy carbon rotating disc electrode (area = 0.12 cm2), using five different rotation rates (400, 900, 1,600, 2,500 and 3,600 rpm). It should be noted that, in the cathodic scan, all the curves show waves for the reduction of Pb(II) to Pb, with a well-defined limiting current plateau extending over a large potential range. The value of the limiting current was dependent on the glassy carbon electrode rotation rate. This behavior is characteristic of a mass-transfer controlled process. According to the literature, application of the Levich equation is an appropriate test to verify whether an electrode process is conducted under a mass-transfer controlled condition (Greef et al., 1990). The limiting currents measured at the midpoint of the plateaux, at a potential of –0.8 V vs SCE, were plotted as a function of the square root of the rotation rates (I vs w 1/2), as shown in Figure 3. As predicted by the Levich equation, the plots were linear, confirming the fact that under the conditions of this study lead deposition became mass-transport controlled at potentials more negative than -0.7 V vs SCE.


Figure 2: Cathodic portions of the voltammograms obtained with a glassy carbon rotating disc electrode. Solution of 50 mg dm3 of Pb(II) in 0.5 M of boric acid and 0.05 M of sodium nitrate. Potential range of 0.0 to -1.0 V vs SCE. Scan rate 2 mV s-1. Rotation rates indicated on the graph.



Figure 3: Levich plots for the limiting currents taken at a potential of -0.8 V vs SCE.


Pb(II) Diffusion Coefficient Determination

During lead reduction, hydrogen evolution is always a competitive parallel process. In this case hydrogen evolution amplifies the response without apparently changing its shape. Taking this fact into account, a new series of voltammograms were recorded under the same conditions as those in Figure 2, using the support electrolyte without lead. Currents recorded during potential scanning are the result of hydrogen evolution. Then the current densities of the proton reduction, at a potential of -0.8 V vs SCE, were subtracted from those obtained in Figure 2, such that the resulting values are exclusive for lead reduction. Figure 3 shows the three curves, identified as "total, hydrogen and lead." Data from the last curve were used for the estimation of the diffusion coefficient (D) of Pb(II) in the chosen medium, provided the slope (s) in Levich’s plot can be expressed as


where n is the kinematic viscosity and CPb is the lead concentration. Table 1 shows data used for lead diffusion coefficient calculation that, according to equation (13), gives 2.0 10-5 cm2 s-1. This value is in good agreement with data found in the literature for lead in a 0.5 M NaCl solution (Ponce de Leon and Pletcher, 1996). Diffusion coefficients of metallic ions in dilute solutions present too small differences, as can be seen in the literature (Greef et al., 1990). The diffusion coefficient of Cu(II) in sulfate medium is 4.9 10-5 cm2 s-1 (Pletcher et al., 1991b), and a value of 4.0 10-5 cm2 s-1 has been reported for Co(II) in the same medium (Bertazzoli and Sousa, 1997).


Table 1: Parameters used for calculation of diffusion coefficient of Pb(II) in the support electrolyte from the slope taken from Levich’s plot in Figure 3

A cm-2 s-1/2

e- mol-1

cm2 s-1

mol cm-3

cm2 s-1

4.54 10-5


1 10-2*

2.41 10-7

2.0 10-5

* as a good approximation (Greef et al., 1990)


Cell Performance for Electrolytic Removal of Lead

The initial Pb(II) concentration in the catholyte, shown in Table 2, was added to 3.5 dm3 of a solution with the same composition as that used in the preliminary experiments. A potential of -0.8 V vs SCE was applied at the RVC cathode for the electrodeposition of lead. This potential value was the midpoint of the limiting current plateaux obtained in the experiments with the GCRDE.


Table 2: Initial Pb(II) concentrations for each experiment and the electrolysis times for 90% and 99% reductions in concentration


60 dm3 h-1

120 dm3 h-1

240 dm3 h-1


C(0) mg dm-3

t90% min

t99%   min

C(0) mg dm-3

t90%   min

t99% min

C(0) mg dm-3

t90%   min

t99% min










































Thus, as long as the hydrodynamic boundary layer with the RVC electrode is equal to or greater than that at the glassy carbon rotating disc electrode, this potential will result in a mass transfer limited operation. Twelve experiments resulting from combinations of RVC cathode porosity (20, 45, 60 and 80 ppi) and electrolyte flowrate (60, 120 and 240 dm3 h-1) were carried out.

Table 2 shows the initial values of lead concentration, C(0), and the times for 90% and 99% removal with respect to the twelve experiments. The Pb(II) concentration decreased to 1% from the initial value after an electrolysis time of 13 to 130 minutes, depending on RVC cathode porosity.

Figure 4 illustrates the decrease in normalized Pb(II) concentrations [C(t)/C(0)] with length of electrolysis, using different RVC cathode porosities (20, 40, 60 and 80 ppi) at catholyte flowrates of (a) 60 , (b) 120 and (c) 240 dm3 h-1. All the curves had the same profile, in which the lead ion concentration dropped nearly exponentially in time. To reach a 90 or 99% reduction in concentration, electrolysis required less time for higher porosities. This behavior reflects differences in the specific surface areas of RVC cathodes, since an increase in RVC porosity results in a larger area being available for electrodeposition. Under the conditions of the experiments shown in Figure 4(c), concentration of 0.1 mg dm-3, which corresponds to a 99.8% reduction, was achieved in 20, 30, 40 and 120 minutes using sponges of 80, 60, 45 and 20 ppi, respectively.


Figure 4: Normalized concentration [C(t)/C(0)] vs. time curves, obtained for flowrates of (a) 60 dm3 h-1, (b)120 dm3 h-1 and (c) 240 dm3 h-1, using the cathode porosities shown. Potential of –0.8 V vs SCE. INSETS: Plots of ln [C(t)/C(0)] vs. time for the data shown.


As stated earlier, controlled potential electrolysis at a reticulated cathode in a recycle mode is described by equation (7). Since Ve/VT is constant, the values of kmAe, taken from the slopes of ln C(t)/C(0) vs time plots (see the insets in figure 4) presented in Table 3, give an indication of cell efficiency for each operating condition. Considering that Ve/VT is 0.027 for the cell configuration used in this study and taking into account the approximate electrode areas taken from the RVC manufacturer’s literature, it is possible to calculate the mass transport coefficient, km, also presented in Table 3.


Table 3: Values of kmAe and km taken from the slopes of the ln [C(t)/C(0)] vs time plots shown in the insets in Figure 4(a-c)


Cathode Porosity/ppi - Cathode Area/cm2 cm-3


20 - 11.2

45 - 27.2

60 - 37.4

80 - 51.2

Flowrate Dm3 h-1

km Ae s-1

km ´ 10–3 cm s-1

km Ae s-1

km ´ 10–3 cm s-1

km Ae s-1

Km ´ 10–3 cm s-1

km Ae s-1

Km ´ 10 –3 cm s-1





























The influence of electrolyte flowrate on the effectiveness of electrolysis is also depicted in Figure 4 and in Table 3. The data show that the higher flow rates enhance the mass transfer coefficient, km, increasing the reduction rate of Pb(II).

The current efficiency for the configuration using an 80 ppi cathode and a flowrate of 240 dm3 h-1 was 14% for the removal of 99% of the metal ion, which meant a reduction in the Pb(II) concentration from 43.3 mg dm-3 to 0.43 mg dm-3 in 13.4 minutes. In the experiments reported here, the electrolysis was never terminated before the Pb(II) concentration reached 0.1 mg dm-3 or less. As shown in Figure 4(c), reduction to 0.1 mg dm-3 occurred in 20 minutes of electrolysis for cell configuration with a 80 ppi cathode and a flowrate of 240 dm3 h-1

Figures of Merit of the Flow-Through Electrolyic Reactor

Most of the contributions to the enhancement of the mass transfer coefficient and to the limiting current in the three-dimensional materials come from the changes in specific area and flowrate and from the intensity of turbulence in the neighborhood of the cathode. All these features can be related by equation (8) via dimensionless Sherwood, Schmidt and Reynolds numbers. Figure 5 shows a Sh/Sc0.33 vs Re log-log plot for the four reticulated carbons used in this study. Table 4 shows data used for the dimensionless numbers calculations using equations (9), (10), (11) and (12). Linear relationship depicted in Figure 5 allowed the estimation of coefficients m and n from equation (8).


Figure 5: Sherwood-Reynolds correlation for the four cathode porosities.



Table 4: Data used for the calculation of dimensionless numbers Re, Sh and Sc

Hydraulic diameter
L = 0.075 m


Flowrate/ L h-1- Linear velocity/ m s-1




Dynamic viscosity
m = 10-3 kg m-1 s-1


60 – 2.2 10-3





r = 103 kg m-3


120 – 4.4 10-3



Diffusion coefficient
D = 2 10-10 m2 s-1


240 – 8.8 10-3




Within the errors introduced by using values of Ae supplied by the RVC manufacturer to separate the area and mass transport factors, it is not possible to demonstrate large differences in the mass transport properties of the four sponges. Hence, the data for all four materials has been fitted to the approximate correlation of equation (8) as follows:


This may be evidence that RVC sponges are poor turbulence promoters and, as stated earlier, most of the improvement in removal rates and in the mass transfer coefficients reflects differences in the specific surface areas of RVC cathodes, since an increase in RVC porosity results in a larger area being available for the reaction. 

It is not possible to compare this Sherwood-Reynolds correlation with data reported by Pletcher et al (1991a), Ponce de Leon and Pletcher (1996) and by Langlois and Coeuret (1989); these authors chose to base their studies on the three-dimensional cathode material. We have preferred to focus our attention on the reactor as a whole. Unlike these authors, the cathode in our cell is sided by a turbulence promoter (see Figure 1) that has enhanced the performance of the equipment, diminishing the thickness of the diffusion layer and then increasing the mass transport coefficient. Although the Re numbers we have used are smaller than those used in the above-referenced studies, the value of m, characteristic of our reactor, is five times greater.



Hydrodynamic voltammetry was adequate for studying the Pb(II) reduction reaction under mass transport control. The limiting current plateaux in the resulting voltammograms showed the range of potential over which the Pb(II) reduction reaction is mass-transfer controlled. Thus, as long as the hydrodynamic boundary layer with the RVC electrode is equal to or greater than that at the glassy carbon rotating disc electrode, those potentials resulted in mass transfer limited operation in the reactor. As a consequence, the cell used in this study showed a good performance in removing lead from simulated effluents, and the concentration of Pb(II) was reduced to 0.1 ppm during recirculation times ranging from 20 min to 2 hours, depending on RVC porosity and flowrate. The best rates of lead removal and highest values for the mass transfer coefficient were obtained at the higher cathode porosities and flowrates.

Mass transfer coefficients and hydrodynamic data were correlated through equation (14), and the configuration of the reactor used in this study resulted in a value for m five times greater than those found in the literature. This is due to the inclusion of a turbulence promoter mounted on the RVC cathode that also prevented the development of preferential flow channels, as confirmed by the uniform color change in the cathode after each experiment.



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* To whom correspondence should be addressed.

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