Electrochemical Characterization of Mass Transport in Porous

Article pubs.acs.org/IECR

Electrochemical Characterization of Mass Transport in Porous Electrodes Quentin de Radiguès, Pierre-Yves Sévar, Frédéric Van Wonterghem, Ronny Santoro, and Joris Proost* Université catholique de Louvain (UCL), Institute of Mechanics, Materials and Civil Engineering (iMMC), B-1348 Louvain-la-Neuve, Belgium ABSTRACT: Mass transport in reticulated vitreous carbon electrodes in flow by mode has been studied with the cathodic deposition of copper as a model reaction. Two methods characterizing mass transport are being compared. The first one relies on determination of the electrorecovery kinetics under mass-transfer limiting conditions in galvanostatic mode. The second method is the determination of the limiting current by a linear potential sweep technique. This technique has been modified to allow for a more unambiguous limiting current determination. In some cases, the modified linear sweep technique can also be used to measure the influence of a gaseous reaction side products on mass transport.

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INTRODUCTION Three-dimensional (3-D) electrodes have been widely used for various environmental applications, particularly for the electrorecovery of metals from dilute effluents.1,2 They offer a high specific surface area, allowing one to recover metals down to the ppm level. Among these, reticulated vitreous carbon (RVC)-based electrodes are the most commonly used, because of their low cost, chemical inertness, low resistance to fluid flow, and good electrical conductivity.3 Electrorecovery of metals in a flow cell is widely discussed in the literature,4−11 with many of these flow cells using RVC as cathode material. Mass transport through porous electrodes can be assessed using various techniques, such as interferometric12,13 and freezing methods.14 Electrochemistry provides an alternative and convenient way to measure mass transfer, for instance, by measuring the limiting current with a linear sweep technique5,6,15 or via the determination of the electrorecovery kinetics under mass-transfer limiting conditions in galvanostatic mode.7 This paper focuses on the electrochemical characterization of mass transfer during copper electrorecovery on RVC in flow-by mode, with the cathodic deposition of copper being chosen as the model reaction. The influence of the electrolyte flow rate on the mass transfer under these conditions have already been addressed both with the limiting current method11 and via the determination of the electrorecovery kinetics under galvanostatic conditions.7 The advantage of the latter technique is that it does not require the insertion of a reference electrode in the setup. Results obtained by the linear sweep technique confirm a major drawback observed in the literature:11 the limiting current regime usually presents a slope, making it difficult to unambiguously determine a limiting current value. This has been overcome using the tracer method.16 However, the tracer method requires to assume a mass-transfer equation while the aim of the present study is to obtain this equation. The slope in the limiting current regime has been overcome in the present work by subtracting the results of blank experiments to obtain a current characteristic, showing a minimum, identified as the limiting current. © 2012 American Chemical Society

Results obtained by the modified limiting current approach have been compared to mass-transfer coefficients obtained with the galvanostatic method. It has been observed that mass transfer is more pronounced under galvanostatic mode than during the linear sweep method used to determine the limiting current. It is believed that the difference is due to gas bubbles evolving at the cathode under galvanostatic conditions. Under these conditions, the hydrogen reduction side reaction occurs when the limiting current is lower than the applied current. Enhancement of mass transfer by the presence of gas bubbles has been observed in the past on both flat and 3-D electrodes. On flat electrodes, mass transfer has been observed to increase by air sparging on rotating disk electrodes.5 Microporous gas spargers have also been found to increase mass transfer in electrochemical cells with a membrane separation between the anode and the cathode.17 The presence of bubbles of an electrochemically active gas has been shown to enhance mass transfer in parallel-plate electrolyzers.8 Other authors18 have modeled the mass transfer in parallel-plate gas-sparged electrochemical reactors in order to take into account this enhancement by uprising gas bubbles. On 3-D electrodes, gas evolution has been shown to enhance mass transfer on packedbed electrodes.9,10,19 It is generally admitted8−10,19 that the enhancement of mass transfer by gas bubbles can be due to two effects. First, the bubbles stir the solution, disrupting the boundary layer physically, even for electrochemically inert gases. Second, the gas bubbles can collide with the 3-D electrode, disrupting the boundary layer even further.10 This is also the case with reacting gas bubbles, which can perturb the boundary layer at the electrode surface.8 Some authors20,21 have reported that the mass transfer is proportional to the square root of the evolved gas flow rate or that the thickness of the diffusion layer is proportional to the square root of the current density of the gas Received: Revised: Accepted: Published: 14229

January 11, 2012 August 21, 2012 August 28, 2012 August 28, 2012 dx.doi.org/10.1021/ie3000979 | Ind. Eng. Chem. Res. 2012, 51, 14229−14235

Industrial & Engineering Chemistry Research

Article

For the potential sweep experiments, solutions were N2 purged before the experiments, while N2 was also constantly blown on the surface of the Cu2+ solution during the experiment. Metal ion concentrations have been analyzed ex situ with a Varian ICP-OES on 10 mL samples taken from the bulk catholyte at fixed time intervals during each electrorecovery experiment. Analysis of the anolyte at the end of the experiments revealed that there was no Cu2+ leakage through the membrane down to 0.1 mg/L. During linear-sweep experiments, a sample has been taken at 0.4 V vs the standard hydrogen electrode (SHE). The current and potential were controlled and measured using a Autolab PGSTAT302N potentiostat. The galvanostatic experiments were carried out with the applied current equal to 0.27 A. For the potential sweep experiments, a potential sweep rate of 5 mV/s was used.

production. The present work also shows that reactive gas bubbles enhance mass transport more than inert gas bubbles. In summary, this paper will explore the possibility of electrochemically characterizing of the influence of the electrolyte flow rate on mass transfer both in the presence and in the absence of reactive and inert gas bubbles. In the first part, the results of galvanostatic experiments are presented. In these experiments, inevitable gas bubbles evolve at the cathode and thus modify the mass transport. These results are then compared with the results of limiting current experiments with and without inert gas sparging. In the last part, the influence of reactive gas bubbles evolving at the cathode on mass transfer is measured electrochemically.

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EXPERIMENTAL DETAILS The experimental set p is shown schematically in Figure 1. It is comparable to the setup already described in ref 7, except that a

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RESULTS AND DISCUSSION During the experiments, a copper sulfate solution was circulated though the RVC cathode. The following reactions are expected at the cathode: Cu 2 + + 2e− ⇒ Cu

(1)

2H+ + 2e− ⇒ H 2

(2)

1 O2 + 2H+ + 2e− ⇒ H 2O (3) 2 with eq 1 showing the reaction of interest and eqs 2 and 3 considered to be parasitic reactions. The anodic reaction was 1 H 2O ⇒ O2 + 2H+ + 2e− (4) 2 Galvanostatic Experiments. A typical result of the concentration decrease with time during a galvanostatic experiment is shown in Figure 2, both on a linear scale (Figure

Figure 1. Schematic view of the experimental setup.

Hg/Hg2SO4 reference electrode has been added above the cathode. It consists of a filter press cell where anodic and cathodic compartments are separated by a Nafion membrane. The 3-D cathode, 35 mm × 35 mm × 10 mm in volume (Ve), was cut from 100-ppi, 30-ppi, and 10-ppi reticulated vitreous carbon (RVC) with a specific surface area (Ae) of 66 cm2/cm3, 18 cm2/cm3 and 4.9 cm2/cm3 respectively developing a surface area of 8.1 dm2, 2.0 dm2 and 60 cm2 respectively. RVC has a void volume of 0.97.3 The RVC electrode was pressed against the cathode feed plate, and charged in flow-by configuration, i.e., fluid flow perpendicular to the electric field. The hydraulic circuit is comprised of two pumps forcing the circulation of the electrolyte in each compartment of the filter press cell. The electrolyte then flows back into a 1-L stirred tank. Therefore, the filter press cell containing the RVC cathode can be considered to work as a plug-flow reactor with perfectly stirred tanks. The pumping rate was adjusted in order to obtain an electrolyte flow varying from 0.03 to 1.2 L/min in the catholyte compartment and constant at 1.2 L/min in the anolyte compartment. The corresponding mean linear flow velocity (v), defined as the ratio of the volumetric flow rate to the electrode cross-sectional area, varied from 0.2 × 10−2 to 5.4 × 10−2 m/s in the catholyte compartment. Two types of experiments were carried out: galvanostatic and potential sweep experiments. All experiments were carried out at room temperature from 1-L catholyte solutions. For galvanostatic experiments, 0.5 M sulfuric acid catholyte solutions with an initial concentration (C0) aimed at 5 mM of Cu2+ was used. The anolyte was 0.5 M sulfuric acid. For the potential sweep experiments, 0.5 M Na2SO4 catholyte solutions with an initial nominal concentration (C0) aimed at 1 mM of Cu2+ were used, and the anolyte was 0.5 M Na2SO4 with the acidity adjusted to pH 2 in both solutions using sulfuric acid.

Figure 2. Evolution of the metal concentration with time on (a) a linear scale and (b) a normalized semilogarithmic scale (I = 0.27 A, v10 ppi = 0.5 m s−1, v30 ppi, and v100 ppi = 0.4 m s−1).

2a) and a semilogarithmic scale (Figure 2b). These graphs clearly show two distinct regimes. From the literature,22 it is well-established that, in the case of a plug-flow reactor in batch recycle mode operated under galvanostatic conditions with the applied current I lower than the limiting current IL, the concentration C in the bulk solution decreases linearly with time t: ηIt C = C0 − (5) zFV 14230

dx.doi.org/10.1021/ie3000979 | Ind. Eng. Chem. Res. 2012, 51, 14229−14235


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supporting electrolyte24 and 4.9 × 10−6 cm2 s−1 for the experiments with Na2SO4 as the supporting electrolyte.25 The thickness of the diffusion boundary layer is influenced by the velocity of the fluid. A widely used characterization of the influence of the velocity of the fluid on mass transport includes the adimensional numbers of Reynolds (Re), Sherwood (Sh), and Schmidt (Sc), which are defined as22,23,25

with C0 the initial concenctration, η the current efficiency, z the number of exchanged electrons, F the Faraday constant, and V the volume of the catholyte solution. Defining the slope of the linear regime k1 as

C = C0 − k1t

(6)

and comparing eqs 5 and 6, one arrives at k1 =

ηIt zFV

(7)

We have shown previously7 that the current efficiency of the linear regime can be derived from experiments carried out at different applied currents. In the case of Cu electrorecovery on RVC, it was found to be close to unity (η = 0.88 ± 0.01), even for solutions that have not been N2-purged. In the case of a plug-flow reactor in batch recycle mode operated under galvanostatic conditions, the limiting current can be defined as22 ⎡ ⎛ k A ⎞⎤ IL = zFQC ⎢1 − exp⎜ − m ⎟⎥ ⎝ Q ⎠⎦ ⎣

(8)

Sc =

ν D

(15)

Q BS

(16)

2BS B+S

Sh = kRe aSc1/3

(17)

(18)

As the Schmidt number is constant in our experiments, we can simplify eq 18 into

(10)

Sh = KRe a ⇒ ln(Sh) = K + a ln(Re)

(19)

with K and a to be determined experimentally. Figure 3 shows the results of the logarithm of the Sherwood number versus the logarithm of the Reynolds number for the electrorecovery of copper in galvanostatic mode on RVC cathodes with various porosities. The Sherwood and Reynolds numbers used in Figure 3a are calculated using de as the relevant length scale of the cathode. All the results were fitted using one single linear regression shown as a solid line in Figure 3a, as regressions on each porosity shown as dashed lines in Figure 3a were statistically equal to a regression including all data points. The determined regression parameters have been summarized in Table 1. When calculating the Re and Sh numbers using dp as typical length of the cathode, as shown in Figure 3b, the linear regressions on the plot of the logarithm of Sh vs the logarithm of Re on each porosity were significantly different from the regression through all porosities as shown in Table 2 . We therefore concluded that the typical length scale de was more appropriate in our experiments. Through the rest of the paper,

(11)

allowing us to calculate the mass-transport coefficient from the slope in the second regime. The mass-transport coefficient km can be written as22,23 D δ

(14)

Numerous experiments22,23,25 have been fitted with these adimensional numbers, using an expression of the form

⇒ km

km =

k md D

de =

(9)

⎛ k A ⎞⎤ 1 ⎡ ⎢1 − exp⎜ − m ⎟⎥ k2 = Ve/Q ⎣ ⎝ Q ⎠⎦ Vk ⎞ A ⎛ ln⎜1 − e 2 ⎟ Q ⎝ Q ⎠

Sh =

where B and S are, respectively, the width and thickness of the RVC cathode. Because the void volume fraction of RVC is very high, the volume of RVC is neglected in the velocity calculation. The characteristic dimension d can either be taken to be equal to the mean pore diameter of the RVC foam (dp), taken to be equal to the inverse of the porosity or, as done more frequently,25 equal to a characteristic length scale of the RVC cathode, defined as

Comparing eqs 9 and 10 and assuming b = k2tc, one then arrives at the expression

=−

(13)

v=

where Ve is the volume of the electrode. From the semilogarithmic plot in Figure 2b, the slope k2 of the second regime can be determined from linear fits of the form ⎛C⎞ ln⎜ ⎟ = −k 2t + b ⎝ C0 ⎠

vd ν

with ν being the kinematic viscosity (taken to be constant; ν = 1 × 10−6 m2 s−1), v the mean linear velocity, and d a characteristic dimension of the cathode. The mean linear velocity v is considered to be the volumetric flow rate divided by the area through which the catholyte flows:

where km is the mass-transfer coefficient, A the surface area of the electrode (A = AeV), and Q the volumetric flow rate through the electrode. One can see that, during the experiment, the limiting current will decrease as a result of the decrease of the concentration. When the limiting current reaches the value of the applied current at a critical time tc, the concentration starts to decrease exponentially with time, as can be seen in Figure 2b. The evolution of the concentration with time after the critical time can be described by22 ⎛ C(t ) ⎞ ⎛ k A ⎞⎤ t − tc ⎡ ⎢1 − exp⎜ − m ⎟⎥ ln⎜ ⎟=− Ve/Q ⎣ ⎝ Q ⎠⎦ ⎝ C(tc) ⎠

Re =

(12)

with D being the diffusion coefficient and δ the thickness of the diffusional boundary layer. The diffusion coefficient for copper varies with the composition of the electrolyte and is taken to be 6 × 10−6 cm2 s−1 for the experiments with H2SO4 as the 14231



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Figure 3. Plot of the logarithm of the Sherwood number (Sh), calculated by the slope in the second kinetic regime, versus the logarithm of the Reynolds number (Re) for copper electrorecovery on RVC foams of various porosities. Typical lengths for the Sherwood and Reynolds numbers are (a) a characteristic length scale of the RVC cathode (de) and (b) the mean pore diameter of the RVC foam (dp). Solid lines indicate a regression on all data points and dashed lines indicate regressions through data points of same porosities (I = 0.27 A).

Figure 4. Current versus cathode potential curves for copper electrorecovery showing the total current (“total”), the current of the parasitic reactions “blank” and the calculated copper current (“Cu”) (v = 0.014 m/s, RVC 30 ppi, 9 × 10−4 mol/L Cu2+, potential sweep rate = 5 mV s−1, N2-purged catholyte).

be due to a rough copper deposit at higher deposition potential, uncompensated IR drop,15 or a nonuniform current distribution.6 To take the contribution of the reactions described by eqs 2 and 3 into account on the current−voltage characteristic, linearsweep experiments have been carried out with a blank solution for each linear velocity (“blank” in Figure 4) . The linear-sweep experiments on the blank solution have been carried out on a RVC cathode containing ∼5 mg of copper deposit from the first experiment (“total” in Figure 4) in order to account for the possible catalytic properties of copper on the parasitic reactions as well as for the increased cathode surface area due to the rough deposit. The result of each linear-sweep on the blank solution was then subtracted from the corresponding “total” experiment with the copper solution. The result of this subtraction is the calculated copper electrorecovery current without parasitic reactions shown in Figure 4 (see “Cu” curve). The limiting current is taken to be the minimum on the Cu curve in Figure 4. Indeed, the limiting current is defined as the horizontal part of the current characteristic. The decrease of cathodic current at more negative potential is interpreted as follows: as copper continues to deposit on the RVC cathode in this part of the experiment, the cathode used to carry out the blank experiment contains more deposited copper than the cathode used for the reduction of copper, overestimating the parasitic reactions due to the catalytic properties and the higher surface area of the copper-covered RVC cathode. Figure 5a shows the evolution of the observed current versus potential at different mean linear velocities. These curves correspond to the “total” curve in Figure 4. One can clearly see that the limiting current corresponding to the plateau increases with mean linear velocity, as expected from the literature.25 These authors observed that the current “plateaus” become less visible at higher mean linear velocity. This is also the case in Figure 5a. Figure 5b shows the evolution of the copper current versus potential at different mean linear velocities. These curves correspond to the “Cu” curve in Figure 4. The minimum on these curves was taken to be the limiting current, as justified before. The limiting current IL being identified as the minimum on the curves in Figure 5b, the mass-transfer coefficient can be calculated using eq 8. The adimensional numbers of Reynolds and Sherwood can now also be calculated, using eqs 13 and 14. The mass transport when the limiting current is reached can be

Table 1. Parameters of eq 19 Determined by Concentration Decrease Method at Various Porosities Using de as the Relevant Length Scale porosity

a

K

10 ppi 30 ppi 100 ppi fit through all porosities

0.53 ± 0.07 0.496 ± 0.008 0.50 ± 0.08 0.51 ± 0.07

4.0 ± 0.4 3.74 ± 0.04 4.3 ± 0.4 4.1 ± 0.4

Table 2. Parameters of eq 19 Determined by the Concentration Decrease Method at Various Porosities Using dp as the Relevant Length Scale a

porosity 10 ppi 30 ppi 100 ppi fit through all porosities

0.52 0.495 0.50 0.68

± ± ± ±

K 0.08 0.002 0.08 0.07

3.2 2.454 2.2 2.1

± ± ± ±

0.3 0.006 0.1 0.2

Reynolds and Sherwood numbers will therefore always be defined based on de. Linear-Sweep Experiments. Sherwood numbers were also calculated by deriving the limiting current via linear-sweep voltammetry experiments. Figure 4 shows a typical result of a current versus potential curve for the reduction of 1 mM Cu2+ on 30 ppi RVC. This porosity has been chosen as it appears to give more precise results, as shown in Tables 1 and 2. In the range −0.150V to −0.450V vs SHE, the copper deposition reaction has been reported to become completely masstransport-controlled and a slightly sloped limiting current regime has been observed.25 Figure 4 shows the same trend. For potentials more negative than −0.450 V vs SHE, the hydrogen evolution reaction (eq 2) becomes dominant. The presence of slope in Figure 4 makes it difficult to determine a unique value of the limiting current. This slope is thought to be caused by the onset of parasitic reactions described by eqs 2 and 3. While the solution was carefully purged to avoid the reduction of dissolved oxygen (eq 3) and the acidity of the solution was limited to pH 2 to minimize the reduction of water to hydrogen (eq 2),25 none of them can be totally eliminated. The slope in the mass-controlled region could also 14232



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sintered material. The results of these experiments also are shown in Figure 6 (“with N2”). By comparing the linear regressions “with N2” and “without N2” in Figure 6, one can clearly see that the nitrogen sparging increases the mass transport during the electrorecovery. However, by comparing Figures 3 and 6 or equivalently all results in Table 3, one can see that mass transport during the galvanostatic experiments was still higher than mass transport during the linear-sweep experiment injecting nitrogen bubbles in the solution. Since the hydrogen reaction occurs at the cathode surface, the hydrogen bubbles can modify the diffusion layer close to the surface of the cathode as suggested by ref 8. Furthermore, the size and number of hydrogen bubbles generated at the cathode surface also possibly increase the mass transfer more than the nitrogen bubbles injected externally. Therefore, the influence of hydrogen production on mass transfer was characterized electrochemically as well as by analyzing, in more detail, the potential range where hydrogen evolution is observed during the linear-sweep experiments without injection of N2 bubbles. In this respect, the logarithm of the calculated cathodic copper electrorecovery current without parasitic reactions ln(−ICu) has been plotted versus the logarithm of the cathodic current in the blank solution ln(−Iblank) in Figure 7. This figure again shows the limiting current regime to be in the ln(−Iblank) range from −6 to −3. For ln(−Iblank) > −2, the hydrogen evolution reaction starts to interfere.

Figure 5. Current versus cathode potential curves for copper electrorecovery, showing the effect of mean linear velocity ((i) v = 0.012 m/s, (ii) v = 0.024 m/s, (iii) v = 0.029 m/s, (iv) v = 0.040 m/s, (v) v = 0.051 m/s): (a) measured current and (b) calculated copper electrorecovery current without parasitic reactions (RVC 30 ppi, 9 × 10−4 mol/L Cu2+, potential sweep rate = 5 mV s−1, N2-purged catholyte).

characterized using eq 19. The logarithm of the Sherwood number calculated by potential sweep techniques versus the logarithm of the Reynolds number has been plotted in Figure 6

Figure 6. Comparison of the logarithm of the Sherwood number calculated by the modified potential sweep technique vs the logarithm of the Reynolds number for copper electrorecovery on RVC with and without injection of N2 bubbles in the catholyte (potential sweep rate = 5 mV s−1, N2-purged catholyte, 30 ppi).

Figure 7. Logarithm of the calculated cathodic copper electrorecovery current without parasitic reactions versus logarithm of the cathodic current in the blank solution, showing the effect of hydrogen evolution on copper electrorecovery at various mean linear velocities ((i) v = 0.012 m/s, (ii) v = 0.024 m/s, (iii) v = 0.029 m/s, (iv) v = 0.040 m/s, (v) v = 0.051 m/s; RVC 30 ppi, 9 × 10−4 mol/L Cu2+, potential sweep rate = 5 mV s−1, N2-purged catholyte).

(“without N2”). The parameters of eq 19 derived by the linear regression in Figure 6 are shown in Table 3. Comparing the Table 3. Parameters of eq 19 Defined by Two Different Methods method

a

K

concentration decrease potential sweep without N2 bubbles potential sweep with N2 bubbles

0.51 ± 0.07 0.37 ± 0.01 0.30 ± 0.02

4.1 ± 0.4 4.2 ± 0.1 4.9 ± 0.1

For the lower mean linear velocities ((i), (ii), and (iii) in Figure 7), current instabilities caused by hydrogen evolution are clearly visible when ln(−Iblank) > −2. This is thought to be caused by the appearance of a sluggish or heterogeneous flow when the gas flow (determined here by the “blank” current) becomes relatively important, compared to the mean linear velocity of the liquid.17 Such a heterogeneous flow is characterized by the formation of larger-sized bubbles traveling faster than the smaller bubbles. During sluggish flow, slugs (column-shaped bubbles) are formed by large bubbles, perturbing the mass transport even further. For the higher mean linear velocities ((iv) and (v) in Figure 7), a linear regime is observed for ln(−Iblank) > −1.5. This linear regime is believed to be indicative of a copper electrorecovery

results without N2 in Figure 6 with the results obtained earlier via the galvanostatic experiment in Figure 3, one can see that the latter results in an increased mass transfer through the porous electrode. This is attributed to the presence of hydrogen bubbles due to side reaction (eq 2) in the galvanostatic experiment. To investigate more details of the effect of such bubbles on the limiting current, linear-sweep experiments were repeated while sparging N2 in the catholyte solution using a porous 14233



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confirmed this effect, while suggesting a further enhancement by gas bubbles produced at the cathode surface. Finally, the modified linear sweep method also allowed us to quantify the enhancement of mass transport by gas bubbles produced at the cathode surface, but appeared to be difficult to apply in the case of sluggish or heterogeneous gas flow.

current being influenced by the hydrogen evolution, as justified below. The hydrogen bubbles modify the diffusion profile close to the cathode, promoting mass transfer.21This microconvection adds up with the macroconvection of the external flow. Therefore, the electrorecovery current in the potential range where the hydrogen evolution reaction is observed can be higher than the current measured in the “plateau” region without hydrogen evolution. Some authors have proposed a power law to model the influence of the gas evolution rate on the mass-transfer coefficient:6 k m ∼ ϕn

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Corresponding Author

*Tel.: +32 (0)10 47 93 42. Fax: +32 (0)10 47 40 28. E-mail: [email protected].

(20)

where ϕ is the gas evolution rate. A similar approach has been used here, considering that Iblank is an estimate for the current due to hydrogen evolution. This assumes that the contribution to the blank current of the reduction of dissolved oxygen is constant. We considered that, (i) upon hydrogen evolution, copper deposition is masstransfer-limited during the limiting current regime at less negative potential and (ii) ICu is still the limiting current. Based on eq 20, a power law can then be proposed to model the influence of the hydrogen current Iblank on ICu:

ICu = IHn 2

Notes

The authors declare no competing financial interest.

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I H 2 ⎞⎤ Q⎡ ⎛ ⎢ln⎜1 − ⎟⎥ A⎣ ⎝ zFQC ⎠⎦

REFERENCES

(1) Ferreira, B. K. Three-dimensional electrodes for the removal of metals from dilute solutions: A review. Miner. Process. Extract. Metall. Rev. 2008, 29, 330−371. (2) Jüttner, K.; Galla, U.; Schmieder, H. Electrochemical approaches to environmental problems in the process industry. Electrochim. Acta 2000, 45, 2575−2594. (3) Wang, J. Reticulated Vitreous CarbonA New Versatile Electrode Material. Electrochim. Acta 1981, 26, 1721−1726. (4) Bertazzoli, R.; Widner, R. C.; Lanza, M. R.; Iglia, R. A. D.; Sousa, M. F. Electrolytic Removal of Metals Using a Flow-Through Cell with a Reticulated Vitreous Carbon Cathode. J. Braz. Chem. Soc. 1997, 8, 487−493. (5) Ettel, V. A.; Tilak, B. V.; Gendron, A. S. Measurement of Cathode Mass Transfer Coefficients in Electrowinning Cells. J. Electrochem. Soc. 1974, 121, 867−872. (6) Selman, J. Techniques of Mass-Transfer Measurement in Electrochemical Reactors. AIChE Symp. Ser. 1981, 77, 88−102. (7) de Radigues, Q.; Santoro, R.; Proost, J. Kinetic transitions during Ag and Cu electrorecovery on reticulated vitreous carbon electrodes in flow-by mode. Chem. Eng. J. 2010, 162, 273−277. (8) Economou, D.; Alkire, R. Two-phase mass transfer in channel electrolyzers with gas-liquid flow. J. Electrochem. Soc. 1985, 132, 601− 608. (9) Mobarak, A.; Abdo, M.; Hassan, M.; Sedahmed, G. Mass transfer behaviour of a flow-by fixed bed electrochemical reactor composed of a vertical stack of screens under single and upward two phase flow. J. Appl. Electrochem. 2000, 30, 1269−1276. (10) Soltan, E. A.; Nosier, S. A.; Salem, A. Y.; Mansour, I. A. S.; Sedahmed, G. H. Mass transfer behaviour of a flow-by fixed bed electrochemical reactor under different hydrodynamic conditions. Chem. Eng. J. 2003, 91, 33−44. (11) Pletcher, D.; Whyte, I.; Walsh, F. C.; Millington, J. P. Reticulated Vitreous Carbon Cathodes For Metal-Ion Removal from Process Streams. 2. Removal of Copper(II) from Acid Sulfate Media. J. Appl. Electrochem. 1991, 21, 667−671. (12) Tvarusko, A.; Watkins, L. Laser interferometric study of the diffusion layer at a vertical cathode during non-steady-state conditions. Electrochim. Acta 1969, 14, 1109−1118. (13) Tvarusko, A.; Watkins, L. S. Interferometric Study of the Concentration Change at High Cathodic Current Densities. J. Electrochem. Soc. 1971, 118, 580−583. (14) Brenner, A. Proc. Am. Electroplat. Soc. 1940, 95, 4. (15) Nahle, A.; Reade, G.; Walsh, F. Mass Transport to reticulated vitreous carbon rotating cylinder electrodes. J. Appl. Electrochem. 1995, 25, 450−455. (16) Wang, H.; Chen, S.; O’Keefe, T.; Degrez, M.; Winand, R. Evaluation of mass transport in copper and zinc electrodeposition using tracer methods. J. Appl. Electrochem. 1989, 19, 174−182. (17) Tailoka, F.; Fray, D. Enhancement of mass transfer using microporous sparger materials. Trans. Inst. Min. Metallurgy, Sect. C Min. process. extractive. metall. 1993, 102, C1−C6.

(21)

Taking into account eq 8, we can further express eq 21 as km = −

AUTHOR INFORMATION

(22)

The parameter n of eq 21 was determined as the slope of the linear regression on ln(ICu) for ln(−Iblank) > −1.5. It was found to be n = 1.209 ± 0.005 and n = 1.307 ± 0.007 for v = 0.051 m/ s and v = 0.040 m/s, respectively. As such, the improved linear sweep method also allows for the electrochemical characterization of the influence of reactive gas evolution at an electrode. The low error on n shows that the proposed power law (eq 21) fits the experimental data quite well. However, it cannot be applied in the case of heterogeneous or sluggish flow of bubbles in an electrolyte. In that case, calculation of the mass-transport coefficient can still be done via the determination of the electrorecovery kinetics under mass-transfer limiting conditions in galvanostatic mode.

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CONCLUSIONS This paper first presented a simple and straightforward method to characterize mass transport in an electrochemical reactor. It is based on the analysis of kinetic rate constants in the masstransport-limited regime during galvanostatic copper electrorecovery. It does not require the use of a reference electrode. This method measures mass transport in the presence of hydrogen bubbles evolving at the cathode. Limiting current measurement with a linear potential sweep technique were then performed to validate the results obtained by the first method. The classical potential sweep technique was modified in order to determine a unique limiting current value in case the limiting current regime shows a slope. The masstransfer coefficient obtained by this modified linear sweep technique appeared to be significantly lower than those obtained by the first method. This is indicative for the enhancement of mass transport by hydrogen gas bubbles produced by the side reaction in galvanostatic mode. Injection of inert gas bubbles during the linear sweep experiments 14234



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Electrochemical Characterization of Mass Transport in Porous

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