**3. Results**

## *3.1. pH Measurements*

Table 1 lists the pH values measured inside the channel at the vicinity of coupons C4, C7 and C9 and outside the channel, in the "input section" of tank #1. The value measured outside the channel was in any case between 7.8 and 8.0. At days 33 and 53, the measurements were performed with seawater flowing normally inside the channel and the values obtained for coupons C4 and C7 were identical (or did not differ significantly) to those measured outside the channel. In contrast, the pH measured near coupon C9 was always slightly higher.

**Table 1.** Local pH measurements. The accuracy was estimated at ±0.1 pH via three successive measurements.


1 pH measured outside the channel, in the "input section" of tank #1 (see Figure 2).

On day 28, the seawater flow was accidentally stopped. It was actually observed that the 3-mm diameter tube connecting the channel to the aquarium pump (Figure 3) was clogged with rust particles coming from the insufficiently protected coupons. The measured pH values revealed that the pH was increasing all along the channel, from 8.7 close to C4 to 9.5 close to C9. This increase of pH is the consequence of CP, which increases the cathodic reaction rate and so the production of OH− ions, as expressed by reaction (1). When the seawater flow was stopped, OH− ions could be only transported by migration and diffusion. The observed increase of pH shows that the production of OH− ions was sufficiently fast so that the local OH− ions concentration could increase. Conversely, when seawater flowed inside the channel, the produced OH− ions were also carried away by advection and could not accumulate at the vicinity of the coupons surface.

The results obtained near coupon C9 are, however, slightly different as the pH is also higher when seawater flows inside the channel. A detailed view of the experimental design is shown in Figure 4. It reveals that pH was actually measured in a corner of the channel far from the electrolyte pathway. The effects of advection in this confined region of the channel are thus insufficient to avoid the accumulation of OH− ions.

**Figure 4.** Schematic representation of the channel around coupon C9. The blue line corresponds to the Ag/AgCl microelectrode. The large bended red arrow displays (schematically) the water flow.

The pH was monitored all along the experiment (approximately every two weeks). For each coupon, it fluctuated around the values given in Table 1 for days 33 and 53, i.e., did not change significantly over time.

## *3.2. Potential Measurements*

The potential corrected from ohmic drop, *E*IR free, was measured as described in Section 2.2. for coupons C1, C4, C9 and C12. The evolution over time of these potentials is displayed in Figure 5.

**Figure 5.** Evolution over time of the potential, measured with respect to the paired Ag/AgCl microelectrode, of coupons C1, C4, C9 and C12. A measurement was also performed at the end of the experiment for coupon C6 (see Section 2.2).

First, it can be seen that *E*IR free increases inside the channel from C1 to C12, whatever the considered time. The additional value measured for C6 at day 109 falls also between those obtained for C4 and C9, which validates the methodology used to obtain data for C6. This variation is due to the ohmic drop, which increases inside the channel as the distance from the reference electrode used to control the applied potential *<sup>E</sup>*app increases.

Secondly, it is observed that:

$$
\langle E\_{\text{IR free}}(\text{C9}) - E\_{\text{IR free}}(\text{C4}) \rangle > \langle E\_{\text{IR free}}(\text{C4}) - E\_{\text{IR free}}(\text{C1}) \rangle > \langle E\_{\text{IR free}}(\text{C12}) - E\_{\text{IR free}}(\text{C9}) \rangle
$$

This shows that the ohmic drop is the highest between C9 and C4. These two coupons are separated by the central region of the channel where the cross-sectional area is the smallest. Consequently, the electrical resistance of the electrolyte in this part of the channel is the highest. It must be recalled that the resistance *R* of a given volume of an electrolyte with resistivity *ρ* is given by:

> *R*

$$
\rho = \rho L / A \tag{5}
$$

In this equation, *L* is the length of the electrolyte volume and *A* its cross-sectional area, perpendicular to the current flow (assumed uniform). For similar *L* and *ρ*, *R* is then inversely proportional to *A.* In the main part of the channel, *A* = 2.5 cm2, while in the central part, *A* = 0.75 cm2. The ratio between the two cross-sectional areas is then 3.3. At day 41, the potentials are −1.046, −1.014 and −0.912 V vs. Ag/AgCl-seawater for coupons C1, C4, and C9, respectively. This leads to {*E*IR free(C9) − *E*IR free(C4)} = 102 mV and {*E*IR free(C4) − *E*IR free(C1)} = 32 mV, thus a ratio of 3.2 between both potential differences. Note that the distance between C4 and C9 is larger than that separating C1 from C4, and that the cross section area is larger in the bends, so that the theoretical ratio between both potential differences would be actually slightly higher than 3.7.

Conversely, the cross-sectional area (and the distance *L*) is the same between C12–C9 and C4–C1. The associated resistance is then the same. The ohmic drop is *RI* and depends on the current. The counter-electrode for CP is immersed in the "input section" of tank #1 so that the current, which flows between each coupon towards the counter-electrode, flows inside the channel. Consequently, the current that flows in the C12–C9 section corresponds

to the sum of the currents required for the CP of coupons C12, C11 and C10. In contrast, the current that flows in the C4–C1 section is the sum of all currents (except that of C1). This explains why the ohmic drop is higher between C4 and C1 than between C12 and C9.

Note that the current that flows in the C9-C4 section is then smaller than the current that flows in the C4-C1 section. This explains why the measured ratio between the corresponding potential differences (i.e., 3.2) is smaller than the theoretical ratio only based on the variation of the resistance *R* inside the channel (~3.7).

Thirdly, it is observed that the values of the potentials were initially high and decreased with time during the first 32 days. At the beginning, the values ranged from −0.95 V vs. Ag/AgCl-seawater for C1 to −0.6 V vs. Ag/AgCl-seawater for C9 and C12. This implies that C1 was correctly protected as soon as CP was applied while the protection was insufficient for C9 and C12. This could be visually appreciated as illustrated in Figure 6. The picture was taken five days after the beginning of the experiment. Coupons C11 and C2 clearly illustrate the effects of the increase of *E*IR free inside the channel. C11 is obviously entirely covered by a rust layer, i.e., is not correctly protected, while C2 is covered by a whitish layer, i.e., the calcareous deposit, which demonstrates that this coupon is indeed protected against corrosion.

**Figure 6.** Image of the channel showing the surface of the steel coupons after 5 days of experiment. Coupons C1 (right of the image), C4, C9 and C12 are hidden by the corresponding counter-electrode set in the opposite side of the channel.

The potential of each coupon decreased with time during the first 32 days and stabilized afterwards. At the end of the experiment, all the *E*IR free values were below −0.85 V vs. Ag/AgCl-seawater, i.e., all the coupons could be considered as correctly protected according to CP standards, e.g., [11]. This decrease in potential is due to the decrease in the ohmic drop, which is necessarily due to a decrease in the current required for CP because the other parameter, i.e., the resistance of the electrolyte circuit, does not vary significantly (if at all). This decrease with time in the current required for CP is a well-known effect of calcareous deposition [1–4]. The mineral layer hinders the diffusion of O2, decreases the active area of the metal, and thus slows down the cathodic reaction rate.

As shown in Figure 5, the potential of C1 decreased rapidly from −0.95 to −1.03 V vs. Ag/AgCl-seawater, and a calcareous deposit could form in a few days on its surface [3,4]. As shown in Figure 6, the whole surface of C2 was covered with such a mineral layer after 5 days. The decrease in the current flowing from C3, C2 and C1 consequently led to a decrease in the ohmic drop for C4 and its potential dropped from −0.75 to −0.97 V vs. Ag/AgCl-seawater after ten days. C4 was then itself progressively covered with a

calcareous deposit. The current required for CP decreased in turn for C4, then C5, C6 and so on, so that the potential of all coupons finally decreased down to an acceptable value.

To illustrate the reproducibility of the results, the potentials measured at day 18 during the three experiments (21-day experiment and two 3.5-month experiments) are given in Table 2. It can be seen that at that time, the values measured for C12 vary significantly from one experiment to the other. Coupon C12 is the farthest from the entry of the channel and its behavior depends on that of each of the other coupons. However, the values finally measured for C12 at the end of the two 3.5-month experiments were similar (about −0.9 V vs. Ag/AgCl-seawater).

**Table 2.** Potential values (V vs. Ag/AgCl-seawater) measured at day 18 for each of the 3 experiments.

