Accesorios de tuberías

The amounts of silver nanoparticles retained on the basis of acid-digestion and ICP- determination in the different experiments are listed in Table 4.1 and are, in descending order: iron oxide (0.2 mg nAg/g soil) > uniform quartz (0.01mg/g) > well graded quartz (0.0073 mg/g). There was some concern that the nAg stabilizing agent CMC90k could interfere with nAg retention in this study as it has been shown that a) nanoparticle stabilizing agents can alter retention behaviour by competing for deposition sites [El Badawy et al., 2013] and b) CMC90k has demonstrated an affinity for iron oxide surfaces [Pensini et al., 2013]. However, the concentration of nAg retained on the quartz sand agrees well with previously published nAg/quartz isotherm data [Abraham et al., 2013] providing confidence that CMC90k was not interfering with nAg retention on the quartz sands. In addition, the retention data presented above agrees with previous studies that have demonstrated – in absence of a stabilizer - greater retention on iron oxide sands compared to quartz [El Badawy et al., 2013; Lin et al., 2011] which suggests that site competition with CMC90k was not a significant factor here.

Retention is often conceptualized as a two-step system: 1) nanoparticle transport towards the collector and 2) nanoparticle retention by the collector. As expected, the retention data (Table 4.1) shows that surface chemistry (i.e., favorable/unfavorable) controls the second step, retention at the collector surface. This finding matches the

favorable/unfavorable conditions predicted by the DLVO curves in Figure 4.4 in the supplementary informationindicating the presence of an electrostatic energy barrier on the quartz sands but not on the iron oxide sand and confirms that the iron oxide and quartz sands employed by this study represent favorable and unfavorable conditions, respectively. This highlights that, while immobile zones are hypothesized to contribute to temporary hydraulic retention of nanoparticles, attachment on the collector surface dominates the overall retention in favorable conditions.

Figure 4.2 examines the nAg breakthrough in the column effluent for the three

experiments as a function of pore volumes injected. The nAg concentration values were obtained via ICP-determination of each collected effluent sample normalized to the ICP- determined influent concentration (Co). The effluent BTCs were compared to CFT predictions via the upscaled CFT equation: C/Co = (1-η)Nc where C is the concentration after passing by a number of linearly aligned collectors (Nc)[Johnson and Hilpert, 2013]. Assuming the average diameter of a grain is 500 μm, Nc can be calculated by

representing the column as a long string of grains (Nc~100). The upscaled CFT equation was used to calculate the collector contact efficiencies for each experiment (ηexpt). To minimize the influence of dispersion, ηexpt was determined only for the peak C/Co values at 3 PV. These ηexpt values were compared to those obtained from the Nelson and Ginn [Nelson and Ginn, 2011] ηCFT correlation equation and are presented in Table 4.2. The Nelson and Ginn [Nelson and Ginn, 2011] ηCFT value (0.003) over predicts the column- scale iron oxide ηexpt value (0.002) by 50%. This over prediction is consistent with previous findings that CFT-predicted η values are generally larger than experimentally- determined η values for nanoparticles in favourable conditions [Long and Hilpert, 2009;

Long et al., 2010; Nelson and Ginn, 2011]. This suggests that the single-collector CFT model presented in Figure 4.1a does not adequately account for all the relevant

A comparison of the quartz sands’ ηCFT and ηexpt values is complicated by the presence of the electrostatic energy barrier. CFT cannot predict ηCFT in unfavorable conditions and requires the ‘attachment efficiency’ (α) fitting parameter to compensate for the presence of an electrostatic energy barrier. Attachment efficiency is typically fit from experimental data and is calculated as: ηexpt = α × ηCFT. Table 4.2 presents the calculated α for each experiment. While attachment efficiency is used for unfavorable conditions, the

overprediction of ηCFT, due to mechanisms such as immobile zones, yields α values < 1 in favorable conditions as exhibited by the iron oxide column experiment (α = 0.67). As expected, the quartz sands’ α values are significantly smaller than the iron oxide α, 0.17 for uniform quartz and 0.03 for well graded quartz. Both quartz sands have identical surface chemistries and a similar grain d50 which, according to CFT, should yield identical retention rates and ηCFTvalues. The ηexpt and α values are close to an order of magnitude larger for the uniform quartz than the well graded quartz despite the identical surface chemistries. This suggests that some physical mechanism related to the

distribution of grain and pore sizes can inhibit nAg retention rates and influence both ηexpt and the accuracy of single-collector CFT models.

Table 4.2: Comparison of Experimental and Predicted Contact Efficiency (η) at Maximum C/Co

Uniform Iron Oxide Uniform Quartz Well Graded Quartz

Experimental (ηexpt) 0.002 0.0005 0.00009

Nelson-Ginn [Nelson

and Ginn, 2011] (ηCFT) 0.003 0.003 0.003

Attachment efficiency

Figure 4.2: Effluent sample C/Co breakthrough on a log-log scale to emphasize extended tailing in the

samples. The grey box represents the nAg injection period and the white background represents the elution. The vertical dotted line indicates when the advective front reached the top of the column. The red, blue and black lines are the results of Equation 4.1 fitted to the elution portion of the uniform iron oxide, uniform quartz, and well graded quartz breakthrough curves respectively. Co

was measured at the start and end of the 3 PV injection period. Error bars representing C/Co for the

maximum and minimum measured values of Co are plotted but are smaller than the marker size for

each data point and are not visible.

The elution behaviour in Figure 4.2 was examined for evidence of extended tailing, specifically for evidence of power law tailing. Power law tailing appears as a linear decrease in C/Co on a log-log plot [Haggerty et al., 2000] and is usually described by:

T = W X Y Z _4.1

Where C is concentration, t is time or pore volumes injected, and k and b are fitted coefficients. As mentioned previously, tailing in colloid experiments is typically only associated with unfavorable conditions when colloids re-entrain into the bulk pore space from the secondary minimum [Johnson and Hilpert, 2013; Landkamer et al., 2013; Li et al., 2005]. If re-entrainment from the secondary minimum was the dominant source of

extended tailing, the tailing should only occur in the quartz sand experiments and not the iron oxide, as both the DLVO profile in Figure 4.4 and the column-scale retention data indicates that nanoparticles are irreversibly attached onto the iron oxide sand. However, all three experiments in Figure 4.2 exhibit the linear decrease in concentration indicative of power-law tailing. This suggests that extended tailing of nanoparticles can occur in both favorable and unfavorable deposition scenarios and, in these systems, is not linked to reversible/irreversible retention behaviour on the collector surface.

To compare the magnitude of tailing for the unfavorable (quartz) and the favorable (iron oxide) experiments, eq 4.1 was fit to the elution portion of each BTC. The fitted equation is represented by a line overlain on the tailing portion of each BTC in Figure 4.2. The parameter k from eq 4.1 represents the slope of the elution phase in log-log space. The unitless fitted k values, with +/- 95% confidence intervals, are: uniform iron oxide = 4.0+/- 0.4, uniform quartz = 3.6 +/- 0.8, well graded quartz = 3.7 +/- 0.2. Thus, the tailing behaviour observed in Figure 4.2 for the iron oxide and quartz experiments are

statistically similar. This similar behaviour indicates that elution from the iron oxide and quartz sands are governed by a mechanism that is independent of surface chemistry, implying that nanoparticle re-entrainment from the secondary minimum is not an important mechanism in the two quartz experiments. As the tailing behaviour is independent of surface chemistry, a physical mechanism is likely responsible. The conducted tracer tests (presented in Figure 9.3) reinforce the observation that physical mechanisms are likely responsible for nAg tailing. The tracer tests all exhibited extended tailing during elution and linearly decreasing concentration in log-log space. The linear decrease occurred over approximately 3 orders of magnitude of concentration. The high repeatability of the tracer experiments indicate that this observed tailing, for both the tracer and the nAg, are real and consistent for the experimental systems

employed. The unitless k values from eq. 4.1 were fitted to each of the tracer test elution curves and were relatively consistent across all tracer experiments (uniform quartz: 7.6 +/- 1.2, 6.3 +/- 0.8, 7.9 +/- 0.6; well graded quartz: 7.3 +/- 0.6, 7.0 +/- 0.7; uniform iron oxide: 7.1 +/- 0.8, 6.4 +/- 0.6). The tracer k-values are higher than the nAg values, indicating a higher slope of eluted concentration and therefore less extended tailing

relative to the nAg. This is hypothesized to be due to the fact that the higher diffusivity of solutes yields higher diffusive mass fluxes relative to nanoparticle diffusion.

Traditional CFT models (i.e., Figure 4.1a) do not include physical mechanisms that could yield the extended tailing behaviour in Figure 4.2. The immobile areas that were

hypothesized to be the source of the CFT discrepancies in Table 4.2 are likely the source of the tailing behaviour in Figure 4.2. Specifically, diffusive mass transfer into and out of the immobile areas is the hypothesized source of temporary hydraulic retention. The quantities of nanoparticles interacting with the hypothesized immobile zones are significant enough to yield both extended tailing and reduced attachment rates onto the collectors’ surfaces at the column-scale. This suggests that the pore-scale concentration gradients, responsible for driving diffusive flux towards the collector surface, may be independent of surface chemistry and dominated by immobile zones. The next section will test the hypothesis that immobile zones are present in the three experiments by examining pore-scale concentrations and pore water fluid velocities near grain-grain contacts using pore-scale SXCMT data.