Controlled Deposition of Particles in Porous Media for Effective Aquifer Nanoremediation

In this study, a model assisted strategy is developed to control the distribution of colloids in porous media in the framework of nanoremediation, an innovative environmental nanotechnology aimed at reclaiming contaminated aquifers. This approach is exemplified by the delivery of humic acid-stabilized iron oxide nanoparticles (FeOx), a typical reagent for in situ immobilization of heavy metals. By tuned sequential injections of FeOx suspensions and of solutions containing a destabilizing agent (i.e. calcium or magnesium), the two fronts, which advance at different rates, overlap at the target location (i.e., the central portion) of the porous systems. Here, the particles deposit and accumulate irreversibly, creating a reactive zone. An analytical expression predicting the position of the clustering zone in 1D systems is derived from first principles of advective-dispersive transport. Through this equation, the sequence and duration of the injection of the different solutions in the medium is assessed. The model robustness is demonstrated by its successful application to various systems, comprising the use of different sands or immobilizing cations, both in 1D and 2D geometries. The method represents an advancement in the control of nanomaterial fate in the environment, and could enhance nanoremediation making it an effective alternative to more conventional techniques.


S1.
Possible approach of the injection strategy for field application. Figure S1. Approach for the field application of the injection strategy proposed for the optimization of nanoremediation by the in-situ immobilization of nanoparticles. The stable colloidal suspension of engineered nanoparticles and the destabilizing agent are sequentially injected from the same injection well, separated by a water buffer pulse. The nanoparticles deposit in the area where the front of nanoparticles mixes with the destabilizing agent plume, creating a reactive zone for the pollutant degradation.

S2. Analytical solution for one-dimensional transport in porous media
The one dimensional advective-dispersive transport of a generic species subject to linear sorption in a semi-infinite porous medium in the presence of a uniform flow field is described by the following analytical solution 1,2 : where x and t are the space and time coordinates, respectively, vr (L T -1 ) is the species retarded velocity, lower than the pore water velocity, v, and is the dispersivity coefficient (L).

S3.
Particle immobilization before the center of the column. Figure S2. Immobilization tests performed in 21 cm long columns packed with Sibelco S1 sand using 20 mM CaCl2 solutions as destabilizing agent. The tests were performed using two different durations of the water pulse between particle and divalent cation injections. The first test (blue circles) used the = 248 s as predicted from eq. 3 in the main text for xt equal to half column (xmax = 10.5 cm). A second experiment was then performed applying a shorter water pulse (200 s) (orange squares). The use of a shorter water pulse resulted in the formation of the reactive zone closer to column inlet and outside of the target zone, because of the earlier contact between particles and divalent cations.

S4. Determination of transport parameters
Transport parameters needed to implement eq. 3-4 (main text) can be determined from column transport tests and colloidal stability tests. In particular, the parameter E is obtained from colloidal stability studies similar to those reported in Tiraferri, et al. 3 . The parameters αc, vc and vp are obtained via least-square fitting of experimental breakthrough curves obtained from column transport tests of tracer, particles, and calcium chloride. Assuming that sorption follows a linear isotherm, eq. S1 can be used to fit the experimental data. In this case, the velocity of the retarded species can be written as: where q is the specific discharge (i.e. discharge rate divided by the cross section of the column), ε is the effective porosity available for flow, and R is the retardation factor, equal to 1 for a tracer, and higher than 1 for retarded substances. The effective porosity ε is independent of the transported species, while R and αr, as a general rule, are not 4 .
Experimental breakthrough curves can be least-squares fitted to eq. S1 to determine parameters of eq. 3 in the main text following this approach (in this work, the software MNMs, http://areeweb.polito.it/ricerca/groundwater/software/MNMs.php, was used to this aim):  A tracer test (i.e. injection of a tracer solution -in this work calcium chloride -in the column previously saturated with tracer-free solution) is run and the breakthrough curve is fitted to eq. S1 assuming R=1. ε and αt are thus determined.  A solution of the destabilizing agent (e.g., calcium chloride) is injected into the column previously saturated with calcium-free solution. The breakthrough curve is fitted to eq. S1 using ε from the tracer test: αc and Rc are thus determined, and vc is calculated using eq. S1.  The nanoparticle suspension is injected into the column previously saturated with particlefree solution. The breakthrough curve is fitted to eq. S1 using ε from the tracer test: αp and Rp are thus determined, and vp is calculated using eq. S2.
An example of experimental and modeled breakthrough curves for calcium chloride and FeOx nanoparticles in Sibelco sand is reported in Figure S3. Fitted parameters for the experimental conditions explored in this work are reported in Table S1. In the x-axis, the pore volumes injected into the column. The fluids were introduced at time 0. The key experimental conditions were: pH 7.5-8, pore volume 20.2 mL, temperature 25 °C, and Darcy's velocity 7.8×10 -5 m/s.