# 19F magnetic resonance imaging-informed fate models of PFAS in porous media

Elisabeth Fries, Denis Courtier-Murias, Pierre-Emmanuel Peyneau, Béatrice Béchet, Nathalie Moitrier, Jaime Elías Gil Roca, Eric Michel

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Elisabeth Fries, Denis Courtier-Murias, Pierre-Emmanuel Peyneau, Béatrice Béchet, Nathalie Moitrier, et al.. 19F magnetic resonance imaging-informed fate models of PFAS in porous media. Water Research, 2026, 290, pp.125088. 10.1016/j.watres.2025.125088. hal-05397901

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# ¹⁹F magnetic resonance imaging-informed fate models of PFAS in porous media

Elisabeth Fries<sup>a,b D</sup>, Denis Courtier-Murias<sup>b</sup>, Pierre-Emmanuel Peyneau<sup>b D</sup>, Béatrice Béchet<sup>b</sup>, Nathalie Moitrier<sup>a</sup>, Jaime Elías Gil Roca<sup>c</sup>, Eric Michel<sup>a D,*</sup>

## ARTICLE INFO

### Keywords:

Per- and polyfluoroalkyl substances

Dispersion

Adsorption

Transport

Non-destructive imaging

¹⁹F MRI

Fluorine

Perfluorobutanoic acid

## ABSTRACT

Per- and polyfluoroalkyl substances (PFAS) are persistent contaminants. Predicting their fate in natural or engineered porous media, using accurate models, is essential for effective remediation and contamination management strategies. The mechanisms of transport and retention included in such models, and the associated parameters, are mostly inferred from PFAS concentration vs. time breakthrough curves (BTCs) measured during transport experiments. Still, the interpretation of BTCs may not be unique as they result from a succession of mechanisms taking place inside the porous media. We addressed this issue using ¹⁹F magnetic resonance imaging (MRI) to monitor the transport of perfluorobutanoic acid (PFBA) inside a sand-packed column. The experimental BTC was slightly asymmetric, suggesting that some PFBA may have been adsorbed onto the sand. Hence, a transport model based on the hypothesis that PFBA behaved as a non-sorbing tracer slightly overestimated the concentrations in two regions of the BTC. Surprisingly, the same model matched well the MRI profiles, pointing out that the BTC asymmetry stemmed from an imperfect column exit. Although ¹⁹F MRI requires PFAS concentration above those found in environmental samples, this study showed that the combination of this technique and modeling constitutes a powerful tool to determine the mechanisms involved in PFAS transport in natural or engineered porous media and select appropriate fate models.

## 1. Introduction

The term per- and polyfluoroalkyl substances (PFAS) refers to a large class of substances that are persistent, bioaccumulative, widely used, and ubiquitous in all compartments of the environment (Evich et al., 2022). Some have negative effects on the health of living organisms (Sunderland et al., 2019; Delor et al., 2023). For these reasons, scientists, policy-makers and manufacturers have a strong need to understand — and gain the capacity to predict — the fate of these substances in porous media, either natural (soil, sediments, riverbanks) or man-made (e.g. filters, contaminant sorption devices).

Indeed the fate of PFAS in porous media has received increasing attention in the last two decades. Experiments in batch (adsorption/desorption kinetics and isotherms) have allowed to determine the sorption properties of a subset of these molecules in natural and engineered porous media (Nguyen et al., 2020; Smith et al., 2023). Transport experiments, in columns packed with grains mimicking aquifer material or soils, or with resins or sorbents used to remove PFAS from

contaminated waters, have highlighted factors influencing the transport of PFAS in these media: the molecular structure of PFAS (chain length and head group), the chemistry of the porous media (organic matter content, surface charge), the pore water chemistry (pH, ionic strength) and the presence of air-water interfaces. Vierke et al. (2014), Niarchos et al. (2022), Lyu et al. (2018). This knowledge facilitated the development of PFAS sorbents and models of PFAS fate in porous media. Brusseau et al. (2019b). Still, various strategies have been used to model PFAS sorption in porous media, often in similar experimental situations: instantaneous (equilibrium) or kinetic (out of equilibrium) sorption onto a single type of sorption sites (Brusseau et al., 2019a,b; Guo et al., 2020), kinetic sorption mechanisms onto two different types of sites (Courtier-Murias et al., 2017). This multiplicity of modeling strategies suggests that a generic transport and sorption model of PFAS in porous media is not available yet.

The outputs of transport models have been compared with breakthrough curves (BTCs, PFAS concentrations measured at the outflow of the porous media as a function of time during transport experiments).

<footnote><sup>a</sup> EMMAH, INRAE, Avignon Université, Avignon, 84000, France</footnote>

<footnote><sup>b</sup> GERS-LEE, Univ. Gustave Eiffel, Bouguenais, 44344, France</footnote>

<footnote><sup>c</sup> Laboratoire Navier, CNRS, ENPC, Université Gustave-Eiffel, Champs sur Marne, 77420, France</footnote>

<footnote>* Corresponding author.
E-mail address: eric.michel@inrae.fr (E. Michel).</footnote>
BTC data have been used for more than six decades to gain information on the physical and chemical processes taking place inside porous media and can — in principle — be used to determine the model that describes best these processes. However, the interpretation of BTCs in terms of transport and retention mechanisms may not be unique as they result from a combination of mechanisms taking place inside the porous media. For this reason, the good agreement between a modeled and an experimental breakthrough curve may not always be sufficient to validate the hypotheses of a model. Furthermore, a strong body of literature has shown — relying on the capability of non-invasive imaging techniques to directly observe transport inside a porous media — that BTCs not only depend on the physical and chemical processes that take place in the porous media during transport but are often affected by imperfect entrance and exit into/from the experimental columns (Guillon et al., 2013; Scheven et al., 2007; Lehoux et al., 2016, 2017). These affect the values of transport model parameters calibrated on BTCs (Lehoux et al., 2016, 2017). As a consequence, values of e.g. dispersivity and solid-water partition coefficients, when determined from BTCs only, need to be interpreted with care.

The same holds true for PFAS transport where ¹⁹F MRI is a good candidate to address this problem and monitor directly the fate of these molecules in porous media (Simpson et al., 2007). Fluorine is not naturally abundant in most environmental conditions, which means that this technique can provide a direct, specific, and quantitative detection of fluorine-containing compounds like PFAS. This chemical specificity is essential for accurately tracking PFAS in complex systems. Surprisingly,¹⁹F MRI has only been sporadically used in the past, for example to monitor the dissolution of trifluorobenzene in a model porous media (Zhang et al., 2002, 2007, 2008). Actually, previous ¹⁹F MRI studies on the transport of fluorinated contaminants have only examined “simple” molecules from an NMR perspective (Zhang et al., 2002; Strynar et al., 2004; Simpson et al., 2007; Zhang et al., 2007, 2008). These are molecules containing equivalent ¹⁹F atoms, or ¹⁹F atoms that do not interact with another ¹⁹F atom via indirect dipole-dipole couplings (J-couplings). The latter could lead to a modulation of spin-echoes called J-modulation. This phenomenon is of special importance for MRI and NMR relaxometry experiments because it produces image artifacts and impedes the measurement of NMR relaxation values (Aguilar et al., 2012). Although we have recently applied this approach to the study of PFAS by ¹⁹F NMR (Courtier-Murias et al., 2012), there are no examples of ¹⁹F MRI with complex (in terms of their NMR properties) fluorinated molecules, such as PFAS compounds, in porous media. Some MRI approaches have been developed in medical research based on selective pulses, but a general approach would facilitate the routine application of ¹⁹F MRI in other fields such as PFAS transport in porous media.

In this study, we assessed the capacity of ¹⁹F MRI to acquire temporally and spatially resolved information during the transport of perfluorobutanoic acid (PFBA), a short chain PFAS, in sand. We used a simple but efficient approach to measure ¹⁹F MRI 1D profiles during PFAS transport without J-modulation. We compared these internal data to that obtained from a BTC and showed how this information, once analyzed by a solute transport model, proved useful to better understand the actual behavior of PFAS during transport in porous media.

## 2. Materials and methods

### 2.1. Sample preparation and transport experiment

Fontainebleau sand was dry-sieved (grain size between 125 and 250 µm), acid-cleaned (to remove metal oxides from its surface) following a procedure described (Lehoux et al., 2016, 2017) and wet packed into a polypropylene column (4.9 cm inner diameter, 16.0 cm height). It should be noted that although PFBA has been shown to adsorb to polypropylene (Zenobio et al., 2022) the relative low adsorption (of

the order of ng/cm²) should not affect our study using comparatively higher PFBA concentrations (see below).

Although the ¹⁹F MRI approach presented here is valid for both natural and man-made porous media, the liquid used during packing was intended to mimic groundwater. Synthetic groundwater (SGW) was prepared by mixing CaCl₂, KHCO₃, NaHCO₃ and MgSO₄ in ultrapure water at concentrations of 125, 38, 133, and 80 mg L⁻¹ respectively. The experimental column bulk density ρexp and the porosity (equal to the saturated water content θexp) were computed — in two different ways — from the volume of the column (Vcol) and (i) the mass of sand inside the column (msand) and (ii) the mass of liquid in the column (msGW) respectively. This was done assuming a sand solid density ρsand of 2.66 g cm⁻³, and using the relationship ρexp = ρsand(1 - θexp) between the bulk density and the porosity. Values of ρexp ranged between 1.56 and 1.66 g cm⁻³, and the porosity θexp between 0.38 and 0.41 cm³ cm⁻³.

The column was placed vertically into the MRI coil (device described below). Four entrance and exit points, equally distributed over the column cross-section, were used in an attempt to reduce possible imperfect entrance and exit to/from the column observed by others. At its lower end, the column was connected with four Tygon tubings (Ismatec Tygon 2001, inner diameter 1.02 mm, length 5.7 m) to a peristaltic pump (Ismatec Reglo Digital MS-4/8), which controlled the flow rate. At its upper end, the outflow was collected with four tubings which were — after about 10 cm — joined together into one tubing (4.7 m long) and connected to a fraction sampler that included a conductivity measurement cell (Cytiva Äktaprime) (Fig. S1).

The packed column was conditioned with SGW at a flow rate Q = 0.692 ml min⁻¹ corresponding to a Darcy flow velocity q = 6.1 x 10⁻⁴ cm s⁻¹ until reaching a stable conductivity at the column outlet (0.5 mS cm⁻¹). Then the 0.143 M PFBA solution (CAS 375-22-4, purity 98%, Sigma-Aldrich) and 10⁻⁴ M KBr solution were injected into the sand column at the same time in a Heaviside step over more than 2 PV while the conductivity of the effluent was measured at the column outflow every 18 s. The variations with time of the outflow conductivity will be called “conductivity curve” hereafter. The PFBA concentration used was about 7 times lower than the critical micellar concentration of PFBA in solution (Henriksson and Ödberg, 1974).

### 2.2. ¹⁹F MRI

The PFBA column transport experiment was monitored with a vertical imaging spectrometer (DBX 24/80 Bruker), operating with a 0.5 T static magnetic field and equipped with a double saddle coil in quadrature driving with an inner diameter of 60 mm and a height of 60 mm parallel to the central axis of the column (pixel size 1.25 mm). The column was positioned in the coil to monitor the sand packing next to its exit. We used a multi-spin multi-echo (MSME) sequence based on a succession of 16 echoes, the same sequence that was used by Zhou et al. (2018) in ¹H MRI experiments. The echo time TE was set to 3.2827 ms, and the recycle delay TR to 7.5 s. Each acquisition was the average of 32 scans. With these settings, the acquisition and storage of each MRI data set lasted about 250 s. In each scan, 16 data-points spaced in time by the echo time TE were acquired. The average of the 32 scans was analyzed as a mono-exponential decay characterized by a relaxation time T2 (the validity of this hypothesis will be checked and discussed latter on), so that the MRI signal (Sig) reads:

$$Sig = S_0 \exp(-T_E/T_2) \quad (1)$$

where S₀ is the MRI signal amplitude which is proportional to the number of fluorine atoms at each pixel, and T₂ is the relaxation time of these atoms that depends on their environment (Zhang et al., 2007; Courtier-Murias et al., 2017).
## 2.3. Transport model description

PFBA has been found to adsorb moderately to sand Wang et al. (2015), Lyu et al. (2023), but in the acid washed sand we expected that PFBA may not — or only very slightly, because a perfect cleaning of metallic impurities is difficult to achieve (Godefroy et al., 2001) — adsorb to the surface of the sand grains. For this reason, we analyzed the experimental conductivity and MRI profiles using a model that did not consider PFBA sorption. The model disregarded the possible impact of the anions and cations in the SGW on PFBA interactions with the sand surface that have been reported in the literature for perfluorocarboxylic acids (Gagliano et al., 2020). Furthermore, at a concentration of 0.143 M, the density of the PFBA solution injected in the sand packing was 1.55% higher than that of the SGW initially present in the pore space. Because (i) the PFBA solution transport occurred vertically from the bottom end of the column to its upper end and (ii) we injected a Heaviside step of PFBA, the highest density fluid was always located below the lowest density fluid, and the flow was stable (Lafolie et al., 1997). In a similar experimental situation, a one-dimensional advection-dispersion equation (ADE) has been used to model the transport of a water tracer in packed porous media instead of a full description of the physical problem including explicitly the impacts of the density difference of the two fluids (Lafolie et al., 1997). We follow here the same methodology using the 1D ADE for the three solutes (PFBA and KBr separately, and all anions and cations of SGW together) initially present in the column:

$$ \frac{\partial c_i(x, t)}{\partial t} = D \frac{\partial^2 c_i(x, t)}{\partial x^2} - \frac{q}{\theta} \frac{\partial c_i(x, t)}{\partial x} \quad (2) $$

where $c_i$ is the concentration of solute i in water (kg m⁻³), t is the time (s), x the depth (m), q the Darcy flow velocity (m s⁻¹), θ the water content (that is equal to the porosity because the sand packing is saturated with water), D is the hydrodynamic dispersion coefficient (m² s⁻¹). Both D and θ were assumed to be independent of time and depth. D is related to the dispersivity λ (m), to the pore water velocity v = q / θ (m s⁻¹), to the solute molecular diffusion coefficients D₀ (m² s⁻¹) and to the inverse value of the tortuosity of the pore network estimated as ξ = θ⁴/³ by D = λ (q / θ) + D₀ ξ (Majdalani et al., 2007).

Eq. (2) was implemented in the VSoil modeling platform (INRAE, 2023) and was numerically solved using a Crank–Nicolson time scheme with a second-order finite difference approximation for the space derivatives. The column length was discretized in 101 nodes. The boundary conditions were concentration flux at the column entrance, and zero concentration gradient at the column exit. The flow rate and the concentrations of PFBA, KBr and SGW were computed by the model at each node in the column and for each experimental time. The calculated concentrations were compared to the experimental data as follows. The modeled concentration of the three solutes at the column exit were converted into conductivity values, assuming (i) that the conductivity of each solute varied proportionally to its concentration, (ii) the contribution of each solute to the conductivity was additive, and (iii) there was no interactions between the anions and cations of the SGW with the sand surface. Finally, the sum of the three conductivity values based on the modeled concentrations was computed and compared to the experimentally obtained conductivity curve. The concentration profiles of PFBA computed by the model were transformed into MRI signal amplitude S₀ using a one-point calibration scheme. This point was the averaged experimental MRI signal at the end of the experiment, when — even in the case of kinetic adsorption of PFBA onto the sand — the transient regime was over and the concentration of PFBA in solution in the pores of the sand packing was equal to that of the injected solution. Because the experimental MRI profiles were recorded as the average over time of 32 acquisitions spaced by about 7.8 s, we implemented in the VSoil platform a routine to mimic this acquisition procedure, averaging 32 modeled concentration profiles recorded every 7.8 s, equally distributed before and after the mid-time of each experimental profile.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Conductivity of the column effluents as a function of time. Experimental data (gray continuous line); modeled conductivity based on the hypothesis that PFBA behaves as a tracer of water (no sorption, no transformation), with an optimized dispersivity λ = 101 ± 1 µ m, and a bulk density ρ = 1680 kg m⁻³ corresponding to a porosity φ of 0.368 (red dashed line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The transport model required five parameters. Two of them were determined from experimental conditions: the Darcy flow rate q, and the PFBA diffusion coefficient D₀. D₀ was set to 0.7 10⁻⁹ m²s⁻¹. This value was computed from the diffusion coefficient of butanoic acid in water and the consideration that fluorinated molecules have lower diffusion coefficient than their hydrogenated counterparts (25% lower for PFBA compared to butanoic acid) (Courtier-Murias et al., 2017). The dispersivity λ was not known a priori and was calibrated. The experimental bulk density ranged between 1.56 and 1.66 g cm⁻³ and this parameter was also calibrated. The saturated water content θ was computed from the fitted bulk density hypothesizing a solid density of 2.66 g cm⁻³.

In a first stage, λ and ρ were calibrated using the conductivity curve. Later on, these parameters were calibrated again using the MRI signal profiles — resulting from dissolved PFBA only — recorded at the upper part of the column close to the exit. As the VSoil platform is interfaced with R (R Core Team, 2020), the calibrations were performed using the minpack.lm package, an R interface to the Levenberg–Marquardt nonlinear least-squares algorithm (Elzhov et al., 2023). The algorithm was run several times with different initial guesses of the parameters to ensure that it had not converged to a local minimum. Besides the calibrated parameter values, the statistical uncertainties on the fitted parameters were also computed from the diagonal elements of the inverse Hessian matrix of the objective function and the residual sum of square computed for the optimum set of parameters.

# 3. Results and discussion

## 3.1. Conductivity BTC and MRI profiles

As shown in Fig. 1, approximately 9000 s after PFBA injection, the conductivity of the effluent increased sharply from its initial baseline of 0.5 mS cm⁻¹, caused by the SGW background solution initially present in the column, and rapidly reached a conductivity of 40 mS cm⁻¹ at about 10000 s. The conductivity then slowly reached its maximum value, that of the injected PFBA solution, 44 mS/cm, at a time of about 14000 s. Overall, the fast increasing conductivity followed by
the subsequent slower conductivity increase rate resulted in a slightly asymmetrical conductivity BTC (Fig. 1, gray thick line). Similar asymmetrical BTCs have been reported for PFBA and other perfluoroalkyl carboxylic acids during transport experiments in quartz sand. The asymmetry was ascribed to rate-limited sorption (Lyu et al., 2023).

Each pixel of the MRI profiles (Fig. 2) shows the value of $S_0$ in Eq. (1) and we first checked that this equation described accurately the MRI relaxation signal (i.e. that the relaxation was mono-exponential). Our analysis showed that the errors on the fitted values of $S_0$ were smaller than 10% when $S_0$ values were above of 750 a.u., and reached rapidly their lowest values (about 3%) when $S_0$ was higher than about 1500 a. u. (Figures S2, S3 to S21 upper two panels and S22). The capacity of a mono-exponential decay to describe accurately the MRI signal relaxation shows that the MRI signal was only composed by PFBA measured in a single environment (in solution), characterized by a unique $T_2$, lower than about 34 ms. This relatively short $T_2$ value further indicates that if PFBA had adsorbed onto the sand, its $T_2$ relaxation time would have been shorter than $T_E$: it would not have been measured with the MRI. This limitation of the MRI, not being able to measure adsorbed PFAS, could also simplify data analysis as comparing MRI data to modeled transport of non-adsorbed PFAS will easily indicate if there is PFAS adsorption. It is also worth noting that for long chain PFAS the NMR relaxation values should be shorter (in the case of alkanes it is divided by 2 when chain length is doubled (Freed, 2007) but this decrease should not impede their observation for non-adsorbed long-chain PFAS.

As the PFBA filled the MRI field of view, the values of $T_2$ increased progressively from about 20 ms up to a maximum value of about 34 ms (Fig. S3 to S21, lower two panels). This could originate from the tuning of the ¹⁹F MRI with respect to the sample during the transport experiment. In our case, we optimized the MRI before the experiment using a column similar to that used in the experiments, filled with the PFBA solution. As we are interested in the $S_0$ values and the causes of the changes of $T_2$ values will not (or slightly) affect the quantification of $S_0$ we have not further investigated the evolution of $T_2$ values during the transport experiments.

During the experiment, when the PFBA solution moved upward inside the sand column, the MRI tuning was then not optimal since the PFBA amount inside the NMR coil was relatively low compared to the sample used for tuning, leading to imperfect NMR pulses and thus shorter $T_2$ times (Majumdar et al., 1986). The slightly higher maximum MRI amplitude observed in the first profiles (7248 s - 8993 s) compared to later profiles could also be caused by the MRI tuning. This may be improved in future ¹⁹F MRI transport experiments with fluorinated substances by mismatching the NMR coil to make it less affected by changes in the sample susceptibility. This will lead to longer NMR pulses but will allow to obtain $T_2$ values independently of the PFAS concentration and solely depending on the fluorine environment, which is important for studies where the $T_2$ value gives information about the localization, or chemical interaction with the porous medium.

The experimental MRI profiles of non-adsorbed PFAS, ($S_0$), recorded at the end of the experiment ($t = 9993$ s, 10243 s, 10492 s), when the column pore space was completely saturated with the injected PFBA solution, were flat in a region of about 3.7 cm length in the center of the field of view (FoV), and decreased at the extremities of the FoV (Fig. 2, open circles, bottom line, the flat region is highlighted with white background). Before PFBA reached this flat region, the signal initially fluctuated about a null value (Fig. 2, first line, leftmost profile at $t = 6250$ s). In the following 17 profiles, the signal progressively shifted rightward until reaching its maximum value over the entire flat region. We will focus our analysis on this flat region. The signal intensity loss out of this region probably is an artifact resulting from a non-homogeneous coil and magnetic field, which leads to a non-uniform excitation of the spins throughout the FoV, visible in the MRI profiles at both ends of the FoV.

<caption>**Table 1**</caption>

Parameters calibrated to fit the conductivity curve and MRI profiles.

<table><thead><tr><th></th><th>Conductivity curve</th><th>MRI profiles</th></tr></thead><tbody><tr><td>λ [µm]</td><td>101 ± 1</td><td>52 ± 3</td></tr><tr><td>ρ [kg m<sup>-3</sup>]</td><td>1680 ± 0</td><td>1688 ± 0</td></tr><tr><td>θ<sup>a</sup> [m<sup>3</sup> m<sup>-3</sup>]</td><td>0.368</td><td>0.365</td></tr><tr><td>RSE<sup>b</sup></td><td>0.465</td><td>3.602</td></tr></tbody></table>

## 3.2. Modeling the effluent conductivity BTC

The assumption that PFBA behaved as a tracer described rather well the experimental BTC although the model overestimated the concentrations in two regions of the conductivity curve: at the beginning of PFBA outflow (before the inflection point of the conductivity curve) and right before it reached the influent conductivity (after the inflection point) as the water tracer model could not reproduce the asymmetry of the conductivity curve (Fig. 1, red dashed line). The fitted values of the density and dispersivity were $ρ_{cond} = 1680$ kg m⁻³ and $λ_{cond} = 101 ± 1$ µm respectively. The bulk density was close to the upper value determined experimentally (1660 kg m⁻³). The suffix ‘cond’ indicates that these parameters were determined on the conductivity BTC. The value of $λ_{cond}$ is low compared to that expected, as a rule of thumb one to five times the grain size of the solids constituting the porous medium that in our sand ranged between 125 and 250 µm. This is because the dispersion in this experimental situation is controlled by the higher density of the PFBA solution displacing the initially present low density SGW (Lafolie et al., 1997).

## 3.3. Modeling the MRI profiles

To show the importance of complementing BTC data with imaging methods, and better understand the mechanisms leading to experimental BTC, we simulated the MRI profiles ($S_0$, non-adsorbed PFBA) using the parameters determined by fitting the conductivity BTC data. Overall, the model reproduced well the experimental profiles, and in particular the depth of the PFBA front (Fig. 2). Still, a closer look at this figure revealed that the model consistently underestimated the signal amplitude when the signal was close to its maximum value, to the left of the PFBA infiltration front. This was particularly apparent between 8496 s and 9245 s (Fig. 2).

Fig. 2 also shows that the relatively poor fit of the model to the MRI profiles when using parameters determined on the conductivity BTC was not evenly distributed across the profiles, but was located in their upper half, where the model lagged behind the experimental profile, although the lower half better captured the experimental profiles. This asymmetric misfit suggests that the dispersivity fitted on the conductivity curves was slightly overestimated and that the bulk density was slightly underestimated. To check this hypothesis, we fitted the values of bulk density and dispersivity of the model to the entire profile dataset contained in the white region of Fig. 2. We then compared the fitted values to that previously obtained by fitting the model to the conductivity curve (Table 1). The fitted bulk density $ρ_{prof} = 1688$ kg m⁻³ was close to $ρ_{cond}$, the value determined on the conductivity curve. Surprisingly, the dispersivity $λ_{prof} = 52 ± 3$ µm was about half the value $λ_{cond}$ determined from the conductivity curve. Overall, the fit of the model to the experimental profiles was excellent (Fig. 2, blue continuous line). This almost perfect match of the experimental and modeled MRI profiles — computed with a model that do not consider sorption — indicate that PFBA sorption to sand did not occur, although the slight asymmetry of the breakthrough curve, interpreted in the literature as resulting from adsorption, might have suggested otherwise.

<footnote>a Parameter computed from the fitted value of ρ</footnote>

<footnote>b RSE: Residual Standard Error computed as the ratio of the residual sum of squares and degrees of freedom.</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Experimental (black circles) and modeled MRI profiles in the last 5 cm before the column exit. The modeled MRI signal was computed based on the hypothesis that PFBA behaved as a tracer of water (no sorption, no transformation), with the dispersivity $\lambda = 101 \pm 1$ µm, and bulk density $\rho =1680$ kg m$^{-3}$ optimized on the conductivity curve (red dashed line) or with these parameters fitted on the MRI profiles in the white region highlighted on the graphs (blue thick continuous line, $\lambda = 52 \pm 3$ µm, and $\rho = 1688$ kg m$^{-3}$). Error bars on the MRI signal profiles are displayed in Figures S3 to S21. They are smaller than the datapoint size when the MRI signal is greater than about 1500 a.u. The data displayed in this figure are also available as an animated image in the supplementary material. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Overall, this set of results highlights the importance of internal information (the MRI profiles) and of their quantitative interpretation with ad hoc models to determine the processes occurring during a transport experiment.

### 3.4. Reconciling breakthrough curve and MRI profiles

The reason behind the asymmetry of the breakthrough curve, in the absence of PFBA sorption, remains to be explained. The lower value of $\lambda_{\text{prof}}$, the dispersivity determined from the profiles compared to $\lambda_{\text{cond}}$, the dispersivity determined from the conductivity BTC, points to a possible explanation. This observation is in line with several other studies that systematically found that the dispersion was up to one order of magnitude lower when measured directly inside the porous media compared to a solute or colloid BTC of the same experiment (Guillon et al., 2013; Scheven et al., 2007; Lehoux et al., 2016, 2017) This effect has been ascribed to the “inhomogeneity of the entrance/exit flow” that occur in the experimental columns even when flow distributors are used (Scheven et al., 2007; Lehoux et al., 2016; Raimbault et al., 2021).

The breakthrough curves result in general from an initial deformation of the solute or particle pulse at the column entrance, then some dispersion in the porous media sample, and another deformation at the column exit since the fluid elements farther away from the outflow points reach these points later than those closer to them.

In this study, the deformation of the PFBA pulse at the column inlet was probably counterbalanced by a lateral spread of the PFBA (perpendicular to the column axis) resulting from the higher density of the incoming PFBA solution compared to the SGW. This is supported by the very low dispersivity determined from the MRI profiles next to the column exit (Table 1). This indicates that the deformation at the column outlet was most likely a significant contributor to the asymmetric conductivity curve, leading to an almost twofold increase in dispersivity (Table 1). In addition, two other mechanisms may have also contributed to increase the dispersion of the conductivity curve compared to that determined inside the sand packing. First, the column had four exit points that were connected to four tubings that joined to one after about 10 cm before continuing to the conductivity cell. We speculate that some tubes may have been less involved in the flow than
others, contributing to the asymmetric shape of the conductivity BTC. Second, the dispersion may have increased in the 4.7 m long, 1.02 mm inner diameter tubing connecting the above-mentioned four tubings to the conductivity cell. Indeed, the dimensionless number $Q/(L_{tube}D_0)$ — the ratio of the characteristic time required for the solute to diffuse transversely over the tubing diameter to the mean residence time of the solute in the tubing — is equal to 3.5, suggesting a contribution of this tubing (Batany et al., 2019). However this contribution is small: the tubing accounts for less than 10% of the increase in dispersion between the column (determined by MRI) and the BTC (see Supporting Information).

Overall the imperfect transport of the liquid at the column exit — not PFBA sorption — led to the conductivity BTC tailing. This was confirmed in a separate experiment: a tailed conductivity BTC was also observed during transport experiments of sodium fluoride — a conservative tracer in sand — in the same set-up (Fig. S23).

### 3.5. Benefits, limits and potential of ¹⁹F MRI

Collecting MRI data for a molecule with non-equivalent fluorine atoms was made possible by suppressing J-modulation using a simple but effective approach: working only with short echo times. This straightforward method is quite general and will be useful to investigate the fate of other PFAS molecules in porous media where the relaxation time $T_2$ is made sufficiently low by the physical confinement or the chemical characteristics of the materials constituting the pore space. If samples with long $T_2$ are to be studied, longer echo times will be needed and another general approach, based on the PROJECT NMR sequence (Aguilar et al., 2012) may be used as previously shown for ¹⁹F and ¹H NMR experiments (Courtier-Murias et al., 2017).

As the ¹⁹F MRI experiments need to be conducted with a sufficiently high concentration of fluorinated compounds to provide an adequate signal-to-noise ratio (S/N) while keeping acquisition times short enough to monitor a dynamic process, we chose the PFBA concentration, the flow rate and the appropriate MRI settings without considering common environmental concentrations (Brusseau et al., 2020; Johnson et al., 2022). Still, high concentrations may be found in some technological applications, for example when testing PFAS filter or sorbent systems for industrial waste waters (Barisci and Suri, 2021; O'Connor et al., 2022). Furthermore, we argue that relatively high concentrations of PFAS, such as that used in this work, can still be useful to improve the understanding of the physical and chemical mechanisms controlling the fate of PFAS in environmental samples as shown in several instances (Longstaffe et al., 2012; Masoom et al., 2015; Courtier-Murias et al., 2017). Thus, this approach is not meant to study PFAS transport or leaching of environmentally contaminated samples but to focus on understanding transport mechanism in column experiments in the laboratory and for industrial applications with higher concentrations.

In addition, should we wish to broaden the scope of this work and study samples with lower PFAS concentrations, we point out that with the ¹⁹F MRI settings used in this study, the PFBA concentration could be halved while maintaining a signal-to-noise ratio sufficient for model comparison purposes. Further decrease in fluorinated compound concentration without affecting the signal-to-noise ratio may be achieved by increasing the number of scans during the acquisition of a MRI profile. This would lead to longer acquisition times, and would require performing transport experiments with lower flow rates to be able to monitor a sufficient number of profiles (see Supporting Information).

The ¹⁹F MRI approach presented here paves the way for several practical applications that will help improve our understanding of PFAS fate in porous media. A first interesting option is the study of longer chain PFAS. For instance, using PFOA at approximately one-eighth the concentration of PFBA (in mol L⁻¹) used in the current work, the concentration would be about 0.017 mol L⁻¹. This reduction in concentration is necessary because the solubility of PFOA in water is

around 0.023 mol L⁻¹. As previously mentioned, this lower concentration will reduce the S/N, but this can be easily compensated by reducing the flow rate and increasing the number of scans. Studying long-chain molecules could be particularly interesting concerning PFAS micelles, which are thought to form on adsorbent surfaces and play an important role in PFAS adsorption (Zhang et al., 2011; Gagliano et al., 2020) and have gained increased interest in the last years. Since the critical micelle concentration (CMC) decreases exponentially with chain length (Bhatarai and Gramatica, 2010), it is likely that at this concentration PFOA will exist both as free molecules in solution and as micelles. In this case, a combination of relaxometry and MRI experiments — similar to those used to obtain MRI information on bound and free water in wood samples (Zhou et al., 2018) — could allow us to separately observe PFAS free in solution and PFAS in micelle form during a transport experiment. This approach could also prove useful for obtaining separate MRI information when PFAS are located in different porosities or environments, as recently demonstrated by ¹⁹F NMR relaxometry (Courtier-Murias et al., 2017).

A second new application could be based on Chemical Shift Imaging (CSI), which has shown in the past the potential to selectively observe different fluids in porous media by ¹H MRI. CSI manages to differentiate two protonated molecules (oil and water) in ¹H MRI and could be used in ¹⁹F MRI to monitor the transport of different PFAS molecules. Further developments may be needed to selectively observe by MRI PFAS with similar structures as their chemical shifts are also similar, but could be comparatively easier to apply to differentiate a PFAS molecule such as GenX which has a ¹⁹F NMR peak around -83 ppm which does not overlap e.g. with that of perfluorocarboxylic acids (PFCA). This technique could prove useful for studying the transport of PFAS mixtures and improve our understanding of competitive adsorption.

### 4. Conclusions

This study showed for the first time that it is possible to monitor the fate of PFAS directly inside the porosity of a saturated sand packing, by ¹⁹F MRI. The time- and space-resolved internal ¹⁹F MRI profiles and their comparison with the outputs of a transport model were crucial in understanding which processes were involved in PFBA transport in these columns and which were not. This permitted to select the most appropriate model for describing the fate of PFBA in this porous medium.

The comparison of the modeled and experimental MRI profiles and BTC data revealed that the latter was affected by an imperfect solute exit from the column, a common flaw when conducting transport experiments in homogeneous porous media. It led to a slightly stretched breakthrough curve attributed in the literature to PFAS sorption. A further investigation, leveraging profile data, proved this interpretation to be erroneous. Using only conductivity or solute concentration BTCs as a source of information to choose the mechanisms to be included in a PFAS transport model would have led to a misinterpretation of the processes actually taking place within the sample. As a consequence, past interpretations of transport experiments relying only on BTC information should be considered with care.

Overall, the combination of ¹⁹F MRI data, gathered directly inside a porous medium, with reactive transport modeling constitutes a powerful tool to improve our understanding of the mechanisms controlling PFAS fate in such media, natural or artificial. Although ¹⁹F MRI requires PFAS concentrations much higher than those found in environmentally contaminated samples it opens up promising perspective for transport experiments with PFAS through more complex media (e.g. presence of physical inhomogeneities or layered), and under more complex scenarios including multi-component PFAS solutions, competitive sorption, self-assembly of PFAS. This will help to assess and improve remediation techniques and water filter devices—both of which are essential as an increasing number of sites with PFAS-contaminated soil and groundwater are identified.
## CRediT authorship contribution statement

Elisabeth Fries: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Denis Courtier-Murias: Writing – review & editing, Writing – original draft, Validation, Methodology, Funding acquisition, Formal analysis, Conceptualization. Pierre-Emmanuel Peyneau: Writing – review & editing, Validation, Formal analysis. Béatrice Béchet: Writing – review & editing, Validation, Supervision, Methodology, Conceptualization. Nathalie Moitrier: Writing – review & editing, Software. Jaime Elías Gil Roca: Writing – review & editing, Supervision, Software, Methodology. Eric Michel: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

We acknowledge the financial support of Agence de la transition écologique (ADEME), through the IPANEMA project, contract no C7475. One of us (E. F.) was supported equally by grants from INRAE AgroEcoSystem Division and from Gustave Eiffel University. We also thank the two reviewers for their comments and questions that helped improve the manuscript.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.watres.2025.125088.

## Data availability

Data will be made available on request.

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