Investigating the impact of exit effects on solute transport in macropored porous media

The effect of macropore flow on solute transport has spurred much research over the last forty years. In this study, non-reactive solute transport in columns filled by macropored porous media was experimentally and numerically investigated, and the emphasis was put on the study of exit effects, whose very existence is inherent to the finite size of any experimental column. We specifically investigated the impact of the presence of a filter at the column outlet on water flow and solute transport in macropored systems. Experiments involving breakthrough measurements and magnetic resonance imaging (MRI) 5 showed that solute transport displayed some significant non-unidirectional features, with a strong mass exchange at the interface between the macropore and the matrix. Fluid dynamics and transport simulations indicated that this was due to the nonunidirectional nature of the flow field close to the outlet filter. The flow near the exit of the column was shown to be strongly impacted by the presence of the outlet filter, which acts as a barrier and redistributes water from the macropore to the matrix. This impact was apparent on the breakthrough curves and the MRI images. It was also confirmed by computer simulations 10 and could, if not properly taken into account, impede the accurate inference of the transport properties of macropored porous media from breakthrough experiments.

and in some fundamental studies of transport in porous media (Lehoux et al., 2016;Deurer et al., 2004;Greiner et al., 1997). The perturbations induced by the presence of the entrance and the exit ends of the column can have a concrete incidence (e.g., flow disturbance and recirculation in the system reservoirs, additional solute dispersion). 25 Consequently, the breakthrough curves (BTCs) may be affected by entrance/exit effects and may no longer reflect the intrinsic transport properties of the porous medium, but the transport properties of the whole experimental system (Lehoux et al., 2016;Schwartz et al., 1999;Starr and Parlange, 1977;James and Rubin, 1972). Several parts of the column device can impact the solute breakthrough (Giddings, 2002): upstream and downstream reservoirs, restrictions between the reservoirs and the tubes, and frits or filters positioned at the inlet and outlet. These inert physical filtration devices are often employed to diffuse the 30 incoming water flow evenly on the entrance face of the porous medium and to prevent porous medium particles from exiting and clogging the tubes downstream.
All these parts, located right before and/or right after the porous medium, may trigger disturbance of water flow and solute transport, especially when the porous medium under scrutiny is heterogeneous (Barry, 2009). Heterogeneous columns have in particular been employed in transport studies motivated by questions raised by the complexity of water infiltration and mass 35 transport in real soils. Real soils frequently contain macropores (Beven and Germann, 2013), which are large and continuous openings known to be involved in the rapid displacement of water and chemical substances, and various breakthrough experiments have been performed to study the role played by single macropores embedded in porous medium (Allaire et al., 2009).
Unsaturated conditions being difficult to sustain in a well-controlled fashion, and the effect of macropores being expected to culminate when they are activated (i.e., water-saturated), many results have been obtained from macropored columns operated 40 in the saturated regime, with different artificial systems: packed soils containing constructed macropores, macropored sandy media, glass bead packings crossed by a macropore, etc. (Allaire et al., 2009;Li and Ghodrati, 1997;Ghodrati et al., 1999;Lamy et al., 2009;Batany et al., 2019). However, to our knowledge, the potential impact of entrance/exit effects on solute transfer through macropored porous media has never been investigated so far.
This paper aims to demonstrate the significant influence of the presence of an outlet filter on water flow and non-reactive 45 solute transport within an artificial macropored system (the inlet filter was always set in place to prevent any clogging of the macropore). Using a combination of breakthrough experiments, MRI monitoring and computer simulations, we show that water flow and non-reactive solute transport in macropored porous media are strongly affected by the presence of a filter at the end of the column. This filter influences the velocity field in a sizable fraction of the macropored porous medium and strongly impacts the transport of solute in the macropored porous medium and its elution at the outlet.

Porous media and columns
We have constructed experimental columns filled with Hostun sand (HN 0.6/1.6, Sibelco, France). Before any experiment, the sand was sieved at 0.5 mm with a stainless mesh sieve. The sand was first washed with a 2 mol L −1 nitric acid solution, obtained by diluting nitric acid 65% (Emsure, Millipore) in ultrapure water (Milli-Q Integral 3 Water Purification System, Millipore).
The sand was then rinsed twice with ultrapure water and neutralized with a 0.1 mol L −1 potassium hydroxide solution obtained by diluting 1 mol L −1 potassium hydroxide (Titripur, Millipore) with ultrapure water. Afterwards, the sand was rinsed several times with ultrapure water until the pH of the solution reached the pH of the rinsing solution. Finally, the sand was dried at 105 • C during 24 h and then stored in a plastic container. The particle size distribution of the sand was measured by laser diffraction (Mastersizer 3000, Malvern). It ranged between 0.30 mm and 1.10 mm, with a median particle diameter equal to 60 1.0 mm. Pore size distribution was also characterized by X-ray tomography (SkyScan 1275 micro-CT, Bruker) and the median pore diameter was found to be equal to d 50 = 0.38 mm.
Two kinds of hollow cylinders were used as macropores. They were 3D printed (Form 1+, Formlabs) using a photoreactive resin (Clear Resin, Formlabs). The hollow cylinders had an inner diameter id m = 3.0 mm, an outer diameter od m = 5.0 mm, and a height of 15.0 cm. The first hollow cylinder was plain (no holes), whereas the second one was perforated with 0.5 mm 65 diameter holes resulting in a 25% surface porosity. These two hollow cylinders were used to model impermeable and permeable macropores, respectively: water could flow and solute could cross the boundaries of the perforated hollow cylinder, whereas the plain one was impermeable to water flow and solute transfer.
We used XK 50/30 (Cytiva) columns to pack the porous media. The inner diameter of each column was equal to d col = 5.0 cm and their height was equal to L = 15.0 cm. The macropored columns were set up by inserting the hollow cylinders along 70 the axis of the columns. Then, the Hostun sand was slowly poured around and dry packed thanks to gentle manual vibrations.
Once filled with sand, each column was saturated during 2 h with carbon dioxide, a gas much more soluble in water than air.
The column was then slowly water-saturated with a conditioning solution. Then, it was rinsed with 12 pore volume of the same conditioning solution at different flow rates (from 0.5 to 3.0 mL min −1 ) to stabilize the pH and the electrical conductivity.
Mesh filters (Net Rings, Cytiva) adapted to the XK 50/30 columns with 10 µm pores were positioned just before and right 75 after the porous medium. The exit effect, which is the focus of this study, was studied by removing the outlet filter for some of the experiments.
Three experimental columns (denoted A, B and C) were prepared according to the aforementioned methodology: column A is a homogenous control column, without any macropore, column B contains a perforated hollow cylinder along its axis acting as a permeable macropore and column C contains a plain hollow cylinder along its axis acting as an impermeable macropore.

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The columns are depicted in Fig. 1. The pore volume of each column was estimated by weighting the column before and after saturation. The values were 119.5, 116.6 and 120.2 mL for columns A, B and C, respectively.

Aqueous solutions
We used two conditioning solutions and two tracer solutions. A 1.0 × 10 −4 mol L −1 potassium nitrate (KNO 3 ) solution was used as the first conditioning solution. The first tracer solution was a 1.0 × 10 −2 mol L −1 potassium nitrate solution. Both  All the solutes were considered to behave as tracers, i.e. non-reactive chemical species following the water flow without any sorption, neither to the particles of the porous media nor to the walls of the hollow cylinder.

Breakthrough experiments
Columns were arranged vertically and solutions were injected from the bottom to the top, using a peristaltic pump (Ismatec ISM834A) connected to the injection system of a ÄKTAprime device (Cytiva) with polyether ether ketone (PEEK) tubings having a 0.75 mm inner diameter (Cytiva) and capillary tubing with an inner diameter of 1.55 mm included in the adapters of the XK 50/30 column. This low-pressure liquid chromatography system was used to continuously monitor electrical conductivity, 100 pH, UV absorbance and temperature at the outlet of the column.
Each breakthrough experiment began with the injection of more than 2 pore volumes of conditioning solution to stabilize the pH and the electrical conductivity measured at the outlet of the column. Then, 5 mL of tracer solution were injected. The flow rate was set at Q = 3 mL min −1 , corresponding to a mean Darcy velocity q = 4Q/(πd 2 col ) equal to 0.15 cm min −1 . Each breakthrough experiment was triplicated. The relative concentration was determined from the measurement of the electrical 105 conductivity σ at the outlet as follows, where σ min stands for the minimum electrical conductivity obtained when the conditioning solution is injected and σ 1 is the electrical conductivity of the tracer solution.

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The transport of Gd 3+ within a column, which is an opaque three-dimensional system, was monitored with a vertical nuclear magnetic resonance spectrometer (DBX 24/80 Bruker), operating with a 0.5 T static magnetic field (20 MHz 1 H frequency), and equipped with a birdcage radio-frequency coil delimiting a measurement zone of 20 cm in diameter and 20 cm in height.
Due to its paramagnetic properties, Gd 3+ is known to be an excellent MRI contrasting agent (Pyykkö, 2015), and has already been used to study solute transport in soils (Haber-Pohlmeier et al., 2017).

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As for the breakthrough experiments, the Gd 3+ solution was injected at 3.0 mL min −1 in the column from the bottom with a peristaltic pump connected to the ÄKTAprime device. The sole difference between the classical and the MRI monitored breakthrough experiments was that in the latter case, the connecting tubes were longer (10 m before the entrance and 10 m after the exit of the column), so that the injection system was outside the MRI setup.
Two-dimensional MRI vertical slices of 6 mm thickness, encompassing the axis of the column, were taken at different times 120 during the injection of the solute. Each image had 128 × 64 pixels and was acquired in 3 min 55 s. The field of view was 19 cm × 5.5 cm, providing a spatial resolution of 1.48 mm/pixel × 0.85 mm/pixel. A multi-spin multi-echo (MSME) sequence based on a succession of 16 echoes was used, with an echo time T E = 7.4 ms, and a recycle delay T R = 1.2 s. This multi-echo sequence, schematized in Fig. 2, has been employed to improve the signal-to-noise ratio, without increasing the measurement time, as the measured 16 echoes were added to produce a single two-dimensional image (Zhou et al., 2019), thus preventing 125 direct concentration quantification. Moreover, due to the short recycle delay used to keep measurement time below 4 min, the resulting signal depends simultaneously on the spin-lattice relaxation time T 1 and on the spin-spin relaxation time T 2 , thus complicating quantification through a simple comparison with a reference. The MRI images can nevertheless be used to evaluate where Gd 3+ is present within the column.

Computer simulations 130
Numerical simulations were performed with COMSOL Multiphysics (version 5.4), a commercial finite element software.
COMSOL Multiphysics was used to define the geometry of the problem, to generate the computational mesh and to solve the partial differential equations governing the fluid flow and the non-reactive transport of the solute, with the specified initial and boundary conditions.
To simulate column B, we developed a 2D axisymmetric geometric model (15.0 cm length and 2.5 cm radius) with two 135 regions: one for the sandy matrix and another one for the macropore. The filters were represented as 10 µm thick porous media.
The geometry of the inlet and outlet reservoirs was also taken into account in the numerical model.
The mesh was automatically built by COMSOL Multiphysics. It was adapted to the geometry previously defined with an increase in node density at the interfaces between subdomains and in small subdomains (like the filters or the reservoirs). We checked that the numerical results remained unaffected when the mesh was refined.

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The stationary flow of the carrier liquid within the column was described by the Stokes equations in the macropore (free region) and by the Brinkman equations in the surrounding porous media (Guyon et al., 2015). The Stokes equations read: (2) p stands for the liquid pressure, µ for the dynamic viscosity of the liquid and u for the velocity field of the liquid.
In the surrounding porous medium and in the filters, the Brinkman equations were used to model the liquid flow since 145 momentum transport induced by shear stresses is of importance at the interface between the macropore and the porous matrix (Ochoa-Tapia and Whitaker, 1995). These equations extend Darcy's law to describe the dissipation of the kinetic energy by viscous shear and read: φ is the porosity and κ the permeability of the porous matrix.

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The transport of the non-reactive solute was modeled with the advection-diffusion equation in the macropore and the advection-dispersion equation in the porous medium. Both equations can be written as: In the macropore, D denotes the isotropic tensor D 0 I , D 0 being the molecular diffusion coefficient of the solute and I the second-order identity tensor. In the porous matrix and in the filters, D denotes the transversely isotropic tensor D Lû ⊗û + normalized vector u/|u| and the symbol ⊗ denotes the tensor product. D L and D T combine the effects of both molecular diffusion and mechanical dispersion and can be written as follows (Bear, 1988): τ the tortuosity of the porous medium, λ L the longitudinal dispersivity and λ T the transverse dispersivity. Moreover, we 160 assumed for the sake of simplicity that the transverse dispersivity was equal to one-tenth of the longitudinal dispersivity, Zech et al., 2018). Solving Eqs. 2, 3 and 4 requires the knowledge of the hydraulic and transport properties of the porous medium and the filters. Regarding hydraulic properties, the permeability of the sand was evaluated with the Kozeny-Carman equation (Guyon et al., 2015), d g being the mean diameter of the grains. In order to fit the experimental BTCs, d g was taken equal to 0.57 mm (a value rather close to d 50 = 0.38 mm determined by X-ray tomography), yielding for the sand a permeability of 2.6 × 10 −10 m 2 . The filter was modeled as thin porous slab periodically perforated by square holes of length a = 10µm. The surface porosity of the slab has been taken equal to φ filter = 25%. According to Bruus (2007), the permeability of a channel with a square cross-section of 170 side length a is equal to Numerically, this yields κ sq 3.5 × 10 −2 a 2 . The permeability of the filter was taken equal to κ filter = 3.5 × 10 −2 a 2 φ filter = 8.7 × 10 −13 m 2 . The longitunal dispersivity of the porous matrix was taken equal to the mean pore size, i.e. 0.40 mm for the sand and 10 µm for the filters, and the tortuosity was set equal to 1.

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As for the boundary conditions, a given flow rate was imposed at the inlet of the column and a uniform pressure was imposed at the outlet. For the solute, we considered a concentration flux condition at the entry of the system. To model the injection of a 5 mL volume of tracer solution, we set the concentration flux to 1 during the first 5 mL of injected solution and to 0 afterwards.
Since Eq. 4 is linear in c, the concentration calculated this way is equal to the normalized concentration, whatever the genuine value of the physical concentration of the tracer solution at the inlet of the column. in the absence of the outlet filter and are both slightly asymmetric bell-shaped curves, a standard shape for columns filled with homogeneous porous media. The two BTCs are nearly indiscernable, which implies that the outlet filter has no impact on solute transport in the homogeneous case.
The results are very different for the two macropored columns, B and C. The BTCs measured at the outlet of column B (perforated macropore) are depicted in Fig. 3b, in the presence (blue curve) and in the absence (red curve) of an outlet filter.

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The two BTCs share some features, such as the existence of two distinct peaks. The first peak is very asymmetric, with a short ascent followed by a long tail. Breakthrough starts for small values of the number of pore volumes (PV ≤ 0.02) and the maximum of the first peak is reached for PV 0.05. The second peak is much more symmetric and reaches its maximum after more than 3 pore volumes. However, the two BTCs differ with respect to the position of the maximum of the second peak: it is located at PV 3.2 when the outlet filter is present and at PV 3.6 without any outlet filter. This discrepancy entails 200 that the mean residence time associated with the second peak is affected by the presence of the outlet filter. Besides, this mean residence time is directly related to the mean longitudinal pore velocity of the solute giving rise to the second peak of the BTCs.
Consequently, the difference in PVs means that the flow within the column is affected by the presence of the outlet filter.
The analysis of the BTCs of column B gives further insight into the characteristics of the flow field within this column.
The decrease of the first peak is surprisingly slow. The normalized concentration remains above zero at least up to PV = 1.5,

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whereas the volume of the macropore is only 1% of the total pore volume of the system. The slow decrease of the normalized concentration measured at the outlet of column B thus hints at the existence of a substantial solute transfer between the porous matrix and the macropore.
We performed the same kind of experiments by replacing the perforated hollow cylinder used in column B by a plain one to investigate the possible occurrence of such a transfer. The BTCs measured at the outlet of column C are depicted in Fig. 3c, 210 in the presence (blue curve) and in the absence (red curve) of the outlet filter. The shape of the BTCs is less affected by the presence of the outlet filter than for column B. The comparison of Fig. 3b and Fig. 3c shows that the decrease of the first peak is much more pronounced for column C. In this column, by construction, water and solute exchange is prohibited between the macropore and the porous matrix. Thus, the solute having entered the column through the macropore (respectively, through the porous matrix) remains in the macropore (respectively, in the porous matrix) throughout its transport within the column. the macropore and through the matrix. This is not the case for column B, whose macropore is perforated, and that can thus experience some solute transfer between the macropore and the surrounding matrix. The difference between the BTCs of columns B and C shows that such solute transfer does occur and explains the long tail associated with the first peak measured at the outlet of column B. Moreover, in contrast with column B, the area below the first peak of column C is less than half of 220 9 https://doi.org/10.5194/hess-2020-494 Preprint. Discussion started: 6 October 2020 c Author(s) 2020. CC BY 4.0 License. the total area below the BTC, providing further information on the extent of solute transfer between the macropore and the porous matrix in column B.
Finally, for column C, the second peaks reach their maxima for rather similar values of PV (PV 2.1 in the presence of the outlet filter and PV 2.0 in its absence). These values are smaller than those observed for column B, which means that the mean longitudinal pore velocity of the solute associated with the second peak is significantly greater in column C than in 225 column B. It shows that, besides the alteration of water and solute exchange at the interface between the macropore and the porous matrix, the presence of a plain macropore also modifies the flow field within the column.

MRI monitoring of Gd 3+ transport
A set of successive two-dimensional MRI images illustrating the time evolution of Gd 3+ presence within column B is shown in Fig. 4b and 4c. These images were taken over the course of the injection of the GdCl 3 tracer solution. Due to magnetic field 230 heterogeneity, the images are deformed near the entrance and the exit of the column, leading to the distortion of the column lateral boundary on the images. However, this imperfection does not hinder their qualitative exploitation. Moreover, we also carried out additional breakthrough experiments, this time with GdCl 3 conditioning and tracer solutions (see Fig. 4a). The general features of the GdCl 3 BTCs are similar to those of the KNO 3 BTCs (displayed in Fig. 3b), discussed in the previous section.

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In the successive two-dimensional images displayed in Fig. 4b and 4c, the grey level of each pixel is sensitive to two parameters, the local porosity (since the column is saturated, the higher the local porosity, the higher the quantity of water in a given small volume and the higher the MRI signal) and the Gd 3+ local concentration (the higher the concentration of Gd 3+ , the lower the MRI signal) (Haber-Pohlmeier et al., 2017). In the first image of Fig. 4b, before the beginning of the injection, the macropore, where the local porosity is equal to 1, appears in light grey, whereas the surrounding porous matrix, which local 240 porosity 0.4, appears in medium grey. In the following images (PV 1 -PV 8 ), some solute is present in the column and its local concentration is positively correlated with the pixel level of darkness.
The transport of Gd 3+ within the porous matrix can easily be observed, both in the presence (Fig. 4b) and in the absence of the outlet filter (Fig. 4c). We start the discussion by the case where the outlet filter is present (Fig. 4b). At PV 1 , a dark cone appears just before the outlet filter. Meanwhile, a Gd 3+ front appears in the porous matrix surrounding the macropore at the 245 bottom of the column. Then, as can be seen at PV 2 , the cone extends downwards and laterally towards the lateral boundary of the column. Moreover, the front visible in the porous matrix moves upwards. Subsequently, a brighter zone appears at the center of the cone (at PV 3 ), then invading the whole conical region, except along the boundaries of the cone which remain slightly dark (see PV 4 image). Meanwhile, the Gd 3+ front continues its ascent into the porous matrix. When the Gd 3+ front approaches the column outlet and reaches the tip of the cone, it starts to distort (at PV 5 and PV 6 ) before disappearing (at PV 7 250 and PV 8 ). During this last stage, the front is made of two very distorted parts that move away from the macropore and the central part of the column.
In the absence of the outlet filter (Fig. 4c), the situation differs. The MRI images displayed in Fig. 4c show that, in the matrix, the elution front moves upwards with a nearly horizontal shape, except for a small distortion close to the lateral boundary of the columns. This small deformation of the front is probably due to the existence of a slight preferential flow along the lateral 255 boundary of the column (also visible when a filter is present, cf. Fig. 4b). Moreover, the horizontal shape of the front is altered when it approaches the exit of the column (see PV 5 -PV 8 images), but to a lesser extent than when the outlet filter is present.
We can also notice that the macropore region appears slighly darker at the beginning of the injection (PV 1 and PV 2 images): this change of color is likely related to the transfer of Gd 3+ in the macropore. Furthermore, in the absence of the outlet filter, no conical shape appears close to the outlet of the column.

Finite element computations
We solved numerically Eqs. 2, 3 and 4 in a two-dimensional axisymmetric domain representing column B, with and without an outlet filter. The modeled BTCs (Fig. 5a) and resident normalized concentration (Figs. 5b and 5c) are in good agreement with the experimental data presented in Fig. 4. Moreover, the most eye-catching feature related to the influence of the outlet filter on 270 the experimental BTCs, which is its influence on the position of the second peak, is well reproduced by the numerical BTCs displayed in Fig. 5a. As in the breakthrough experiments (see Fig. 3b), the second peak shifts leftwards, its maximal value increases and its width decreases when the outlet filter is added. On the downside, the modeling of the first peak appears to be challenging and we did not succeed in reproducing quantitatively this portion of the experimental BTCs. Small geometrical details close to the entrance of the column have a sizable effect on the first peak of the numerical BTCs and make it difficult to 275 go beyond the qualitative agreement that we nevertheless highlighted.
The numerical concentration maps are in good qualitative agreement with the MRI images. In the presence of the outlet filter (see Fig. 5b), a conical shape rich in solute appears right after the beginning of the injection close to the exit of the column, as observed in the MRI experiments (cf. Fig. 4b).
In addition, the model predicts the progressive fading of this conical shape with the temporary persistence of a solute-rich region along its boundaries (see PV 3 image of Fig. 5b). It also reproduces the 280 upwards transport of the solute front within the porous matrix: the front in the porous matrix is nearly horizontal during the initial stage of the transport (images PV 1 -PV 4 of Fig. 5b), before being strongly distorted while approaching the exit of the column (images PV 5 -PV 8 of Fig. 5b), in good qualitative agreement with the images acquired by MRI (cf. Fig. 4b).
The numerically computed concentration maps change significantly when the outlet filter is removed, but the agreement between the calculated maps and the MRI images is still good. In the absence of the outlet filter, the solute remains much more 285 located into the macropore at the beginning of the injection, with only a slight diffusion in its surroundings (see images PV 1 -PV 3 of Fig. 5c). Moreover, no conical region appears in the vicinity of the exit of the column. Afterwards, the model predicts the upwards movement of the solute front within the porous matrix, without any distortion and with a progressive exit through the column outlet (images PV 4 -PV 8 of Fig. 5c). This pattern is similar to that observed by MRI (Fig. 4c). The sole perceptible difference is that after PV 4 , the front is curved upward in Fig. 4c, whereas it remains almost flat in the computer simulations.

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We believe that this may be due to the existence of a small preferential flow along the lateral boundary of the experimental column.
The good overall agreement between the numerical results and the observed data allows us to conclude on the way the solute is transfered through column B and to explain the effect of the outlet filter. Without the outlet filter, the solute enters into the macropore and the matrix and is then transported through these subdomains with a very moderate solute exchange between 295 these subdomains. Only a slight solute spread is visible in the upper part of the macropore (images PV 1 -PV 3 of Fig. 5c).
Solute concentration maps are similar in the lower half of the column, whatever the presence of an outlet filter, but drastic changes occur in the upper half of the column depending on the presence of such a filter. The outlet filter triggers a significant solute exchange between the macropore and the matrix, resulting in the appearance of a conical region rich in solute (images PV 1 -PV 3 of Fig. 5b). Meanwhile, a fraction of the solute is transported through the matrix, and the corresponding front 300 remains nearly horizontal until its gets sufficiently close to the column outlet. Then, this front experiences a distortion and moves towards the column lateral boundary.
To summarize, the outlet filter routes a fraction of the solute transiting through the macropore to the matrix before the exit of the column. The presence of the filter also implies that the solute transported through the matrix avoid the macropore and the central part of the column when approaching the column outlet.

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The effect of the outlet filter on solute transport results from its effect on the flow. We analyzed the water flow field to better understand how the presence of the outlet filter modifies the flow and thus impacts solute transport. Various features of the flow field are depicted in Fig. 6. From the analysis of the streamlines (Figs. 6a and 6d), the velocity magnitude maps (Figs. 6b and 6e), and the radial component of the velocity field at the interface between the macropore and the matrix (Figs. 6c and 6f), it is clear that the flow fields, with and without the outlet filter, are similar in the lower half of the column and strongly 310 differ in the upper half. The outlet filter triggers a divergence of streamlines from the macropore to the matrix close to the column outlet (Fig. 6a) and thus a water flux along this direction, as revealed by the positive radial component of the velocity vector at the macropore/matrix interface in the upper half of the column (Fig. 6c). This divergence and the related water flux across the macropore/matrix interface are responsible for the main features visible both in the MRI images (Fig. 4b) and the numerical solute concentration maps (Fig. 5b). Indeed, water routes the solute from the macropore to the surrounding matrix 315 by advection. This flow pattern explains the conical shape associated to solute transport through the macropore (images PV 1 -PV 3 of Fig. 5b). The same divergence routes the solute transported through the matrix far away from the center of the column and thus closer to the column lateral boundary. It explains the strong distortion experienced by the matrix front when it approaches the exit of the column (images PV 4 -PV 8 of Fig. 5b). In the absence of the outlet filter, there is no longer any streamline divergence near the exit of the column exit (Fig. 6d), as the water flux at the macropore/matrix interface vanishes in 320 the upper half of the column (Fig. 6f), yielding the solute to remain in either the matrix or the macropore (images PV 1 -PV 8 of Fig. 5c), except for the possible occurrence of transport by molecular diffusion (Batany et al., 2019).
With its very low permeability, the outlet filter acts as a thin layer impeding flow. The effects of embedded layers in macropored porous media were already discussed by many authors. For instance, Lassabatere et al. (2004) and Lamy et al. (2013) showed that the amendment of geotextiles in soil columns is an efficient way to homogenize flow and then foster pollutant re-325 moval by the matrix. These authors hypothesized that the geotextiles acted as impeding layers and redistributed flow from high permeability conducting zones to lower permeability matrix zones. Even if, in our study, the filter was positioned at the end of the column, the same kind of behavior seems to occur. The low permeability of the filter act as a barrier to the preferential flow in the macropore and routes parts of the water and the solutes to the matrix.
The analysis of the flow field shows that the same homogenizing effect also occurs at the inlet. Indeed, in the presence of 330 the outlet filter, symmetrical streamline distortion and flow field were obtained at the inlet and at the outlet of the column. Figure 6a shows the convergence to the macropore of some streamlines having entered the column through the porous matrix after the inlet filter, and the divergence to the porous matrix of some streamlines coming from the macropore before the outlet filter, an effect already observed in other MRI studies (Deurer et al., 2004;Greiner et al., 1997). The presence of the inlet filter tends to homogenize the magnitude of the fluid velocity right after the filter. Farther from the inlet filter, when its influence 335 on the flow is no longer felt, the streamlines become almost parallel to the axis of the column: because of the symmetry of the streamlines in the presence of the outlet filter, this is only visible in the middle of the column in this case (see Fig. 6a), whereas it is apparent in the upper half of the column in the absence of any outlet filter (see Fig. 6d). In the region where While the breakthrough curve is unaffected by the presence of an outlet filter when the column is homogeneous, this is no longer true for macropored columns, especially when the macropore is permeable to water and solute fluxes. Computer simulations show that this effect on flow and solute transport results from the barrier effect played by the outlet filter: the closer the macropore to the outlet filter, the smaller the velocity of the carrier liquid in the macropore, which leads to a strong divergence of the streamlines of the carrier liquid near the outlet filter. This entails a substantial transfer of water and 360 a joint transport of solute of advective origin from the macropore to the surrounding matrix. Meanwhile, the solute conveyed through the porous matrix is transported away from the central part of the column when approaching the outlet filter. This very significant alteration of the flow before the outlet filter, which is responsible for some distinctive features of non-reactive solute transport within such columns, is obvious on the MRI images and the simulated concentration maps (occurrence of conical shapes) and explains the influence exerted by the outlet filter on the breakthrough curves.

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The numerical results show that the presence of filters (at the outlet, but also at the inlet) can impact the flow of the carrier liquid over a significant part of the column. The flow can display some substantial non-unidirectional features associated with entrance/exit effects. Such finite length effects are expected to be less pronounced as the ratio between the length of the column and its diameter increases, but increasing this ratio is not always an option (e.g. because it entails the use of a greater amount of material and of stock solutions, or because the columns may have to be small due to experimental constraints).

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This study shows that a simple one-dimensional transport model will not necessarily be appropriate, even when L/d col = 3 (ratio we have worked with in this study). Indeed, when it comes to fitting the experimental data, a good knowledge is required regarding i) the stationary flow within the system; ii) the effect of the various elements of the experimental apparatus on solute transfer between domains differing in their hydraulic properties. Our results shows that this knowledge is crucial for the understanding of the outcome of transport experiments in heterogeneous columns and for the accurate inference of transport 375 properties from breakthrough studies.
As emphasized in this work, for different experiments to be reliably exploited and compared, there is a need to report accurately the geometric features of the column and the boundary devices employed when performing transport experiments with heterogeneous media (frits or filters, reservoirs, incoming tubes, etc.). It may only be possible to relate transport parameters to porous medium properties by taking into account the whole experimental apparatus employed. This issue requires a careful 380 consideration of the potential impact of the geometry of the column and the additional boundary devices to draw some quantitative estimates from experimental data obtained with macropored columns. In any case, more in-depth studies devoted to this subject are certainly called for.