Impact of Sharp Soil Interfaces on Solute Transport: Insights from a Reactive Tracer Test in a 2D Intermediate-Scale Experiment

Abstract

Understanding solute transport across interfaces between different porous materials is crucial for subsurface applications. Column tracer experiments have suggested solute accumulation at these interfaces. This effect cannot be explained by standard models based on Fickian flux continuity and the advection–dispersion equation. To analyze this phenomenon, we present reactive transport experiments in a 2D intermediate-scale horizontal tank to visualize and evaluate the spatiotemporal evolution of a solute plume crossing a sharp interface between coarse and fine materials. The plume results from the reaction of two fluid solutions entering the tank in parallel through inlet ports. The reaction product is analyzed using mixing and reaction metrics. Results show the reaction product encounters anomalous resistance when the plume crosses the coarse-to-fine (CF) interface. This effect is less pronounced in the fine-to-coarse (FC) transition. This asymmetric resistance does not produce solute accumulation behind the interface, a difference from the results obtained with the one-dimensional model. Instead, results show enhanced transverse spread of the reaction product in the coarse-to-fine transition, with slow release in the fine material. A sudden decrease in the longitudinal concentration profile across the interface is observed. Mixing metrics show that as apparent transverse dispersivity increases closer to the interface in the CF transition, the scalar dissipation rate and total mass reacted increase, indicating that the CF configuration promotes greater solute reactivity near the interface compared to the FC configuration.

1. Introduction

Groundwater remediation has become a critical global concern due to the persistent challenge of aquifer pollution and the growing demand for clean water resources [1,2]. Understanding how contaminants are transported and how they mixed and react is essential for the successful remediation of polluted aquifers [3,4]. Among various remediation methods, in situ treatment technologies have attracted significant attention in recent years [5,6] because they offer cost-effective and minimally invasive solutions [7]. In this context, the effective mixing of two solutes is crucial to enhancing the performance of in situ treatments [8,9]. Since mixing governs the interaction between the injected remediation fluids and the contaminated groundwater, improved mixing facilitates mass transfer, accelerates chemical reactions, and ultimately results in a more efficient remediation process [10,11,12]. However, mixing in porous media is frequently hindered by the inherent structural complexities of natural geological formations, which can result in unexpected behavior [13,14,15]. Sharp soil interfaces constitute an important building block of a wide variety of heterogeneous geological systems, representing abrupt transitions between materials with differing permeability and grain size [16,17,18]. These interfaces, commonly found at sedimentary layer boundaries, fractured rock formations, and engineered remediation barriers [19,20,21], play a pivotal role in controlling transport and mixing. Sharp soil interfaces in porous media naturally arise from abrupt changes in depositional conditions, such as shifts in energy environments (e.g., a shift from high-energy gravel deposition to low-energy silt accumulation) or shifts in sediment supply, leading to distinct textural and permeability contrasts [22]. Coarse-to-fine and fine-to-coarse configurations are representative of these stratigraphic transitions, which are frequently observed in alluvial, deltaic, or glacial depositional systems [23]. Advancing a quantitative and comprehensive understanding of plume-interface mixing processes is crucial for optimizing remediation strategies to ensure that injected agents can interact effectively with contaminants [24,25,26] and for refining predictive models of contaminant transport in subsurface systems [12,27,28].

Research over recent decades has demonstrated that sharp interfaces significantly alter solute transport dynamics [17,29,30]. One of the first experimental works on this topic, which was conducted by Sternberg [29], revealed that sharp interfaces produce transport behaviors that classical advection–dispersion models cannot accurately represent [31,32,33]. These models assume that dispersion across an interface is a simple weighted average of the properties of both media [34]. However, experimental results show that dispersion adjusts to expected values much faster than predicted, suggesting the presence of an additional mechanism at the interface that accelerates this process [30]. Building upon this, Marseguerra and Zoia [30] investigated solute transport across sharp interfaces between coarse and fine media using the random walk method for particle-transport simulations. They observed a discontinuity in concentration profiles when solutes crossed the interface [34,35,36], which they attributed to solutes accumulating on the coarse side before gradually dispersing into the finer medium. This behavior was also suggested by Berkowitz et al. [17], who, through laboratory column experiments on solute migration in composite porous media, indicated that a conservative tracer moving through a coarse-grained segment encounters resistance when entering a finer medium [37,38]. This results in a “slow release” effect, which causes a delayed breakthrough curve and increased dispersion. Similarly, Cortis and Zoia [39] showed that particles crossing an interface between materials with different dispersion properties experience asymmetric random forces. These forces disrupt the symmetry assumed in classical transport models, leading to a delayed and spatially uneven arrival of the solute, which further complicates predictions of solute migration [40].

Although several studies have focused on understanding the effect of heterogeneity on mixing processes [41,42,43], few works have specifically addressed the impact of sharp interfaces on mixing [44]. It is well understood that sharp soil interfaces generate steep transverse concentration gradients [17] and that these gradients can have significant chemical and biological implications. In such contexts, mixing is most pronounced in the contact zones between regions of differing permeability, as reactions are especially intense along these interfaces [45]. In line with this understanding, Perujo et al. [46] demonstrated that coarse-to-fine transitions facilitate the accumulation and transformation of organic matter at the interface. This transition zone thus becomes a region of enhanced microbial activity, promoting increased biomass growth and organic matter degradation. However, the finer sediments limit biofilm development, ultimately impacting the efficiency of the overall reaction [47]. While these insights have been established, there is still much to understand regarding solute-transport behaviors and the mixing plume dynamics that arise due to sharp soil interfaces [17,44,48]. Specifically, further investigation is needed to visualize the influence of sharp soil interfaces on solute transport, the evolution of the mixing plume, concentration gradients, and mixing efficiency in two and three dimensions. Understanding the influence of sharp soil interfaces on solute transport and where mixing is most promoted within each medium will provide valuable information that can be used to optimize remediation strategies and improve our overall understanding of subsurface processes [24,25,26,49].

As a contribution, this article conducts and analyzes a novel laboratory-scale experiment to investigate and understand the impact of sharp soil interfaces on solute accumulation at the point prior to crossing the interface. Data were collected by visualizing and quantifying the spatiotemporal evolution of a reactive plume. Conservative and reactive transport experiments were conducted in a 2D intermediate-scale horizontal tank composed of a bilayer porous medium with a sharp soil interface. A set of four experiments were conducted, considering four different configurations of porous media (porous media packing): fine (F), coarse (C), fine-to-coarse (FC), and coarse-to-fine (CF). Conservative tracer tests were conducted to visualize the evolution of the solute pulse and obtain concentration breakthrough curves (BTCs), which characterize non-reactive solute-transport behavior. In the reactive experiments, colored products were generated and quantified using pixel-by-pixel calibration, which converts light intensities into concentration values. The experimental setup makes it possible to monitor and visualize in real-time the spatiotemporal evolutions of the tracer and the mixing plume. Using this approach, this work aims to demonstrate the following: (i) transport behavior and mixing processes strongly depend on the flow direction; (ii) the sharp soil interface plays distinct roles in solute transport; (iii) the sharp soil interface influences both solute reactivity and mixing efficiency.

The structure of this article is as follows. Section 2 describes the experimental setup, the porous-medium configurations used, the procedure for the reactive transport experiments and tracer tests, the chemical solutions employed, the procedure for image acquisition, the processing techniques used to capture the evolution of non-reactive and reactive transport, and the explanation of key variables and metrics used for analysis. Section 3 presents the main findings, including an analysis and discussion of the following: non-reactive solute transport, the spatiotemporal evolution of the reaction product, the longitudinal profiles of the reaction product, and the mixing metrics and their corresponding profiles. Finally, Section 4 provides a summary of the key insights from the study, emphasizing the impact of sharp soil interfaces on mixing processes and transport behavior.

2. Materials and Method

2.1. Experimental Setup

Experiments were conducted in a transparent intermediate-scale horizontal tank made of Plexiglass with the following dimensions: 26 cm in length (L), 20 cm in width (W), and 2 cm in height (H) (refer to Figure 1a). To provide uniform flow conditions, the tank has eight inlet and outlet ports evenly spaced 2 cm apart. All inlet ports are connected to a high-precision multichannel Ismatec IP-N Digital Peristaltic Pump (Ismatec Labortechnik SA, Glattbrugg, Switzerland). The inlet ports are divided into two groups by means of two four-channel flow cells to allow the injection of two different fluids, in parallel, through the inlet face of the tank. The outlet ports are ultimately connected to a single tube that freely discharges into a waste container at atmospheric pressure. The height of this tube provides a fixed constant head boundary condition during the experiments. When required for the conservative tracer test, the outlet tube is connected to an Albillia FL24 fluorimeter (Albillia Sàrl, Neuchâtel, Switzerland). (see Figure 1a). A pair of piezometers are installed, one at the inlet and the other at the outlet of the tank, to measure the effective hydraulic conductivity of the porous medium. The experiments were carried out in a dark room to prevent interference from external light (Figure 1b). Images were captured during both reactive and conservative tracer tests using a Nikon D7100 camera equipped with a Tamron SP AF 17-50mm F/2.8 XR Di II LD Aspherical (IF) Model A16 lens (Tamron Co., Ltd., Nara, Japan). Transmitted light was used for both experiments, with an LED light placed underneath the tank. Continuous monitoring was performed throughout the experiment, with a fluorometer recording data every second (BTC) and photographs taken every 30 s.

2.2. Configurations of the Porous Media

The horizontal tank was packed in four different configurations of porous media (refer to Figure 1c): (a) fine (F), using 1 mm glass beads; (b) coarse (C), using 2 mm glass beads; (c) fine-to-coarse (FC), with a vertical sharp interface transitioning from 1 mm glass beads to 2 mm glass beads; and (d) coarse-to-fine (CF), with a vertical sharp interface transitioning from 2 mm glass beads to 1 mm glass beads. In the configurations with the sharp soil interface, the interface was positioned at the midpoint of the tank, at $x\approx 13$ cm. This vertical interface was created using a 0.1 mm thick methacrylate bar. During packing, the bar was inserted into the middle of the tank to separately distribute the fine and coarse grains and was carefully removed before the tank was sealed. In each configuration of the porous media, the tank was wet packed with deionized water (Milli-Q) and it was ensured that the tank was always filled with water before the glass beads were added. This step was crucial to maintaining saturated conditions and preventing the incorporation of air bubbles into the system.

2.3. Reactive Transport Experiments and Tracer Tests

For each configuration of the porous media, the experiment was divided into three stages (Figure 2. The first stage involved the injection of a conservative tracer test pulse (Figure 2a). This stage was conducted for the purpose of characterizing non-reactive solute transport. Data collected consisted of measuring concentration breakthrough curves (BTCs) at the tank outlet and recording images that showed the spatiotemporal evolution of the pulse. This test involved injecting a fluorescein pulse (0.05 mg/L) at a constant flow rate (Q = 7.96 mL/min) for 10 min. Following the injection, deionized water was injected for 120 min to flush the tracer. The second stage involved the injection of six standard solutions with known concentrations of Tiron molybdate (${\mathrm{MoTi}}_2^{-4}$) (Figure 2b). In this stage, six light-intensity images of Tiron molybdate at a constant steady-state concentration were recorded with the purpose of establishing a clear pixel-wise relationship between concentration and color intensity. Each standard solution was injected into the tank sequentially, starting from the lowest concentration (C₁) and progressing to the highest (C₆). Each was injected for 1 h and 30 min before imaging was conducted. The tank was flushed with distilled water for another hour and a half between injections. The third stage involved the simultaneous injection of molybdate solution (W₁) and Tiron solution (W₂) through the two separate groups of inlet ports. This setup allows the chemical solutions to uniformly enter into the porous medium through half of the tank’s inlet area, promoting interaction and mixing in the middle section of the tank (Figure 2c). This stage defines the reactive transport experiment, which is aimed at investigating the influence of the sharp interface on solute transport. The total injected flow rate (Q) was 7.96 mL/min. This total flow was equally distributed between the two four-channel flow cells (Q/2), with each receiving a flow rate of 3.98 mL/min. At the tank outlet, a constant head of 90 cm above tank elevation was imposed. The reactive transport experiment lasted 3 h to ensure that concentrations reached a steady state. To prevent density issues, since both W₁ and W₂ were denser than distilled water, the tank was presaturated with a 0.4363 M NaCl solution before the reactive transport experiment was carried out.

Transport experiments were conducted under advection-dominated flow conditions (the properties of each configuration of the porous media are presented in

Table 1. Initial experimental conditions.

Symbol	Properties	Fine	Coarse	Units
Q	Total flow rate	$1.33\times {10}^{-7}$	$1.33\times {10}^{-7}$	${\mathrm{m}}^3/\mathrm{s}$
d1	Glass bead size	1		mm
d2	Glass bead size		2	mm
D	Water molecular diff (*)	$1\times {10}^{-9}$	$1\times {10}^{-9}$	${\mathrm{m}}^2/\mathrm{s}$
Re	Reynolds number	1.08	1.98	-
$\nu$	Kinematic viscosity (**)	$9.87\times {10}^{-4}$	$9.87\times {10}^{-4}$	${\mathrm{m}}^2/\mathrm{s}$
$\mu$	Dynamic viscosity	$1\times {10}^{-3}$	$1\times {10}^{-3}$	$\mathrm{g}/\mathrm{m}·\mathrm{s}$
$\rho$	Density of fluid	$1.0136\times {10}^3$	$1.0136\times {10}^3$	${\mathrm{g}/\mathrm{m}}^3$
A	Section area	$4\times {10}^{-3}$	$4\times {10}^{-3}$	${\mathrm{m}}^2$
L	Tank length	$2.6\times {10}^{-1}$	$2.6\times {10}^{-1}$	m
W	Tank width	$2\times {10}^{-1}$	$2\times {10}^{-1}$	m
H	Tank height	$2\times {10}^{-2}$	$2\times {10}^{-2}$	m
${\varphi }_1$	Porosity	0.31		-
${\varphi }_2$	Porosity		0.34	-
v1	Darcy velocity	$1.069\times {10}^{-4}$		m/s
v2	Darcy velocity		$9.75\times {10}^{-5}$	m/s
Pe	Grain Péclet number	106.9	195	-
$\Delta h_1$	Height difference	0.025		m
$\Delta h_2$	Height difference		$1.4\times {10}^{-2}$	m
$\Delta i_1$	Hydraulic gradient	$9.615\times {10}^{-2}$		-
$\Delta i_2$	Hydraulic gradient		$5.384\times {10}^{-2}$	-
K1	Hydraulic conductivity	29.8		$\mathrm{m}/\mathrm{d}$
K2	Hydraulic conductivity		53.22	$\mathrm{m}/\mathrm{d}$

Note: Information obtained from Perkins and Johnston [50] (*). The dynamic viscosity of pure water was used, as the variation due to solutes in the solution was minimal (**).

). The grain Péclet number for each configuration of the porous media was calculated using $\mathrm{Pe}=vd/D$, where v represents the fluid velocity (calculated from the total inflow rate Q, the cross-sectional area A, and the porosity $\varphi$ through $v=Q/A\varphi$), d represents the diameter of the glass beads, and D represents the molecular diffusion coefficient of water. The Reynolds number was calculated using $\mathrm{Re}=vd/\nu$, where $\nu$ is the kinematic viscosity of the fluid. The kinematic viscosity was calculated as $\nu =\mu /\rho$, where $\mu$ is the dynamic viscosity and $\rho$ is the fluid density. In our experiment, the dynamic viscosity of water was $\mu =1.003\times {10}^{-3}\mathrm{kg}/(\mathrm{m}·\mathrm{s})$ (estimated for a temperature of 20 °C), and the density of water was $\rho =1.0136{\mathrm{kg}/\mathrm{m}}^3$ (measured for water with NaCl), resulting in a kinematic viscosity of $\nu =9.91\times {10}^{-7}{\mathrm{m}}^2/\mathrm{s}$. The hydraulic conductivity (K) for each configuration of the porous media was obtained through Darcy’s law from the piezometric head difference of the tank ($\Delta h$). The porosity ($\varphi$) for each configuration of the porous media was determined by converting the weight of the glass beads used to fill the tank into volume.

2.4. Chemical Solutions

The reactive transport experiment was conducted using a colorimetric reaction involving two solutions: W₁, containing 0.01 M (mol/L) of sodium molybdate dihydrate (MoNa₂O₄·2H₂O), and W₂, containing 0.02 M of Tiron (1,2-dihydroxybenzene-3,5-disulfonic acid, Ti⁻²) (refer to

Table 2. Chemical properties of reactive and stock solutions.

Properties	W1 (Mo)	W2 (Ti)	Stock 1	Stock 2
MoNa2O4	0.01 M	-	0.025 M	-
Ti	-	0.02 M	-	0.05 M
Succinic Acid	0.13 M	0.13 M	0.13 M	0.13 M
NaOH	0.26 M	0.26 M	0.26 M	0.26 M
NaCl	0.0761 M	-	-	-
RI (Refraction Index) *	1.337	1.337	-	-
Density (g/${\mathrm{cm}}^3$)	1.0136	1.0136	-	-

Note: * The measurements were obtained using a refractometer.

). This reaction resulted in the formation of Tiron molybdate (${\mathrm{MoTi}}_2^{-3}$ and ${\mathrm{MoTi}}_2^{-4}$) through the following reaction scheme:

$$M{o}^{-1}+T{i}^{-2}\rightleftharpoons MoT{i}^{-3}+2H_{2}O,$$

(1)

$$MoT{i}^{-3}+T{i}^{-2}\rightleftharpoons MoT{i}_2^{-4}+O{H}^{-}+H_{2}O.$$

(2)

During this process, the colorimetric reaction occurs almost instantaneously, with ${\mathrm{MoTi}}_2^{-4}$ being the colorimetric species [51] and thereby the only component quantified in the image analysis. The color of ${\mathrm{MoTi}}_2^{-4}$ varies from yellow to dark red. The preparation of the solutions used in the mixing experiment followed the chemical protocol described by Oates and Harvey [52] and Bertran Oller [44], with slight modifications in this study. To prepare the molybdate solution, W₁, and the Tiron solution, W₂, a buffered solution of succinic acid and NaOH was first prepared to maintain the appropriate pH range for the colorimetric reaction. Since ${\mathrm{MoTi}}_2^{-4}$ remains stable within a pH range of approximately 6.6–7.5, it was essential to ensure that the pH remained within this range during preparation. Finally, Ti and Mo (MoNa₂O₄) were added to their respective buffer solutions to obtain W₂ and W₁. To further balance the solutions, NaCl was added to the molybdate solution, W₁, to compensate for the slightly higher density of the Tiron solution, W₂. For the quantification of ${\mathrm{MoTi}}_2^{-4}$, a visual calibration was created based on the relationship between the image color intensity and the concentration of the generated product. To achieve this, several standard solutions were prepared by combining different volumes of a 0.05 M Ti stock solution and a 0.025 M molybdate stock solution, both buffered to pH 6.6 with 0.13 M succinate and 0.26 M NaOH (refer to Table 2). In addition to a blank, six standard solutions were prepared with concentrations of 0.0002 M, 0.0011 M, 0.0029 M, 0.0042 M, 0.0059 M, and 0.0090 M. These solutions were then used to create a calibration curve, which allowed the interpolation of product values based on the observed color. To perform the conservative tracer test and capture the breakthrough curves for each configuration, a 0.05 mg/L fluorescein solution, prepared with distilled water, was used.

2.5. Image Acquisition and Processing

During experiments, the camera continuously captured 24 bit RGB color images to record the spatio-temporal evolution of the solute plume in each configuration of the porous media (${\mathrm{MoTi}}_2^{-4}$ or fluorescein). The camera settings were manually adjusted and kept constant throughout the experiment, with a relative aperture of f/2.8, a shutter speed of 1/30 s, and an ISO setting of 200. The ${\mathrm{MoTi}}_2^{-4}$ images were processed using the OpenCV library in Python (OpenCV version 4.8.0, Python version 3.12.0) [53,54], following the methodology proposed by Bertran Oller [44]. The concentration of ${\mathrm{MoTi}}_2^{-4}$ was determined pixel-by-pixel following the method outlined by Castro-Alcalá et al. [45], where the light intensity of each pixel was correlated with those of the standard solutions. This was done using piecewise linear interpolation, with the known concentrations derived from standard solution images obtained prior to conduction of the reactive transport experiment. The processing workflow consisted of the following steps: (a) conversion of both the experimental images and the standard images obtained from each experiment from the raw format (NEF) to 16-bit TIFF images; (b) cropping the images to focus on the region of interest (ROI), with a resolution of 3975 × 3000 pixels, each measuring 0.0066 mm²; (c) centering all images from the reactive transport experiment and the standard solutions to the same (x, y) coordinates to ensure proper interpolation; (d) subtraction of the background $I_{\mathrm{bg}}$ (chosen for each configuration of the porous media) from all standard and experimental images:

$${\overline{I}}_{\exp }(x,y,t)=I_{\exp }(x,y,t)-I_{\mathrm{bg}}(x,y),$$

(3)

$${\overline{I}}_i(x,y,t)=I_i(x,y,t)-I_{\mathrm{bg}}(x,y),$$

(4)

where $I_i(x,y,t)$ is the light-intensity image of the ith standard solution and $I_{\mathrm{bg}}(x,y)$ is the light intensity of a blank image obtained under steady-state flow conditions prior to each experiment; (e) channel selection, considering only the green band $I_i^{\ast }(x,y,t)$ and $I_{\exp }^{\ast }(x,y,t)$ for the ith standard and experimental images, respectively; the green channel was chosen because it provided accurate differentiation of the intensities for each standard solution recorded; (f) calculation of the concentrations $C(x,y,t)$ using a piecewise linear interpolation model that relates the green-band intensities from the experiment $I_{\exp }^{\ast }(x,y,t)$ to those of the standard solutions $I_{\mathrm{std}}^{\ast }(x,y)$ and their corresponding concentrations $C_i$. The concentration is calculated as follows:

$$C(x,y,t)=C_i+{\displaystyle \frac{C_{i+1}-C_i}{I_{i+1}^{\ast }(x,y)-I_i^{\ast }(x,y)}}\left(I_{\exp }^{\ast }(x,y,t)-I_i^{\ast }(x,y)\right),$$

(5)

where $I_{\exp }^{\ast }(x,y,t)$ lies in the range $[I_i^{\ast }(x,y),I_{i+1}^{\ast }(x,y)]$ and the $I_i^{\ast }(x,y)$ values for each calibration point represent the green-band intensity for each pixel in the ith standard image. The concentration $C_i$ is the known concentration associated with the ith standard solution.

2.6. Key Variables and Metrics for Analysis

To evaluate the results, we will use key variables and metrics that characterize transport behavior and mixing processes within the system. The transverse extent of the product plume ($ϵ$) defines the influence of mixing along the direction transverse to mean flow. For each configuration of the porous media, the transverse extent $ϵ$ was determined by binarizing the steady-state plume image using a concentration threshold of $C(x,y,t)={10}^{-5}\mathrm{M}$, which was established through visual calibration to accurately define the plume edges. After binarization, the plume extent was quantified by measuring the maximum transverse distance (in the y-direction) for each position along the x-axis. In the binary images, black pixels represented the plume region (above threshold), while white pixels indicated the absence of the solute product. From this, an apparent transverse dispersivity (${\alpha }_T$) was calculated using the relationship between the transverse extent of the plume and the transverse dispersion reported by De Simoni et al. [55] in homogeneous porous media for the same problem. This can be written as follows:

$${\alpha }_T={\displaystyle \frac{{ϵ}^2}{24x}}.$$

(6)

Two other mixing metrics will be also used to analyze the results. On the one hand, the total mass produced by the reaction, i.e., the total mass of ${\mathrm{MoTi}}_2^{-4}$ (g), was calculated for each configuration by integrating the concentration $C(x,y,t)$ (mol/L) of ${\mathrm{MoTi}}_2^{-4}$ over the volume of the domain (V) (see Table 1):

$$M(t)=\varphi {\int }_{V}C(x,y,t)dV.$$

(7)

This formulation assumes a uniform porosity $\varphi$ across the entire domain. However, in the C–F and F–C configurations, the porous medium is composed of two distinct materials with different porosities. In such cases, using a single porosity value leads to an inaccurate estimation of the total reacted mass. To account for the spatial variation in porosity, the calculation must be adjusted by including the porosity inside the integral. Specifically, the domain is divided into two subdomains: $V_1$ and $V_2$, corresponding to the coarse and fine materials, which have porosities ${\varphi }_1$ and ${\varphi }_2$, respectively (see Table 1). The corrected expression for the total mass becomes the following:

$$M(t)={\int }_{V_1}{\varphi }_1·C(x,y,t)dV+{\int }_{V_2}{\varphi }_2·C(x,y,t)dV.$$

(8)

Concentrations in mol/L were converted to g/L using the molecular mass of ${\mathrm{MoTi}}_2^{-4}$, 841.37 g/mol based on $M_{\mathrm{Mo}}=175.95$ g/mol and $M_{\mathrm{Ti}}=332.21$ g/mol. On the other, mixing will also be characterized through the scalar dissipation rate, defined by Le Borgne et al. [42] as

$$\chi (t)={\int }_V{C}^2(x,y,t)dV.$$

(9)

In both cases, the unit volume was defined as the product of the pixel area in the $x,y$-plane and the tank height W as follows: $V_{\mathrm{pixel}}=W\Delta x\Delta y$. In addition, the results will be used to analyze the longitudinal distribution of the reaction product, which provides insight into the temporal evolution of the longitudinal front of the product plume. To do this, we will use the vertical average of concentrations along the tank width, defined as follows:

$$\overline{C}(x,t)={\displaystyle \frac{1}{W}}{\int }_0^{W}C(x,y,t)dy.$$

(10)

Results will be presented using a dimensionless time expressed as pore volume with respect to half of the volume of the tank ($V/2$). Let us denote as $V_A$ the volume of the first half of the tank and $V_B=V-V_A$ the remaining volume. In our experiment, A can be one material type and B a different one. The water residence times in $V_A$ and $V_B$ can be estimated as $t_A^{\ast }=V_A{\varphi }_A/Q$ and $t_B^{\ast }=V_B{\varphi }_B/Q$, respectively. From this, the pore volume is defined as follows:

$$P_V(t)=\left\{\begin{array}{cc}t/t_A^{\ast },\hfill & \mathrm{if}t<t_A^{\ast },\hfill \\ 1+(t-t_A^{\ast })/t_B^{\ast },\hfill & \mathrm{if}t\ge t_A^{\ast },\hfill \end{array}\right.$$

(11)

Thus, when $P_V=1$ the injected water has filled the first half of the porous medium, and when $P_V=2$ the injected water has filled the entire porous medium.

3. Results and Discussion

3.1. Non-Reactive Solute Transport

The impact of the sharp soil interface was first evaluated by analyzing the behavior of the breakthrough curves (BTCs) of the conservative solute pulse obtained for each configuration of the porous media and its spatiotemporal evolution through a series of images, as shown in Figure 3 and Figure 4. Figure 3a presents the BTCs in terms of normalized concentration (C/C₀) and pore volumes $P_V$. For a closer look at the arrival and tailing, they are also shown on a logarithmic scale in Figure 3b. The results obtained from the non-reactive transport experiments demonstrate a clear direction-dependent transport behavior, which aligns with previous experimental observations [17,23,48]. The BTCs for the coarse (C) and fine (F) porous media exhibit Fickian–Gaussian behavior, a typical characteristic of homogeneous porous systems. On comparison of the BTCs, the coarse medium (C) shows an earlier arrival, a lower peak, and a faster tail exit compared to the fine one (F), a result in line with theoretical expectations [56]. The BTC of the fine-to-coarse (FC) medium also exhibits Gaussian behavior. In Figure 3a, it can be observed that both the arrival time and the tailing behavior are similar to those observed in the coarse medium (C), while the peak value is similar to that observed in the fine medium (F). This suggests that the fine-to-coarse (FC) porous medium behaves as if it were a single homogeneous porous medium, incorporating characteristics of both media; however, previous experiments have indicated that this behavior may depend on the flow rate [57]. In contrast, the BTC obtained for the coarse-to-fine (CF) medium exhibits an asymmetric, non-Fickian behavior, consistent with the experimental results reported by Berkowitz et al. [17]. It presents an early arrival, which has been attributed to preferential flow paths [49], along with a low peak value and a long tail—typical features of breakthrough curves (BTCs) obtained from porous media exhibiting mass transfer processes [58,59].

The impact of the sharp interface on solute transport is clearly evidenced through the spatiotemporal evolution of the solute pulse. Previous solute transport experiments captured only breakthrough curves (BTC), limiting the ability to fully visualize transport processes at the interface [17,23]. In the present study, three key moments are identified for both the fine-to-coarse (FC) and coarse-to-fine (CF) configurations of the porous media: the point just before the plume front reaches the interface ($P_V=1$), the point when the plume front is at the interface ($P_V=1.4$), and the point just after the plume tail exits the interface ($P_V=1.8$). In the fine-to-coarse (FC) configuration of the porous media, before crossing the interface (Figure 4a), the pulse presents a relatively regular front, with a slight tendency to develop more rapidly in the upper part of the tank. As the pulse passes through the interface (Figure 4b), this tendency becomes more pronounced. When the pulse has passed almost through the interface, it begins to recover its previous shape. After it has completely crossed the interface (Figure 4c), the pulse does not show significant variation, maintaining a shape similar to that observed before it crossed the interface.

On the other hand, in the coarse-to-fine (CF) configuration of the porous media, a slight tendency for the pulse to move faster along the bottom side of the tank is observed before it reaches the interface (Figure 4d). When the pulse reaches the interface (Figure 4e), this tendency becomes more pronounced, as the pulse shows a strong inclination to propagate along the bottom edge of the tank, forming small-scale preferential flow channels, a phenomenon previously reported in studies of fine-scale heterogeneity of alluvial aquifers [60,61]. The upper portion of the pulse experiences a significant delay, resulting in a deformation that causes the pulse to lose its original shape after the plume passes through the interface (Figure 4f). The pulse becomes distorted, adopting an asymmetrical sigmoidal form.

The results obtained from the non-reactive transport experiments demonstrate that the sharp interface plays multiple roles in transport behavior. In the fine-to-coarse (FC) configuration of the porous media, the breakthrough curve (BTC) follows a Gaussian distribution, suggesting that the entire medium behaves as a single, homogeneous porous system. The BTC combines features of both porous materials: the arrival time is similar to that observed in the coarse medium BTC, while the peak concentration closely aligns with the BTC from the fine configuration. Regarding the role of the sharp interface, a smooth transition in transport properties is observed, suggesting that the interface apparently acts as a continuous boundary, allowing solute transport to occur as if through a homogeneous medium. In contrast, in the coarse-to-fine (CF) configuration, the resulting breakthrough curves (BTCs) exhibit strong non-Fickian features that align with previous experimental results obtained by Berkowitz et al. [17], including an apparent double peak and an extended tail, which suggests that the coarse-to-fine (CF) porous medium behaves like a dual-permeability system with the interface limiting the mass transfer [6,40]. The retention of tracer before it crosses the interface leads to a slow release in the fine material, which may be associated with a lower peak value and which contributes to the much longer tail observed in the BTCs. Visual analysis of the tracer shows that the sharp interface acts as a hydraulic barrier. When the solute pulse reaches the transition, it appears to collide with a wall, which distorts the flow field as it crosses into the fine porous material. This distortion forces the solute pulse to redistribute through localized preferential flow paths. Nonetheless, it is plausible that the observed behavior is not solely due to the interface between the two soils; instead, it may be significantly influenced by microscopic heterogeneities within the fine soil itself. These heterogeneities, at a scale between the tank and grain/pore scales, could create an imperfect homogeneity (microstructure) that enhances the channeling effect even for a single tracer. Such microstructural complexity might play an important role in driving the non-Fickian transport features and associated observations.

3.2. Spatiotemporal Evolution of the Reaction Product

We now examine the spatiotemporal evolution of the reaction product plume through a selected series of three images for each configuration of the porous media, capturing different stages: at the interface ($P_V=1.2$), after passing through it ($P_V=1.7$), and upon reaching a steady state ($P_V=2.5$), as shown in Figure 5. Upon comparing all cases, we immediately observe that the morphology of the reaction product plume varies depending on the direction, with different transverse extents based on the grain size, a result that aligns with previous experimental results [62,63]. In the fine (F) medium, as shown in Figure 5a, the plume initially exhibits an elliptical shape $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 4\times {10}^{-4})$, elongating and widening at the front as it progresses (Figure 5b). By the third stage (Figure 5c), it adopts a final horn-like form, characterized by concave edges, a narrow initial section, and a wider final shape $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 7\times {10}^{-4})$. In the fine-to-coarse (FC) medium, as shown in Figure 5d, the plume also begins with an elliptical shape $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 4\times {10}^{-4})$. As it advances into the coarse medium (Figure 5e), it expands transversely, adopting a significantly greater transverse extent than it had in the fine medium. In the final stage (Figure 5f), the plume exhibits a narrow shape in the fine medium, transitioning into a much wider form and ultimately taking on a funnel-like shape $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 7\times {10}^{-4})$. In the coarse (C) medium, the plume initially exhibits a much greater width than in the fine medium $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 5\times {10}^{-4})$,a characteristic associated with increased transverse dispersion (Figure 5g). As it advances, it maintains convex edges and an overall oval shape. In the final stage (Figure 5i), the plume develops a bell-like form, adopting a significantly greater thickness than in the fine-grained medium $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 7\times {10}^{-4})$. In the coarse-to-fine (CF) medium, the plume initially presents a thickness similar to that observed in the coarse medium $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 5\times {10}^{-4})$ but ceases to spread laterally upon entering the fine medium, maintaining a constant thickness. After crossing the interface, it adopts a rectangular form with straight edges $({\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(M)\sim 7\times {10}^{-4})$, eventually transitioning into a bullet-like shape in the final stage (Figure 5l).

The results indicate that the shape of the reaction product plume is direction-dependent. Grain size governs dispersion [62,63], which in turn determines the transverse extent of the mixing plume [64,65,66,67]. This implies that in coarse media, the transverse extent is greater than in fine media, as previously reported by Sternberg [29]. Consequently, the sharp interface plays different roles in shaping the morphology of the plume depending on the direction: in the fine-to-coarse (FC) configuration, the interface enhances lateral spreading due to increased dispersion in the coarse region, while in the coarse-to-fine (CF) configuration, it restricts lateral spreading, resulting in a constant uniform plume width.

3.3. Longitudinal Profiles of the Reaction Product

The effect that sharp soil interfaces have on reactive transport and mixing processes can be analyzed in greater detail by examining the temporal evolution of the longitudinal distribution of the reaction product. Figure 6 shows the longitudinal profiles of ${\overline{\mathit{C}}}_{{\mathrm{MoTi}}_2^{-4}}(M)$ concentrations for each configuration of the porous media at five different times P_V1 = 0.7, P_V2 = 1, P_V3 = 1.5, P_V4 = 2, y P_V5 = 2.8, illustrating the temporal evolution of the reaction product front along the tank length. The most notable result is that the reaction product encounters anomalous resistance when the plume crosses the interface between coarse and fine material. This effect is much less pronounced in the fine-to-coarse (FC) configuration when the direction of flow is reversed. To analyze this behavior, we begin with the fine-to-coarse (FC) configuration, as shown in Figure 6b. Initially, the concentration profiles follow a trend similar to that seen in the fine medium ($P_{V_1}=0.7$, $P_{V_2}=1$). However, at $P_{V_3}=1.5$, a marked discontinuity appears in the concentration profile.

Before the plume reaches the interface, the concentration gradually decreases, but upon the plume’s arrival at the transition zone, it suddenly drops, and a significant jump in concentrations follows immediately. One possible explanation for this behavior is a very rapid local increase in flow velocity at the coarse-to-fine (CF) transition—to a velocity higher than that in either the coarse or fine porous media sections—which is limited in width in the transverse direction. This localized acceleration likely reduces tracer concentration sharply as the solute passes through this narrow zone; the concentration later stabilizes in the fine porous media downstream, providing a plausible mechanism for the concentration jumps observed near the interface. At later times, specifically at $P_{V_4}=2$ and $P_{V_5}=2.8$, the concentrations reach values significantly higher (${\overline{\mathit{C}}}_{{\mathrm{MoTi}}_2^{-4}}\sim 4\times {10}^{-4}\mathrm{M}$) than those observed in the fine medium at equivalent times, suggesting that mixing is enhanced when the plume enters the coarse medium.

In the coarse-to-fine (CF) configuration (Figure 6d), the profiles of the reactive product at times $P_{V_1}=0.7$ and $P_{V_2}=1$ exhibit behaviors similar to that seen in the coarse medium (C). However, at $P_{V_3}=1.5$, a discontinuity in concentration is also observed. Initially, the profile follows a trend consistent with that seen in the coarse medium, but as it approaches the interface, the concentration drops sharply to very low values—lower than those observed in the fine-to-coarse (FC) configuration. However, contrary to previously reported one-dimensional results [17,30,39], this asymmetric anomalous resistance to crossing the interface does not produce solute accumulation behind the interface in the coarse-to-fine (CF) configuration. After the initial drop, the concentrations begin to increase again, but in a gradual manner, rather than with the abrupt jump observed in the FC case. For times $P_{V_4}=2$ and $P_{V_5}=2.8$, the sharp drop in concentration remains evident and can also be observed in the longitudinal profiles. Following this, the concentrations gradually recover and eventually exhibit trends similar to those observed in the coarse medium.

3.4. Mixing Metrics and Profiles of the Reaction Product

To further investigate the impact of the sharp soil interface on the reactive product concentration, we jointly analyze the transverse extent of mixing ($ϵ$), the apparent transverse dispersivity (${\alpha }_T$), and the longitudinal concentration profile ($\overline{C}$). These metrics allow us to characterize the behavior of the solute plume as it crosses the interface in each configuration of the porous media. Our results shows an unexpected significant enhancement of the transverse spread of the reaction product in the coarse-to-fine (CF) configuration, with a slow release in the fine material —an effect that is not observed in the fine-to-coarse (FC) configuration and cannot be explained by standard modeling approaches based on Fickian flux continuity and the advection–dispersion equation. We summarize the evidence supporting this behavior below.

• In the coarse-to-fine (CF) configuration of the porous media, the transverse extent ($ϵ$) initially follows a trend similar to that seen in the coarse medium ($ϵ>2\mathrm{cm}$) (Figure 7a); however, it surprisingly increases just before the plume reaches the interface ($ϵ>10\mathrm{cm}$), indicating an unexpected greater transverse dispersion of the plume. After the plume crosses the interface, the transverse extent ($ϵ$) stabilizes ($ϵ\sim 10.5\mathrm{cm}$) and remains constant until the plume reaches the end of the tank. Similarly, the apparent transverse dispersivity (${\alpha }_T$) starts with values similar to those obtained in the coarse (C) porous medium (${\alpha }_T\sim 0.3\mathrm{cm}$) (Figure 7b), but as the plume approaches the interface, the value significantly increases to about ${\alpha }_T\sim 0.32\mathrm{cm}$. Beyond this point, the apparent transverse dispersivity (${\alpha }_T$) decreases linearly, with a final value of roughly $0.2\mathrm{cm}$. Regarding the longitudinal concentration profile ($\overline{C}$), a clear discontinuity is observed, with this metric reaching its minimum value at the sharp interface (${\overline{C}}_{{\mathrm{MoTi}}_2^{-4}}(\mathrm{M})\sim 1.5\times {10}^{-4}$); see Figure 7c. Afterward, the concentration begins to rapidly rise again, although the values remain significantly lower than those observed in the coarse medium.
• In the fine-to-coarse (FC) configuration, the transverse extent of the reaction product plume ($ϵ$) exhibits a dual behavior (Figure 7a), with an inflection point at the interface ($\mathrm{length}=13\mathrm{cm}$), where the curve abruptly dips before rising in a sigmoidal manner. From the interface to the end of the tank, the transverse extent ($ϵ$) remains significantly larger than that observed in the fine medium, and the final value is also greater ($ϵ>8\mathrm{cm}$). For the transverse dispersivity (${\alpha }_T$), a constant value of ${\alpha }_T\sim 0.05\mathrm{cm}$ is observed in the first half of the tank (Figure 7b); this value then increases significantly after the plume crosses the interface, reaching final values of ${\alpha }_T\sim 0.14\mathrm{cm}$. Regarding the longitudinal concentration profile ($\overline{C}$) (Figure 7c) in the fine-to-coarse (FC) media, the curve initially exhibits a slope similar to that observed in the fine (F) medium. However, upon the plume reaching the interface, the FC curve experiences a slight decline before steepening significantly, leading to notably higher concentration values (${\overline{C}}_{{\mathrm{MoTi}}_2^{-4}}(\mathrm{M})>3.5\times {10}^{-4}$).

Although the importance of heterogeneity in controlling solute mixing and reactivity has been widely recognized in previous studies [17,41,42,43,68], no direct studies have specifically analyzed the effect of soil interfaces on mixing. In this section, we assess the mixing metrics for each scenario by analyzing the mixing efficiency through two key variables: the total reaction product mass of ${\mathrm{MoTi}}_2^{-4}$, denoted as ${\mathit{M}}_{{\mathrm{MoTi}}_2^{-4}}$ (g), and its corresponding scalar dissipation rate $\chi$, as shown in Figure 8. This analysis is crucial for understanding where mixing occurs most effectively within a discontinuous heterogeneous porous medium. Upon comparing all cases, we observe different behaviors in the scalar dissipation rate and total mass production near the interface, indicating an asymmetric flow-direction dependence of mixing efficiency and reactivity. To describe this behavior more clearly, we present below a summary of the evidence.

• In the coarse-to-fine (CF) configuration, the total reaction product mass follows the same trend seen in the coarse medium up to around P_V = 1.6 (Figure 8a). From this point onward, the total reaction product begins to decline, resulting in lower final values compared to those obtained in the coarse medium (${\mathit{M}}_{{\mathrm{MoTi}}_2^{-4}}(\mathrm{g})\sim 5.5\times {10}^{-2}$). Nevertheless, the CF configuration consistently produces a higher total product mass than the FC transition along the entire length of the tank, indicating that even after the decline, mixing and reactivity remain more efficient than in the reverse-flow configuration. Regarding the scalar dissipation in (Figure 8b), the coarse-to-fine (CF) curve reaches a final scalar dissipation value similar to that of the fine-to-coarse (FC) curve (${\chi }_{{\mathrm{MoTi}}_2^{-4}}$ (${\mathrm{g}}^2/\mathrm{L}$) $\sim 3\times {10}^{-2}$). However, their temporal evolutions are notably different. In particular, the CF configuration consistently exhibits higher values along the length of the tank.
• In the fine-to-coarse (FC) configuration, the total reaction product mass initially follows a pattern similar to that seen in the fine medium up to approximately $P_V=1.8$ (Figure 8a). Beyond this point, the total reaction product mass increases exponentially, eventually surpassing the values observed in the fine medium (${\mathit{C}}_{{\mathrm{MoTi}}_2^{-4}}(\mathrm{g})>4.5\times {10}^{-2}$). Regarding the scalar dissipation (Figure 8b), the curve exhibits a sigmoidal behavior similar to that observed in the coarse medium. However, after the plume passes through the interface, the slope decreases significantly, eventually reaching much lower values.

Corresponding mixing metrics show that the apparent transverse dispersivity increases as the plume approaches the interface in the CF transition and that the scalar dissipation rate and the total mass reacted also correspondingly increase, indicating that the CF configuration tends to promote greater solute reactivity near the interface than the FC configuration.

4. Conclusions

Sharp soil interfaces formed in porous media between materials with differing grain sizes introduced unexpected effects on solute transport, challenging conventional assumptions about solute transport and reactivity. Understanding their impact on mixing processes and transport behavior is crucial for improving groundwater-remediation strategies and predictive models of contaminant migration in subsurface systems. While the impact of sharp soil interfaces has been extensively explored through numerical solute-transport models, Darcy-scale experiments designed to visually assess the mechanisms governing their impact on transport behavior and mixing have remained largely unknown. To address this gap, we presented well-controlled laboratory experiments conducted in an intermediate-scale horizontal tank and simulating sharp transitions between fine and coarse porous materials. The experimental setup allowed for the real-time monitoring and visualization of the spatiotemporal evolution of solute plumes. Finally, we conclude that:

• The sharp soil interface plays different roles in transport behavior. In the coarse-to-fine (CF) porous medium, the sharp interface acts as a hydraulic barrier, distorting the flow as it crosses into the fine material, forcing solute redistribution through small-scale preferential flow paths. This leads to an apparent dual-permeability system, with a breakthrough curve (BTC) displaying non-Fickian features, including early arrival, a low peak value, and a long tail. In contrast, the fine-to-coarse (FC) configuration is associated with a smooth transition of transport properties; it behaves as though it were a single homogeneous medium, with a BTC that follows a Gaussian distribution and integrates characteristics of both porous materials.
• The reaction product encounters anomalous resistance when the plume crosses the interface between coarse and fine material. This effect is much less pronounced in the fine-to-coarse (FC) transition when the direction of flow is reversed. However, in contrast to the reported one-dimensional results (column experiments), this asymmetric anomalous resistance to crossing the interface does not result in solute accumulation behind the interface. Instead, the results show an unexpected significant enhancement of the transverse spread of the reaction product in the coarse-to-fine transition (CF), with a slow release in the fine material. As a result, a sudden decrease in the longitudinal resident concentration profile across the heterogeneity interface is observed. Corresponding mixing metrics show that the apparent transverse dispersivity increases as the plume approaches the interface in the CF transition; correspondingly, the scalar dissipation rate and the total mass reacted also increase, indicating that the CF configuration tends to promote greater solute reactivity near the interface than the FC configuration.

These findings are particularly relevant for researchers aiming to model interfaces between contrasting porous materials, as they reveal key transport phenomena that must be reproduced—especially the behavior of the solute plume immediately before it crosses the coarse-to-fine (CF) interface, where an unexpected significant enhancement in transverse spread and a sudden drop in the longitudinal resident concentration profile are observed. Accurately capturing these effects in numerical models requires going beyond idealized advection–diffusion frameworks and accounting for microscopic heterogeneities and their role in generating preferential flow paths, which may not be easily predicted but that strongly influence mixing. These experimental insights can also support remediation efforts, particularly those involving the injection of reactive or neutralizing solutions into contaminated aquifers, by helping identify interface zones where mixing—and thus reaction—can be naturally enhanced, guiding more efficient design and placement of treatment zones.