Discernible Orientation for Tortuosity During Oxidative Precipitation of Fe(II) in Porous Media: Laboratory Experiment and Micro-CT Imaging

Abstract

In the mixing zone, where submarine groundwater carrying ferrous iron [Fe(II)] meets seawater with dissolved oxygen (DO), the oxidative precipitation of Fe(II) occurs at the pore scale (nm~μm), and the resulting Fe precipitation significantly influences the seepage properties at the Darcy scale (cm~m). Previous studies have presented a challenge in upscaling fluid dynamics from a small scale to a large scale, thereby constraining our understanding of the spatiotemporal variations in flow paths as porous media evolve. To address this limitation, this study simulated subsurface mixing by injecting Fe(II)-rich freshwater into a DO-rich saltwater flow within a custom-designed syringe packed with glass beads. Micro-computed tomography imaging at the representative elementary volume scale was utilized to track the development of Fe precipitates over time and space. Experimental observations revealed three distinct stages of Fe hydroxides and their effects on the flow dynamics. Initially, hydrous Fe precipitates were characterized by a low density and exhibited mobility, allowing temporarily clogged pathways to intermittently reopen. As precipitation progressed, the Fe precipitates accumulated, forming interparticle bonding structures that redirected the flow to bypass clogged pores and facilitated precipitate flushing near the syringe wall. In the final stage, a notable reduction in the macroscopic capillary number from 3.0 to 0.05 indicated a transition from a viscous- to capillary-dominated flow, which led to the construction of ramified, tortuous flow channels. This study highlights the critical role of high-resolution imaging techniques in bridging the gap between pore-scale and continuum-scale analyses of multiphase flows in hydrogeochemical processes, offering valuable insights into the complex groundwater–seawater mixing.

1. Introduction

Australia is renowned for possessing the world’s largest reserves of iron (Fe) ore [1]. The dissolution of Fe-bearing minerals in geological formations releases Fe ions into groundwater systems [2,3,4]. At the land–ocean interface, the mixing of terrestrial groundwater and oxygenated seawater generates a dynamic geochemical reaction front where ferrous ions (i.e., Fe(II) or Fe²⁺) oxidize to ferric ions (i.e., Fe(III) or Fe³⁺) via dissolved oxygen (DO) from seawater [5]. This process leads to the precipitation of ferric hydroxides (i.e., Fe(OH)₃) beneath the sand beach surface [6]. Iron-oxide-coated sands (IOCS) with Fe precipitates have been observed in the intertidal areas of coastal bays globally [7,8,9]. Such Fe accumulations act as geochemical barriers, regulating the transport of dissolved chemicals from inland to the ocean [10,11,12,13], often referred to as the “iron curtain” in coastal settings. Although the oxidative precipitation of Fe(II) is a prominent process, other mechanisms, such as bioclogging [14], clay minerals [15], and microbe-mediated Fe oxidation [16], can also influence the properties of porous media in intertidal zones. For instance, biofilm growth, strongly linked to Fe oxides in the presence of DO, can create flow obstructions that modify the porosity and permeability [17,18]. Similarly, clay minerals contribute to structural changes by reducing pore spaces and altering flow paths. These processes, along with Fe precipitation, collectively shape the complex hydrogeochemical dynamics of porous media in natural systems.

Tortuosity, defined as the ratio of the effective flow path length to the straight-line distance between the inlet and outlet in porous media [19,20], captures the influence of pore-scale heterogeneity and flow path redistribution due to Fe precipitation [21,22]. In the mixing zone, Fe(II)-rich groundwater encounters oxygenated seawater, resulting in the oxidative precipitation of Fe(II) at the pore scale (nm~μm), which modifies the pore structure by occupying the interstitial spaces between particles [23,24]. This phenomenon leads to a decrease in porosity, a subsequent reduction in permeability, and a corresponding increase in tortuosity at the Darcy scale (cm~m) [21,25]. These changes slow down groundwater flow and solute transport across field scales (m~km) [26]. Therefore, fluid–solid interactions spanning multiple spatial and temporal scales create complicated flow dynamics governed by viscous and capillary forces [27,28,29]. The capillary number (Ca) quantifies the balance between these forces [30,31,32], characterizing multiphase flow regimes in porous media [33,34,35,36]. At the pore scale, intermittent pathway flows, marked by periodic disconnections and reconnections, significantly influence continuum-scale behavior [37,38,39,40]. However, scaling these dynamics from the pore scale to the continuum scale is challenging due to limited sample sizes and the resolutions of existing imaging techniques [36,41,42]. Recent advancements in micro-computed tomography (micro-CT) and high-performance computing (HPC) [43] have improved the visualization of pore structures, enabling detailed assessments of the pore connectivity, mineral distribution, and seepage properties [44,45,46]. Nevertheless, direct observations of pore-scale variations in representative elementary volume (REV)-scale samples remain limited [29]. Moreover, the effect of secondary mineral precipitation on the tortuosity of porous media is a broad and complex phenomenon [24,47]. Abiotic Fe oxide formation provides a representative example, particularly in predicting the discernible orientation of tortuosity as the pore matrix evolves during Fe precipitation [21,48,49]. However, biotic processes, such as those mediated by microbial activity, will be considered in future studies.

To address this gap, this study integrated laboratory experiments and non-invasive imaging techniques to investigate the spatiotemporal evolution of flow paths during the oxidative precipitation of Fe(II) in porous media. To achieve this, a co-injection test, utilizing a custom-designed syringe apparatus, introduced Fe(II)-rich freshwater into a background flow of DO-rich saltwater. This experimental setup provides a simplified representation of subsurface mixing in coastal groundwater systems and isolates abiotic Fe oxide precipitation while excluding other processes, such as microbe-mediated interactions, to focus on this particular mechanism. High-resolution micro-CT imaging captures temporal and spatial variations in Fe distribution within the pore matrix, which enables the identification of changes in the flow paths. This collaborative approach enhances our understanding of fluid–solid interactions in porous media and provides practical insights for the prediction of seepage properties at the Darcy scale, with implications for evolving porous media in diverse applications at field scale.

2. Materials and Methods

2.1. Co-Injection Experiment

The co-injection experiment was conducted in the GeoSystems Research Laboratory, University of Queensland (UQ), Australia. Figure 1a,b shows the custom-designed syringe apparatus with a length of 95 mm and an internal diameter of 22 mm, yielding a cross-sectional area of 380 mm². The syringe was packed with uniform glass beads to create a saturated porous medium, and the experiment was designed to replicate abiotic Fe oxide precipitation under simplified conditions.

Four cylinders (C1, C2, C3, and C4 in Figure 1a) were connected to the syringe via flexible tubes to monitor the hydraulic gradients (see Equation (1)) across specific intervals between the inlet and outlet.

$$i={\displaystyle \frac{∆h}{∆z}}={\displaystyle \frac{\frac{W_1}{{\rho }_f{A}_c}-\frac{W_2}{{\rho }_f{A}_c}}{∆z}}$$

(1)

where i is hydraulic gradient, Δh is the head difference between the two cylinders, Δz is the vertical interval between the measurement points, W₁ and W₂ are scale readings from the respective cylinders, ρ_f is the fluid density, and A_c is the cross-sectional area of the cylinder.

Before the experiment, the column was carefully filled with de-aerated saltwater to eliminate air bubbles and ensure complete saturation. This was achieved by slowly injecting saltwater from the base, allowing air to escape through the outlet at the top. Visual inspections and flow stabilization checks confirmed the absence of trapped air. During the experiment, Fe(II)-rich freshwater and DO-rich saltwater were co-injected using peristaltic pumps (Chonry ZS100, maximum flow rate: 82.61 mL/min) at a constant inflow rate of 6.0 mL/min, yielding a Reynolds number (Re) of 0.5 for the applicability of laminar flow conditions. Outflow was collected in a volumetric container placed on a digital scale. The laboratory temperature was maintained at 21.5 ± 1 °C, minimizing temperature effects on the fluid viscosity and density.

The Fe(II) solution (0.2 mol/L) was prepared by dissolving ferrous chloride tetrahydrate (FeCl₂·4H₂O, Sigma Aldrich, St. Louis, MO, USA) in de-bubbled deionized water, while the saltwater solution (35 ppt or g/kg) was produced by dissolving sodium chloride (NaCl) in aerated deionized water. Washed glass beads (2 mm diameter, Sigma Aldrich) were used as the porous media. This diameter was chosen to balance the time required for micro-CT scanning with the need for a high imaging resolution. Glass beads, primarily silicon dioxide and chemically similar to quartz sand, offered the better visualization of Fe precipitation during the experiment and provided enhanced contrast for the interpretation of the microscopic images. The densely packed glass beads formed a porous sample with a 22 mm diameter, adhering to the standard dimensions for permeability measurements [29]. This sample size also met the criteria for the concept of REV, which ensured the validity of the results for practical applications. The porosity was calculated using the volumetric saturation method, while the permeability was determined using the constant-head method [19].

The Fe(II) concentration used in this study exceeded natural concentrations (<10⁻⁴ mol/L), but it was set at 0.2 mol/L to replicate high-stress geochemical environments, such as industrial discharge zones, and to investigate clogging under extreme scenarios. No pH buffers were added to the syringe, allowing natural variations in pH to occur as a result of the mixing of the Fe(II)-rich freshwater (pH = 3) and DO-rich saltwater (pH = 8). This detail is noted to highlight the experimental constraints and to provide clarity for reproducibility. Key experimental parameters are summarized in

Table 1. Experimental parameters of porous media and solutions.

Category	Description	Value
Porous media properties (glass beads)	Dry density, ρd (kg/m3)	1450 [a]
	Initial porosity, n0 (-)	0.37 [a]
	Initial permeability, k0 (m2)	2.0 × 10−10 [a]
	Median particle size, d50 (mm)	2.0 [a]
Freshwater properties (containing Fe(II))	Fe(II) concentration, CFe(II), fw (mol/L)	0.2
	Density, ρfw (kg/m3)	1020
	pH	3.0 [a]
	Dynamic viscosity, µfw (Pa·s)	0.001 [b]
Saltwater properties	DO concentration, CDO, sw (mol/L)	2.25 × 10–4 [c]
	Density, ρsw (kg/m3)	1025
	pH	8.0 [a]
Injection scheme and transport properties	Inflow rate, Q (mL/min)	6.0
	Vfw/Vsw (-)	1.0
	Duration, t (d)	25

Note. [a] Derived from laboratory measurements [21,50]. [b] Viscosity of freshwater at 20 °C. [c] Equivalent to 7.2 mg/L based on oxygen solubility in saltwater (35 ppt or g/kg) at 20 °C.

.

The experiment lasted 25 days, during which a reduction in outflow was observed. Daily high-definition (HD) photographs were taken using a 40-megapixel camera (1/1.7 inch, f/1.8 aperture, 27 mm equivalent lens) to document changes in the Fe precipitation zone. Seepage tests were conducted every 5 days to obtain the permeability reduction caused by Fe precipitates, while balancing the experimental schedule and micro-CT imaging cost. Meanwhile, the mass of Fe retained in the sample was estimated by comparing the syringe’s initial and measured weights over time. Comprehensive scans of the sample were performed using a micro-CT system (Comet Yxlon FF35 CT, equipped with a 225 kV directional beam tube) to capture spatiotemporal changes in the pore structure resulting from the oxidative precipitation of Fe(II).

2.2. CT Imaging Processing

Micro-CT scanning was conducted using a Comet Yxlon FF35 CT system at the Centre for Advanced Imaging, UQ, Australia. The scan employed X-ray energy of 140 kV and power of 21.5 W. Saturated conditions (with and without Fe precipitation) were scanned across the entire sample, with each scan taking approximately 60 min. Each scan involved 2500 projections, captured with a 1/3 s integration time per radiograph. The imaging field of view (FOV) covered 2860 × 2860 × 5760 voxels, with a voxel size of 20 μm (or 0.02 mm), achieving the highest resolution available for full-scale sample imaging. The 3D reconstruction of the sample was performed using the VGSTUDIO MAX software (Volume Graphics, Version: 2022.4).

Raw micro-CT images consist of a grid of pixels (2D) or voxels (3D) represented in grayscale, where the intensity values correspond to the material’s density or attenuation coefficient (Figure 2a). Image segmentation was conducted to differentiate regions of interest, such as pores (with fluid), solid particles (glass beads), and Fe precipitates. Segmentation was based on variations in grayscale intensity (Figure 2b), calibrated against reference images of known Fe oxide phases and glass beads to ensure accurate component distinction. The segmented images were used to extract quantitative data on the pore structure, including porosity and connectivity. Figure 2c presents the segmentation process, with the pore space rendered in distinct colors for clarity.

Following segmentation, the 3D microstructure was visualized using volume rendering techniques (Figure 3a). Skeletonized images enabled the delineation of the pore network, identifying pore bodies and throats characterized by their geometrical properties and connectivity. These features were observed to be either filled with saline fluids or hydrous Fe oxides. The digital microstructure, with its sufficient size and resolution, serves as an REV for the prediction of geo-/petrophysical properties such as porosity.

2.3. Macroscopic Capillary Number

The macroscopic capillary number (Ca) quantifies the relative importance of viscous and capillary forces during multiphase flows in porous media [33,34]. Higher Ca values (typically > 1) indicate a viscous-dominated regime driven by pressure gradients, whereas lower Ca values (typically < 1) reflect a capillary-dominated regime controlled by interfacial tension and capillary effects. In this study, Ca was calculated using the definition commonly adopted in the published literature [16,51]:

$$Ca={\displaystyle \frac{Q{\mu }_{f}L}{Apk}}={\displaystyle \frac{Q{\mu }_{f}L}{A\left({p_{r}p}_0\right)\left(k_r{k}_0\right)}}$$

(2)

where Q is the volumetric flow rate, µ_f is the fluid viscosity, L is the sample length, A is the cross-sectional area, p is the average pressure across the domain, k is the average permeability of the porous media, p₀ is the entry pressure due to pump-driven injection, k₀ is the initial permeability, p_r is the relative pressure (>1.0), and k_r is the relative permeability (0~1). The parameters p_r and k_r describe temporal changes in pressure and permeability relative to their initial values (p₀, k₀) at t = 0. Specifically, p_r represents the ratio of local pressure at a given time t to p₀, while k_r quantifies the ratio of evolving permeability at a given time t to k₀.

Salinity effects on the fluid density and viscosity were accounted for using Equations (3) and (4), as previously recommended [50,52]. Specifically, Equation (3) calculates the density of the fluid mixture, considering the contribution of saltwater based on its respective mass fraction, while Equation (4) determines the dynamic viscosity of the mixture, incorporating a polynomial relationship that depends on the mass fraction of saltwater and the viscosity of freshwater.

$${\displaystyle \frac{1}{{\rho }_f}}={\displaystyle \frac{1-w_{sw}}{{\rho }_{fw}}}+{\displaystyle \frac{w_{sw}}{{\rho }_{sw}}}$$

(3)

$${\mu }_f={\mu }_{fw}\left(1+0.4819w_{sw}-0.2774w_{sw}^2+0.7814w_{sw}^3\right)$$

(4)

where ρ_f is the density of the fluid mixture, ρ_fw and ρ_sw are the densities of freshwater and saltwater, w_sw is the saltwater mass fraction, µ_f is the dynamic viscosity of the fluid mixture, and µ_fw is the dynamic viscosity of freshwater.

For this study, the sample length was 95 mm, with a cross-sectional area of 380 mm² (internal diameter: 22 mm). The velocity boundary condition was converted to a pressure condition using Darcy’s law, resulting in an estimated entry pressure of 53.86 Pa at the inlet. The initial Ca value of 3.0, calculated from an inflow rate (Q = 6.0 mL/min), mixed density (ρ_f = 1022 kg/m³), and viscosity (µ_f = 0.00127 Pa·s), indicated a viscous-dominated flow regime at the Darcy scale. Over the experiment, Ca would decrease due to the permeability reduction caused by Fe precipitation, reflecting a transition toward a capillary-dominated regime.

3. Experimental and Imaging Results

3.1. Visual Observation of Fe Precipitation

Figure 4a illustrates the spatial distribution of the Fe precipitates near the inlet (0–30 mm height from the syringe bottom) over the 25-day experiment. During the initial stage (0–10 days), Fe precipitation uniformly coated the surfaces of the glass beads, forming loosely packed layers around the solid particles. By days 15–20, a noticeable flush of Fe precipitates was observed along the syringe’s inner wall, driven by hydraulic pressure from co-injection. After day 20, the Fe precipitation near the inlet appeared to stabilize, and distinct dendrite-like flow channels along the inner wall became prominent as the pumping pressure redirected the flow paths.

Figure 4b–d show the temporal evolution of Fe precipitation, its impact on the syringe’s outflow rate, and the total permeability of the sample. Over the 25-day experiment, 13.5 g of solid-phase Fe formed within the syringe. The outflow rate decreased from 6.0 g/min to 5.5 g/min, representing an 8.3% reduction by day 25. While the amount of Fe precipitates did not reach steady-state conditions, the curve flattened over time, with minimal changes (<1% over 5 days) in the total permeability observed after day 20. These trends suggested a transition in the flow regime within the porous media, characterized by evolving pore-scale features.

The pattern of Fe precipitation observed on the particle surfaces is consistent with previous studies, which found that hydrous Fe oxides tend to spread evenly on quartz surfaces in chloride systems due to the abundance of Cl⁻ ions in aqueous solutions [53,54]. This phenomenon also agrees with field observations of iron oxide-coated sands (IOCS) in sediment cores retrieved from the intertidal area of Waquoit Bay, Massachusetts, USA. These oxides, visible as dark red, yellow, and orange layers, form through the oxidation of Fe(II)-rich groundwater near the groundwater–seawater interface [8]. In precipitation-dominated regimes, the accumulation of Fe precipitates reduces the pore throat sizes, clogs the pore spaces, and increases the particle surface area at the pore scale [24]. These changes reshape the flow channels and modify the seepage properties at the continuum scale [19]. On one hand, narrower flow paths reduce the reactivity and limit further Fe precipitation [55]. On the other hand, they lead to more tortuous flow paths and decrease the permeability [56]. Notably, these changes are governed by pore structure heterogeneity rather than the total amount of Fe precipitates. A heterogeneous Fe distribution allows the flow to bypass heavily precipitated regions, minimizing the impacts on the global outflow until pore clogging occurs. Therefore, it is essential to quantify the critical zone near the inlet, where Fe precipitation is the most intensive.

3.2. Determination of an Appropriate REV

To extend continuum mechanics to highly heterogeneous geomaterials, the concept of the REV is applied to a matrix of solid particles and void spaces. It is defined as the smallest volume at which the mean value of a microscopic property (e.g., porosity) becomes independent of the size of averaged volumes [57]. This ensures statistically stable packing conditions, such as a constant dry density, void ratio, and porosity [21]. The determination of the REV is essential in linking pore-scale flow behavior to the continuum-scale properties of porous media [58]. According to Koestel et al. [59], the designated REV must be large enough that the effective property remains stable with slight increases in volume while being sufficiently small to satisfy statistical homogeneity. In this study, a deterministic REV (dREV) analysis was performed by progressively increasing the cubic side length from the center of the sample (see Figure 5a). At each increment, the mean porosity of the cube was calculated, yielding the porosity values shown in Figure 5b. The results indicate a steady fluid volume fraction of 37.5% once the cubic length exceeds 10 mm, closely matching the experimental porosity (0.37 in Table 1) obtained using the volumetric saturation method. While the statistical REV (sREV) approach—utilizing a moving window method—can more accurately account for spatial variations across the entire sample [60,61], it is computationally demanding and time-consuming compared to the dREV approach [58]. For this study, the dREV method provides a practical and efficient means to approximate the REV for porous media analysis.

A plateau in the porosity values (Figure 5b) was observed around a cubic side length of 5 mm, which is in good agreement with the REV size proposed by Halisch [62] and Wang et al. [29]. However, the smaller samples (5–6 mm diameters) used in earlier studies [37,44,63] may not fully capture the geo-/petrophysical properties of porous media. In contrast, the sample in this study, with a diameter of 22 mm, adheres to the standard size for laboratory permeability measurements. This ensures that the REV concept is applicable in practical applications. It also highlights the importance of using full-scale imaging (up to 22 mm diameter) rather than cropped regions to evaluate the spatially heterogeneous properties of porous media effectively.

3.3. Conceptual Model of Tortuosity Orientation

Predicting the exact locations of precipitation formation and changes in flow paths in porous media is inherently challenging due to their stochastic nature. However, a conceptual model can unravel the evolution of preferential flow paths resulting from the oxidative precipitation of Fe(II) in the pore matrix.

Tortuosity orientation refers to the directional preference of tortuous flow paths within porous media, which evolve dynamically as Fe precipitation redistributes the flow. Over time, these paths tend to shift from central regions to peripheral zones due to localized pore clogging and the resulting hydraulic gradients within the syringe. This concept emphasizes how precipitation-induced changes in the pore network influence the spatial reorganization of flow patterns. At the initial stage, the hydrous Fe precipitates exhibit low volume fractions and are loosely distributed within the pore matrix. These precipitates are mobile and not firmly attached to particle surfaces, allowing them to be transported with the flow and temporarily clog paths. As a result, previously clogged channels may reopen, maintaining a relatively straight flow path from the bottom to the top, being slightly off-center (Figure 6b). As the precipitation continues, Fe accumulation in localized regions increases the density of the Fe precipitates and promotes their reattachment to particle surfaces. Initial clogging occurs in narrow pore throats along the central line of the sample, forcing the viscous flow to seek alternative pathways near the syringe wall (Figure 6c). In the final stage, the central area becomes fully clogged, and the flow is redirected into more tortuous, ramified channels along the inner wall, resembling capillary-dominated flow characteristics (Figure 6d). This mechanism produces a highly heterogeneous precipitation pattern, primarily controlled by the flow regime near the inlet.

For the subsequent analysis of the Fe distribution, the REV (shown as a purple rectangle in Figure 6) was selected to focus on the region most affected by these changes.

3.4. Distribution of Fe Precipitates at REV Scale

Figure 7a shows a cross-section of the porous sample before Fe precipitation, with saltwater (dark blue) filling the pore matrix. Figure 7b–d illustrate the spatiotemporal evolution of the Fe precipitates within the pore matrix during the experiment.

The 3D area of interest (Figure 7(b1,c1,d1)) includes the critical zone defined in Figure 6a—a 30-mm-high section near the syringe bottom (Figure 4a)—where Fe precipitation was the most intensive due to the high DO availability. The 2D slices (Figure 7(b2,b3,c2,c3,d2,d3)) were carefully selected to represent the spatial variations in the Fe precipitates in the sample. Although capturing identical slices at different time points is challenging due to micro-CT imaging constraints, the selected slices are highly consistent and correlate with each other. Structural features in the sample were used to align the slices, ensuring the reliable representation of temporal changes in the pore-scale properties and Fe precipitate distribution within the sample.

An analysis of the 3D images reveals that the volume fraction of Fe precipitates increased from 4.6% on day 5 to 23.1% on day 25. Initially, hydrous Fe precipitates (cyan in Figure 7b) were concentrated in the central regions, forming surface coatings around the particles (see 5−10 days in Figure 4a). Over time, the blue zones diminished, indicating a reduction in the central pore and throat diameters. New flow channels appeared to form away from the center, suggesting that previously clogged regions may have reopened (see 15 days in Figure 4a). However, the current images in Figure 7 do not allow the quantitative verification of this process, as they do not consistently track the same 2D slice over time. Future studies could address this limitation via uninterrupted observations of identical 2D slices over time to provide more convincing proof of flow path reconstruction.

By day 25, Fe precipitates fully occupied the central pores, since there are no connected blue areas in Figure 7d. Although the total flow rate decreased after 20 days (Figure 4c), the current images do not show clear evidence of erosion near the inner wall. Quantitative analysis of the Fe precipitate volume near the syringe wall could confirm this hypothesis. A plausible explanation for the observed changes in the flow regime is that intensified capillary effects, or a shift towards capillary-dominated flow, contributed to the development of ramified flow channels.

The observed variation in the particle sizes (Figure 7) is attributed to the location of the 2D slices within the 3D sample. While the porous media consisted of uniformly sized glass beads with a diameter of 2 mm, the appearance of particle sizes in 2D slices can vary depending on the section of the slice relative to the beads. For instance, a slice intersecting the center of a bead displays a larger particle size, whereas a slice near the edge of a bead appears smaller. This is a common artifact of 2D cross-sections in 3D imaging and does not indicate actual heterogeneity in the particle sizes. Efforts were made to select representative slices to minimize this effect, but variations are unavoidable in 2D projections of inherently 3D structures.

3.5. Impact of Ca Number on Flow Regime

The hydraulic gradient (i), as defined in Equation (1), was measured near the inlet at a height of 30 mm using representative cylinders (C1 and C2 in Figure 1). Figure 8a shows temporal variations in i during the experiment, with experimental data represented by purple circles. Partial pore clogging along the central line of the sample redirected the flow towards the cylinder, bypassing the central region and reducing the flow through the syringe outlet. This redirection caused interruptions in the i measurements after day 12. Despite this limitation, the recorded data confirmed an increasing trend in i over time, indicating the progressive accumulation of Fe precipitates within the sample. Hence, the predicted data (blue line in Figure 8a) were used for the subsequent calculation of Ca.

Figure 8b illustrates the temporal evolution of Ca in response to changes in the entry pressure and total permeability as a result of Fe precipitation. The Ca values decreased from 3.0 to 0.05, approaching the lower boundary of the capillary–viscous transition zone (1 < Ca < 100), as documented by Virnovsky et al. [64]. This trend reflects a transition from a viscous-dominated flow regime to one increasingly influenced by capillary forces. The observed shift underscores the role of spatial heterogeneity in shaping flow paths. During the first 15 days, higher Ca values indicated a flow regime dominated by viscous forces, with the flow traveling along relatively direct paths from the inlet to the outlet. After day 15, as Ca dropped below 1.0, capillary forces became dominant, facilitating the formation of more tortuous pathways near the syringe’s inner wall, consistent with the conceptual model presented in Figure 7.

The cross-sectional area (A in Equation (1)) was assumed constant for simplicity throughout the experiment, corresponding to the syringe’s physical dimensions. However, clogging due to Fe precipitation likely reduces the effective cross-sectional area over time, introducing variability in the flow dynamics that was not directly considered in this study. This simplification may partly explain the observed linear trend in Ca (Figure 8b), despite the non-linear variations in the permeability (k) and pressure (p). To improve future analyses, segmented micro-CT data could be utilized to estimate temporal variations in the effective cross-sectional area at the REV scale. Incorporating these estimates would provide a more accurate representation of how clogging impacts Ca and drives transitions in flow regimes. Moreover, this approach would offer deeper insights into the interplay between pore-scale changes and continuum-scale flow behavior.

4. Discussion and Implications

4.1. Dynamic Properties of Fe Hydroxides

Fe hydroxides (Fe(OH)₃) commonly form in hydrogeochemical systems, including coastal aquifers and industrial discharge zones. Their environmental significance arises from their reactivity and their transformation from amorphous ferrihydrite to more stable crystalline forms such as goethite or hematite [65]. Ferrihydrite’s dynamic nature and highly variable density, influenced by its water content [66], introduce complexities in understanding its behavior. Over time, its transformation into denser, less porous crystalline phases reduces the pore volume, decreases the surface area, and alters the reaction kinetics. These changes complicate the direct visualization and microscopic imaging of Fe precipitation and its impact on flow path evolution in porous media.

In this study, Fe precipitates were initially observed as loosely attached hydrous phases that transitioned into denser, crystalline forms over time. Therefore, “hydrous Fe” refers to ferrihydrite, representing newly formed, loosely attached precipitates (depicted in cyan in Figure 7) with a lower density and higher water content. In contrast, “solid Fe” describes more mature, densely packed Fe hydroxides (depicted in orange in Figure 7) that form during later precipitation stages. These phases are differentiated based on the grayscale intensity values in micro-CT imaging, with higher intensities corresponding to denser phases. While this approach provides an initial distinction, future studies incorporating X-ray diffraction (XRD) and microscopy will enhance the phase identification accuracy. Additionally, the simplified approach in this study assumes static physical properties for Fe hydroxides, including a constant density and molar volume, to estimate the coupled evolution of porosity and permeability. Although this assumption offers a foundational framework, it requires further validation through experimental research on ferrihydrite transformations under varying conditions to improve long-term predictions of permeability and porosity evolution.

4.2. Evolution of Interparticle Interactions

The growth and stability of Fe hydroxide aggregates in porous media are influenced by nucleation processes and spatial constraints within the pore network [50]. Our experimental results suggest that nucleation occurs predominantly on the surfaces of the glass beads, where reactive zones facilitate the initial formation of Fe hydroxides. These aggregates grow through interparticle interactions and chemical bonding, forming surface coatings that evolve into denser, more stable structures. However, alternative mechanisms also contribute to precipitate accumulation and pore clogging [67,68]. Physical obstruction due to the accumulation of precipitates in pore throats can reduce the porosity and affect the flow [69]. Additionally, Fe-oxidizing bacteria can accelerate Fe(II) oxidation and enhance heterogeneous clogging through the production of extracellular polymeric substances (EPS), which alter the physical properties of Fe precipitates by creating a gel-like matrix and further reduce the permeability and disrupt the flow paths by intensifying pore clogging [70,71]. Bacteria-mediated Fe(III) precipitation can catalyze Fe(II) oxidation, amplifying localized precipitation and increasing the tortuosity [68,72,73]. Autocatalytic oxidation, where early-stage Fe oxides catalyze further Fe(II) oxidation, can intensify localized precipitation and exacerbate pore clogging in certain regions [55,74,75].

The observed reopening of the flow paths and flushing near the syringe wall can be attributed to the interplay of Fe precipitation, hydraulic pressure, and pore-scale heterogeneity. The localized accumulation of Fe precipitates initially narrows the pore throats in the central regions, redirecting the flow towards less resistant pathways, such as areas near the syringe wall. This redirection of the flow causes localized increases in velocity near newly formed pathways, potentially dislodging loosely attached hydrous Fe precipitates and then reopening previously clogged channels. This dynamic process reflects the interaction between elevated mechanical forces and the weak physicochemical bonds of early-stage precipitates. Additionally, persistent hydraulic gradients from the co-injection process further promote the mobilization and flushing of the precipitates near the syringe wall. These gradients provide sufficient force to detach and redistribute the precipitates within the matrix, particularly in less consolidated regions.

Microbial activity was excluded from this study, as the glass beads were pre-washed to eliminate biological contaminants, and the high Cl⁻ concentration in the saltwater inhibited microbial growth. The observed high intensity of Fe precipitation near the inlet may support the hypothesis of autocatalytic behavior. By comparing micro-CT reconstructions with spectroscopic analyses of Fe phases, the relative contributions of chemical bonding and physical obstruction to clogging could be better clarified. Moreover, incorporating microbial contributions into experimental and numerical investigations through interdisciplinary collaboration among geochemists, hydrogeologists, and modelers would further refine our understanding of abiotic and biotic interactions in porous media. This integration would improve predictions of the Fe precipitation dynamics and their hydrogeochemical impacts in both natural and engineered systems.

4.3. Tortuosity Orientation and Flow Path Shifts

This study focuses on the abiotic Fe precipitation dynamics and simplifies Fe(II) oxidation as only driven by DO availability. The injection of Fe(II)-rich freshwater into a DO-rich saltwater background results in the oxidation of Fe(II) to Fe(III), forming Fe hydroxides (Fe(OH)₃) along the flow path. A peak in the Fe(OH)₃ volume fraction is observed near the inlet, where the DO concentration is the highest. This process reduces the permeability and porosity near the syringe bottom, consistent with the hypothesis of a critical zone governed by DO availability. However, the observed pattern of Fe precipitation near the inlet and syringe wall could be influenced by the boundary conditions, with the high DO concentrations at the inlet driving the elevated precipitation rates in this region. Similarly, localized hydraulic gradients near the syringe wall can create preferential flow paths, consistent with studies on boundary effects in porous media [57,76]. While these effects are pronounced, previous research suggests that the precipitation patterns near boundaries often resemble bulk processes when DO gradients dominate the reaction zone [77]. Thus, our observations remain significant despite the boundary influences.

As Fe precipitates accumulate within the pore matrix, the pore throats become narrow, which reduces the permeability and increases the local hydraulic resistance. This process causes a gradual transition from a viscous-dominated (Ca > 1) to a capillary-dominated (Ca < 1) flow regime. The temporal evolution of the experimental Ca (Figure 8b) has good agreement with this mechanism: during the early stages, high Ca values indicate that viscous forces dominate the flow. Over time, as the permeability decreases due to precipitation, capillary forces become more significant, redirecting the flow along tortuous paths. This transition demonstrates the interplay between chemical reactions and flow regimes, corroborating the findings from systems where mineral precipitation alters the flow properties [25,76].

The discernible orientation for tortuosity reflects the redirection of flow paths caused by pore clogging and is closely tied to the three stages of Fe precipitation in this study. During the initial stage, hydrous Fe precipitates form loosely on particle surfaces, allowing the flow paths to remain relatively linear. This is evidenced by the distribution of the Fe precipitates along the central pore network. As the precipitation continues, the pore throats begin to narrow, forcing the flow to redirect around clogged regions. This redirection increases the tortuosity and creates preferential flow paths near the syringe walls, as constrictions in the central region compel the flow to seek alternative, less resistant pathways. In the final stage, complete pore clogging in the central region results in highly tortuous and ramified channels along the syringe wall, highlighting the dynamic interaction of Fe precipitation, flow reorganization, and evolving tortuosity orientation. This behavior is consistent with models of evolving porous media [78,79]. While this study qualitatively demonstrates this transition, quantitative evidence from segmented micro-CT data could enable the reconstruction of the connected porosity and provide a direct measure of the tortuosity changes based on pore network models. These reconstructions in further research would validate the shift from central flow paths to ramified channels near the syringe wall, offering deeper insights into how pore-scale heterogeneity governs the flow regimes under capillary-dominated conditions.

4.4. Implications for Coastal Aquifer Systems

This study provides valuable insights into the interplay between Fe(II) precipitation, flow dynamics, and permeability evolution in porous media under controlled conditions. The syringe experiment highlights the potential of Fe hydroxides to alter the tortuosity orientation and flow paths in subsurface systems by generating spatial heterogeneity. However, several limitations must be addressed to bridge the gap between laboratory observations and real-world applications, particularly in coastal aquifer systems, where the geochemical and hydrological processes are more complex.

First, the high Fe(II) concentration used in this study was necessary to facilitate observable precipitation over the experimental timescale but exceeded the typical levels in natural groundwater, where the concentrations are constrained by geochemical equilibria and competing reactions [4]. The reaction kinetics, particularly the rates of Fe(II) oxidation and precipitation, were not characterized but are critical in extrapolating these findings to natural settings. Additionally, factors such as the presence of competing anions (e.g., SO₄²⁻, NO₃⁻) influence Fe oxide formation. For instance, Hu et al. reported enhanced precipitation in the presence of sulfate [53]. Yuan et al. demonstrated that nitrate-mediated Fe precipitation immobilized phosphate and heavy metals through the formation of stable Fe–mineral complexes [80]. Future studies will incorporate these factors to better align the experimental conditions with real-world mixing zones, enabling more accurate predictions of the Fe precipitation dynamics in coastal aquifers.

This study also aimed to bridge the gap between pore-scale precipitation and Darcy-scale hydrological responses. The use of micro-CT provides the detailed visualization of pore-scale processes and insights into the spatial distribution of Fe oxides. However, the observed REV, which roughly corresponds to the syringe size, reflects heterogeneity influenced by both boundary effects and the intrinsic properties of the porous media. This limitation highlights the challenges of directly applying these findings to field conditions. Integrating the physio-mathematical model with field-scale reactive transport modeling using TOUGHREACT could scale the laboratory findings to regional hydrogeochemical systems. This approach would simulate localized clogging effects and predict anisotropic permeability changes driven by hydrodynamic dispersion and variable Fe(II) fluxes, supporting the development of environmental strategies.

Finally, the syringe experiment involving Fe(II) precipitation under controlled conditions provides valuable data on spatial heterogeneity and confirms the transition from viscous-dominated to capillary-dominated regimes as pore clogging progresses. While these findings align with established mechanisms, the absence of quantitative data on the reaction kinetics limits the ability to validate the thresholds for complete pore clogging. Scaling REV-scale findings to field applications requires addressing the temporal and spatial heterogeneity in natural systems, as localized precipitation patterns induce anisotropic permeability changes that influence regional hydrogeochemical processes [76,81]. Further research leveraging advanced experiments or existing datasets will enhance the applicability of these findings to diverse hydrogeochemical settings.

4.5. Limitations and Uncertainty of Applied Methods

The controlled environment of the glass-bead-packed syringe may not fully replicate the heterogeneity characteristic of natural porous media in groundwater–seawater mixing zones. Additionally, the syringe-scale experiment may not have captured long-term or large-scale variations, and the fixed injection rates and geometry in the experiment may simplify the variability in the flow dynamics in natural systems. However, these simplifications isolated the key mechanisms and well-defined conditions to focus on the fundamental hydrogeochemical processes underlying Fe(II) oxidative precipitation and its impact on the flow paths and tortuosity orientation. In addition, the experimental duration and spatial scale were chosen to achieve the high-resolution imaging of Fe precipitates and flow path evolution at the micro scale. Despite these limitations, the findings of this study have important implications for groundwater management and remediation in coastal aquifers. The observed reduction in permeability and the evolution of tortuous flow paths due to Fe precipitation indicate that natural geochemical barriers, such as iron curtains, may play a significant role in influencing contaminant transport and nutrient fluxes in coastal ecosystems. These insights provide a basis for the design of engineered barriers that leverage Fe precipitation to immobilize contaminants in groundwater discharge zones. Such engineered solutions could effectively mitigate nutrient and contaminant transport into sensitive coastal environments.

To address the gap between controlled experiments and real-world systems, future studies will incorporate natural sediments with diverse grain sizes, mineralogies, and pore connectivity to more accurately represent the complexity of natural porous media. These studies will also implement variable injection rates and dynamic boundary conditions, utilizing larger columns and field-scale models to extend the findings to long-term and field-scale scenarios. Research on coastal aquifer systems will integrate insights into Fe precipitation with field-scale reactive transport modeling, enabling the assessment of the practical viability of these mechanisms for groundwater management. By simulating more realistic hydrogeochemical conditions and flow dynamics, these efforts will provide a robust understanding of the interactions between Fe precipitation, flow paths, and contaminant transport in natural systems. Such investigations will support the development of sustainable strategies for the management of coastal aquifers.

5. Conclusions

Previous studies on multiphase flows have highlighted the challenges of scaling fluid dynamics from small scales (nm~µm) to large scales (cm~m), particularly when the pore matrix evolves due to precipitation processes such as the abiotic oxidative precipitation of Fe(II). These limitations have constrained our understanding of the spatiotemporal evolution of flow pathways in porous media. This study addressed these challenges by using a simplified experimental setup designed to model the abiotic oxidation of Fe(II) in subsurface mixing zones within estuaries. Fe(II)-rich freshwater was injected into a DO-rich saltwater flow through a syringe packed with glass beads, providing valuable data to evaluate the effects of hydrogeochemical reactions on the precipitation patterns and seepage properties. The micro-CT imaging of an REV-scale sample further enhanced our comprehension of the temporal and spatial evolution of Fe precipitates.

The experimental results revealed three distinct stages of Fe precipitation and their effects on the flow dynamics.

(1)

Early stage (0–10 days): Fe precipitates uniformly coat solid particles, with hydrous Fe exhibiting a low density and weak attachment to particle surfaces. This mobility allows temporarily clogged pathways to reopen despite ongoing precipitation, maintaining the flow paths within the pore matrix.

(2)

Intermediate stage (10–20 days): Accumulated Fe precipitates reduce the sizes of pore throats (i.e., bottleneck effect) and form interparticle bonds, redirecting the flow paths to bypass clogged regions. This stage significantly reduces the permeability and increases the hydraulic gradients, facilitating the flushing of the Fe precipitates near the syringe wall at the inlet.

(3)

Final stage (20–25 days): The precipitation near the inlet stabilizes to a quasi-steady state, with the permeability changes becoming negligible (<1% over 5 days). A diverse array of ramified flow channels develop, and the Ca values decrease from 3.0 to 0.05, indicating a transition from a viscous-dominated regime to one influenced by capillary forces. This transition promotes the formation of more tortuous flow paths within the porous media.

This study underscores the importance of investigating the fluid dynamics at the REV scale, particularly in cases where a true REV may not exist. The findings also demonstrate the broader relevance of this research to field-scale scenarios, where Fe precipitates form interparticle bonds and alter the seepage properties. These changes can create geochemical barriers, such as the IOCS and “iron curtain” observed in intertidal zones, which regulate the transport of dissolved chemicals from land to sea. However, the experimental setup represents a simplified model of natural systems. In natural subsurface mixing zones, more complex water chemistries, lower Fe(II) concentrations, and microbial activity can influence the Fe precipitation dynamics. For example, anions such as SO₄²⁻ enhance Fe oxide formation, and Fe-oxidizing bacteria accelerate these processes while contributing to bioclogging. Future studies should incorporate these complexities to better approximate natural conditions and provide a more comprehensive understanding of how abiotic and biotic processes interact to influence flow and transport.

In conclusion, the insights gained from this study contribute to our comprehension of multiphase flows in evolving porous media across scales, from nm–µm to cm–m. These findings hold broad applicability, ranging from predicting the seepage properties in coastal aquifers to practical solutions in sustainable soil remediation.