The Impact of Biofilm-Induced Dynamic Layered Clogging on Hyporheic Exchange in Streambed

Abstract

The hyporheic zone functions as a critical interface mediating hydrological and biogeochemical exchanges between stream water and streambed. Within shallow streambed layers, sediment transport and biofilm colonization can induce dynamic layered clogging, alter hydraulic conductivity, and foster physical stratification that significantly modulates hyporheic exchange patterns. This study develops a coupled hydrodynamic–mass transport model for a representative streambed bedform to examine the impacts of biofilm-driven dynamic clogging on hyporheic exchange dynamics. Results reveal that dynamic layered clogging reduces pore water velocity and total water flux, causing a 45.1% decline in the total inflow to the hyporheic zone. The transport of non-absorbable solutes exhibits a biphasic pattern: initial rapid penetration transitions to gradual deceleration over time, with dynamic clogging extending the penetration time of the solute center of mass distribution (CMD). Notably, when hydraulic conductivity falls below a threshold (K* < 0.25), CMD penetration time exhibits a positive correlation with hydraulic conductivity, attributed to porosity-induced changes in actual flow velocity. When considering the anaerobic growth in deeper layers, the penetration time become longer because of the clogging present there. This research clarifies the mechanistic connections between biofilm-induced clogging and hyporheic exchange, providing valuable insights for the management of hyporheic ecosystems and the modeling of biogeochemical processes.

1. Introduction

The hyporheic zone is defined as a water-saturated layer of sediment situated at the streambed and extending to both banks of the stream [1]. This region serves as a critical component of river ecosystems [2], serving as essential habitats, feeding grounds, and breeding sites for diverse aquatic organisms [3,4,5]. The exchange between the stream and streambed can be driven by the hydraulic forces generated by the flowing overlying water in rivers, and this is also known as hyporheic exchange [6,7,8]. This exchange leads to the retention, transportation, and transformation of various substances such as solutes and sediment particles in the hyporheic zone [9,10,11,12].

The stratification of streambed structures and the heterogeneity in hydraulic parameters within the hyporheic zone are well-documented phenomena in fluvial systems [13,14,15]. Such internal stratification modulates interfacial flux dynamics and exerts a dualistic influence on solute retention times within the hyporheic matrix, capable of either extending or truncating residence durations [16,17,18]. Due to the transport and deposition of sediment as well as bioturbation within the hyporheic zone, the porosity and hydraulic conductivity of the shallow layers of the streambed may be significantly altered, potentially resulting in the physical stratification of the streambed [16,19].

Similarly, microorganisms modify the physical properties of localized streambed zones through biofilm formation, a process that diminishes sediment permeability and impedes the exchange of specific substances with the hyporheic zone [20,21,22]. Rocks, cobblestones, silt, organic debris, and benthic plant leaves in the hyporheic zone provide a large number of attachment surfaces for benthic microorganisms, thus creating an environment for the symbiotic coexistence of benthic biofilms [23,24]. Biofilms adhering to fine sediment particles generate a viscous matrix that tightly encapsulates and embeds these particles, exerting a pivotal role in sediment stabilization and resuspension resistance [25,26]. Collectively, layered clogging within the hyporheic zone exerts a substantial regulatory influence on the flux of bioactive materials, thereby governing regional biogeochemical cycling [23,25,27].

In terms of the previous studies, it is evident that prior research has elucidated various facets of hyporheic exchange processes and microbial dynamics within streambed environments. Specifically, Jiang et al. [16] executed a series of experiments to analyze the hyporheic flux in layered streambeds, but did not consider the dynamic changes in hydraulic parameters of the streambed. Xian et al. [28] studied the dynamics of biofilm-induced biological clogging using the laboratory cultivation of microorganisms, yet did not explore the potential biogeochemical effects that may arise from this phenomenon. Shogren et al. [29] conducted experiments and found that microbial growth and clogging can limit the rate and pattern of hyporheic exchange. Ping et al. [27] established a coupled process model of flow-solute-microbial metabolism and found that the mechanism of microbial clogging has a significant impact on the source and sink role of nitrogen elements. Caruso et al. [30] developed a hydrobiogeochemical model to elucidate the efficiency of nitrogen transformation under conditions of microbial clogging in streambed sediments. Their work provides valuable insights into the interplay between microbial activity and nutrient cycling in these complex environments. Cook et al. [31] took advantages of flume experiments to study the influence of streambed topography and particle size on biofilm growth and hyporheic exchange, and their study found that sediment particle size is the main factor controlling the growth of biofilm and hyporheic exchange. Using field investigations, Nogaro et al. [32] found that the clogging of the streambed can affect the aerobic and anaerobic respiration processes of microorganisms in the hyporheic zone.

Although prior studies have investigated the environmental and ecological consequences of streambed clogging in hyporheic zones, they have inadequately addressed how dynamic layered clogging influences hyporheic exchange patterns during microbial growth. Consequently, this study focuses on a single representative bedform within the hyporheic zone, developing a coupled hydrodynamic–mass transport mathematical model to simulate the dynamic clogging process associated with microbial growth and hyporheic exchange patterns in the streambed. Furthermore, it elucidates the underlying mechanisms by which dynamic layered clogging affects hyporheic exchange. This paper primarily addresses the following questions: (1) How does dynamic streambed clogging alter pore water flux in the hyporheic zone? (2) What is the mechanism of non-absorbable solute penetration through the bio-layer in the hyporheic zone? By addressing these questions, this research aims to provide a robust theoretical foundation for enhancing our understanding of the biogeochemical processes in river ecosystems. The findings of this study are expected to contribute to the development of more accurate and predictive models of hyporheic exchange, thereby informing sustainable river management practices and ecological restoration efforts.

2. Methodology

This study focuses on a single bedform within the hyporheic zone, utilizing numerical simulation techniques to examine the impact of dynamic layered clogging processes in shallow streambed layers on hyporheic exchange flows. The bedform is two-dimensional (2D), simplified as a triangular shape along the longitudinal direction of the channel, with morphological parameters such as length, height, and stoss-side length referenced from [33] (

Table 1. Parameters for simulations.

Geometric Parameters	Values	Hydraulic Parameters	Values
Average depth of the overlying water	8.2 cm	Initial porosity (n0)	0.40
Length of the bedform	15.2 cm	Stable porosity (ns)	0.34
Height of top of the bedforms	2.0 cm	Water density (ρ)	1000 kg m−3
Length of the stoss side of the bedform	11.4 cm	Longitudinal dispersivities (αL)	0.001 m
Length of the lee side of the bedform	3.8 cm	Transverse dispersivities (αT)	0.0001 m
Minimum bedform height	12.0 cm	Initial hydraulic conductivity (K0)	8.4 × 10−6 m s−1
Thickness of Layer 1 (L)	2.0 cm	Stable hydraulic conductivity (Ks)	4.3 × 10−6 m s−1

). Hydraulic conductivity and porosity parameters are set according to the reference [34]. Generally, the area for biofilm formation is a depth of few centimeters on the surface streambed in the hyporheic zone [35]. Therefore, this study defines the upper 2 cm of the bedform as the bio-layer (Layer 1), where microbial growth and biofilm formation gradually clog the pores, resulting in a progressive decrease in hydraulic conductivity and porosity. The deeper region is defined as the Layer 2, and it can be two types: Inorganic Layer (unaffected by biofilms, with constant hydraulic parameters) and Anoxic Zone (anaerobic bacteria growth here, and the hydraulic conductivity is variable). The interface between the overlying water and the streambed is designated as Surface 1, while the boundary between Layer 1 and Layer 2 is defined as Surface 2 (Figure 1).

This study takes advantage of numerical simulation software to simulate river water flow, pore water flow, and the transport of non-absorbable solutes. This study employs two-dimensional computational fluid dynamics software FLUENT (v14.0), based on the Reynolds-averaged Navier–Stokes equation combined with the k-ω turbulent closure scheme to calculate overlying water flow. The initial parameters and boundary conditions for the overlying water flow are set with references [10,36,37]. The streambed surface pressure simulated by FLUENT is used as a boundary condition for the two-dimensional model based on COMSOL Multiphysics (v5.6), to simulate the pore water flow and the transport of non-absorbable solutes in the bedform [36]. Darcy’s Law and the continuity equation for incompressible flow in a non-deformable medium are used to model the pore water flow. Finally, the transport of solutes is simulated based on the pore water flow field by using module Transport of Diluted Species in Porous Media of the software COMSOL Multiphysics.

2.1. Govern Equations in Streambed

The COMSOL Multiphysics was used to model the flow and solute transport in the streambed. The pore water flow is governed by the combination of Darcy’s Law and the continuity equation for incompressible flow in a non-deformable medium, and thus the groundwater flow can be described as (constant fluid density assumed):

$${\displaystyle \frac{\partial u_i}{\partial x_i}}=0$$

(1)

$$u_i=-K{\displaystyle \frac{\partial h}{\partial x_i}}$$

(2)

where K (m s⁻¹) is the hydraulic conductivity, u_i (i = 1, 2) is the Darcy’s flow velocity component in the x_i (i = 1, 2) direction and h (m) is the hydraulic head. Simulation parameters are shown in Table 1.

By using the following equations, this study modeled the transport of non-absorbable solute in the bedform,

$${\displaystyle \frac{\partial C}{\partial t}}={\displaystyle \frac{\partial }{\partial x_i}}\left(D_{ij}{\displaystyle \frac{\partial C}{\partial x_j}}-u_{i}C\right)$$

(3)

where t (s) is time, C (kg m⁻³) is the concentration of solute in the pore water, and D_ij (m² s⁻¹) is the 2D dispersion coefficient tensor,

$$D_{ij}=({\alpha }_T\left|u\right|+D_e){\delta }_{ij}+({\alpha }_L-{\alpha }_T)u_i{u}_j/\left|u\right|$$

(4)

where α_L (m) and α_T (m) are the longitudinal and transverse dispersivities, respectively; $\left|u\right|=\sqrt{u_1^2+u_2^2}$ (m s⁻¹) is the magnitude of the pore water flow velocity; and D_e (m² s⁻¹) is the effective molecular diffusion coefficient.

2.2. Boundary Conditions in Streambed

The setting of boundary conditions for the streambed is shown in Figure 1. Boundary 1 is a specific pressure distribution boundary for the module Darcy’s Law, and its value is the surface pressure calculated by the FLUENT software. Boundary 1 is an open boundary for module Transport of Diluted Species in Porous Media, which is in the following form,

$$\left\{\begin{array}{c}C=C_t \stackrel{\rightharpoonup }{n}\cdot \stackrel{\rightharpoonup }{u}\ge 0\\ {\displaystyle \frac{\partial C}{\partial \stackrel{\rightharpoonup }{n}}}=0 \stackrel{\rightharpoonup }{n}\cdot \stackrel{\rightharpoonup }{u}<0\end{array}\right.$$

(5)

where $\stackrel{\rightharpoonup }{n}$ is the unit vector normal to the interface (pointing inward), $\stackrel{\rightharpoonup }{u}$ is the flow velocity vector of solute, and C_t (kg m⁻³) is the concentration of solute in the overlying water at time t. The calculation of C_t is calculated based on the settings of an experiment [36]. Boundary 2 is periodic for both the module Darcy’s Law and the module Transport of Diluted Species in Porous Media, where the former is a periodic pressure distribution boundary, and the latter is a periodic concentration distribution boundary. Boundary 3 is no flux for these two modules.

2.3. Case Setup

This paper primarily sets up three different Cases (Case A, Case B, and Case C) to analyze the impact of dynamic layered clogging on the hyporheic exchange in rivers (

Table 2. Conditions and penetration time of different cases.

Cases	Hydraulic Conductivity (K)	Porosity (n)	Penetration Time (T)
Case A	Layer 1: K0	Layer 1: n0	3.838 d
	Layer 2: K0	Layer 2: n0
Case B	Layer 1: Ks	Layer 1: ns	3.839 d
	Layer 2: K0	Layer 2: n0
Case C	Layer 1: Varying from K0 to Ks	Layer 1: Varying from n0 to ns	3.936 d
	Layer 2: K0	Layer 2: n0
Case D	Layer 1: Varying from K0 to Ks	Layer 1: Varying from n0 to ns	3.994 d
	Layer 2: Varying from K0 to Ks	Layer 2: Varying from n0 to ns

). Among them, Case A represents the condition where there is no biological growth in Layer 1, with its hydraulic conductivity and porosity remaining constant over time, and its values being equal to those in Layer 2. Case B represents that the dynamic layered clogging in Layer 2 is set to its maximum value, with its hydraulic conductivity and porosity remaining unchanged over time. Case C represents that the microorganisms gradually grow in Layer 1, with the hydraulic conductivity and porosity gradually decreasing over time in the bio-layer. There can be both aerobic and anaerobic bacteria existing in the streambeds, and generally, the anaerobic bacteria can stay deeper in the streambed [38,39]. To determine how anaerobic bacteria affect the hyporheic exchange, this study sets up Case D. The Case D refers to the fact that considering Layer 2 is located at a deeper level and is an anoxic zone, anaerobic microorganisms will grow and clog there, resulting in changes in its porosity and hydraulic conductivity over time (Table 2).

2.4. The Variations in Parameters

This paper assumes that the hydraulic conductivity and porosity of Layer 1 are time-dependent (Table 2). Due to microbial growth, the pores of bedform become blocked, resulting in a reduction in its hydraulic conductivity. The initial value and specific values of the reduction are referred to the experimental results, where the data points represented by blue circles in Figure 2 are from the experimental results of [34]. To make the variation process smoother, this paper uses an exponential function to fit these measurement results, shown below,

$$K(t)=p_0\exp (-p_{1}t)+K_0-p_0$$

(6)

where t (s) is time, K₀ (m s⁻¹) is the initial hydraulic conductivity, p₀ (m s⁻¹) and p₁ (s⁻¹) are the parameters that needs to be fitted. According to the references [40], the relationship between hydraulic conductivity and porosity is shown below,

$${\displaystyle \frac{K}{K_0}}={\displaystyle \frac{n^3}{{(1-n)}^2}}\cdot {\displaystyle \frac{{(1-n_0)}^2}{n_0^3}}$$

(7)

where n₀ (-) is the initial porosity, n (-) is the variable porosity, K (m s⁻¹) is the variable hydraulic conductivity. Finally, the time-dependent process of hydraulic conductivity and porosity are calculated and shown in Figure 2.

2.5. Definition of Some Parameters

In order to deeply investigate the mechanism by which microbial growth causes clogging in streambed and affects hyporheic exchange, this paper defines several parameters.

(1)

Center of Mass Distribution (CMD)

When solutes enter the streambed, they form a certain distribution of solute clouds. To analyze the motion characteristics of this solute cloud, this paper uses the concept of solving for the expected value through a two-dimensional probability density function, and separately determines the positions of the solute distribution expectations along the x-axis and y-axis, serving as its CMD. The specific formula is as follows,

$$\left\{\begin{array}{c}{x}_{\mathrm{CMD}}={\displaystyle {\int }_{x\min }^{x\max }{\displaystyle {\int }_{y(x)\min }^{y(x)\max }xC}\ast (x,y)\mathrm{d}y} \mathrm{d}x\\ y_{\mathrm{CMD}}={\displaystyle {\int }_{y\min }^{y\max }{\displaystyle {\int }_{x(y)\min }^{x(y)\max }yC}\ast (x,y)\mathrm{d}x} \mathrm{d}y\end{array}\right.$$

(8)

where C*(x, y) (-) is the standardized distribution function for solute concentration, which is,

$$C\ast (x,y)=C(x,y)/{\displaystyle \iint C(x,y)\mathrm{d}A}$$

(9)

where A (m²) is the area of a single bedform. C(x, y) (kg m⁻³) is the distribution function of solute concentration.

(2)

Penetration time (T) and Arrival time (T_a)

Penetration time refers to the time it takes for the trajectory of CMD to pass through Layer 1. Arrival time indicates the time required for the trajectory of CMD to reach a certain depth.

3. Results and Discussions

3.1. The Flux of Pore Water in Streambed

To analyze the influence of dynamic layered clogging on pore water velocity in the hyporheic zone, this study selected Case C, a case with variable hydraulic conductivity, for investigation. Figure 3 illustrates the relative magnitude of Darcy velocity (u* = u/u₀, u₀ = 4 × 10⁻⁸ m/s) in the pore water for Case C. At the initial stage (t = 0), the velocity contours of Layer 1 and Layer 2 are continuous. This is because microbial growth has not yet commenced, and both layers exhibit uniform hydraulic conductivity and porosity, resulting in a seamless velocity distribution in the numerical model. By t = 10 d, microbial growth has progressed, leading to clogging in Layer 1. Consequently, the hydraulic properties of Layer 1 undergo significant alterations: hydraulic conductivity decreases from 8.4 × 10⁻⁶ m/s to 5.6 × 10⁻⁶ m/s, and porosity declines from 0.40 to approximately 0.36 (Figure 2). These changes manifest in the velocity distribution as a distinct discontinuity at the interface (Surface 2) between Layer 1 and Layer 2 (Figure 3). Specifically, velocity abruptly increases from Layer 1 to Layer 2 due to the sharp rise in hydraulic conductivity of the medium. At t = 60 d, microbial growth stabilizes, and biofilm-induced clogging in Layer 1 approaches its maximum effect. Hydraulic conductivity and porosity in Layer 1 further diminish (to 4.3 × 10⁻⁶ m/s and 0.34, respectively). Correspondingly, Figure 3 reveals a more pronounced discontinuity in velocity contours at the Layer 1-Layer 2 interface, along with a reduction in the high-velocity zone (red regions) within Layer 1. This results from prolonged microbial growth exacerbating clogging, thereby further reducing hydraulic conductivity and shrinking the high-velocity areas.

To systematically investigate the influence of dynamic layered clogging on water flux within the hyporheic zone, this study selected Case C for detailed analysis. Figure 4 presents the water flux across different interfaces of the hyporheic zone. Specifically, Figure 4a depicts the flux at Surface 1 (the interface between the overlying water and Layer 1), while Figure 4b represents the flux at Surface 2 (the interface between Layer 1 and Layer 2). All fluxes are defined as positive downward and negative upward, and the directions are shown in Figure 1. As shown in Figure 4a, the positive flux of water entering the hyporheic zone from the overlying water primarily concentrates on the stoss side (x < 11.4 cm), peaking at x = 6.5 cm. At the initial time (t = 0), the peak flux is relatively high, reaching 7.1 × 10⁻⁵ kg m² s⁻¹. When t = 10 d, due to microbial growth and biofilm-induced clogging in the hyporheic zone, both the hydraulic conductivity and porosity of Layer 1 go downwards, leading to a reduction in the peak flux to approximately 4.8 × 10⁻⁵ kg m² s⁻¹. At t = 60 d, microbial growth stabilizes, and biofilm-induced clogging in Layer 1 reaches its maximum extent, causing the peak flux to further decline to 3.9 × 10⁻⁵ kg m² s⁻¹. Compared to the initial value, biofilm clogging reduces the total water flux entering the hyporheic zone by 45.1%. Figure 4b exhibits a similar trend, with the positive flux of water entering Layer 2 concentrated on the stoss side of bedform. The peak flux decreases from an initial value of 2.8 × 10⁻⁵ kg m² s⁻¹ to 2.0 × 10⁻⁵ kg m² s⁻¹ when biofilm clogging stabilizes (t = 60 d). This corresponds to a 28.6% reduction in total flux entering Layer 2 compared to the initial condition. A comparison between Figure 4a,b reveals that the peak positive flux at Surface 2 is shifted further to the right (x = 7.5 cm). This shift occurs because, on the upstream side, water predominantly enters the hyporheic zone in a downward-rightward direction (Figure 3).

Figure 5 illustrates the temporal variations in the summed inflow and outflow fluxes at Surface 1 and Surface 2. The results indicate that for both interfaces, all flux values exhibit a gradual decline over time and stabilize when t > 30 days. Notably, the inflow and outflow fluxes are equal at the initial stage (t = 0), after which a progressive divergence emerges between these two flux types, ultimately resulting in slightly lower outflow fluxes compared to inflow fluxes. This phenomenon is attributed to the high hydraulic conductivity of Layer 1 during the initial phase, which allows relatively unrestricted water exchange within the hyporheic zone, leading to balanced inflow and outflow fluxes. As time progresses, biofilm accumulation progressively obstructs Layer 1, impeding water discharge from the hyporheic zone and consequently causing the outflow flux to become marginally smaller than the inflow flux.

3.2. The Transport of Non-Absorbable Solute in Hyporheic Zone

To systematically analyze the transport of solutes in the hyporheic zone, this study first examined the variation patterns of solutes in the overlying water (Figure 6). Figure 6a illustrates the relative concentration of solutes in the overlying water (C/C₀) over time under three different cases, with the x-axis (time) represented in a linear scale. Figure 6b, on the other hand, transforms the x-axis of Figure 6a into a logarithmic scale. A comprehensive review of both subfigures in Figure 6 reveals that the trends and values of solute concentration in the overlying water across the three scenarios are remarkably similar. Notably, during the initial 0 to 5 days, the relative concentration decreases rapidly from 1.0 to approximately 0.85, followed by a gradual decline. After 100 days, the relative concentration stabilizes around 0.78. Upon closer examination of the distinctions between Case A and Case B, it becomes evident that the final stable concentration in Case B is slightly higher than that in Case A (by 0.57%). This difference can be attributed to dynamic clogging in Layer 1, which reduces porosity and consequently diminishes the volume of solutes transported from the overlying water into the hyporheic zone. Additionally, a detailed analysis of Case C illustrates that its solute concentration changes are situated between those of Case A and Case B. In the first 5 days, the values for Case C are more aligned with those of Case A, while after 20 days, they approach those of Case B. The period between 5 and 20 days represents a transitional phase, during which the concentration curve for Case C gradually shifts from Case A towards Case B. This shift is attributed to the ongoing microbial growth within Layer 1, with the clogging process intensifying progressively over time.

Figure 7 illustrates the relative concentration (C/C₀) distribution of non-absorbable solutes in the hyporheic zone for Case C. And Figure 8 represents the transport path of the CMD of solute in the hyporheic zone for Case C. By combining these two figures, it can be observed that at t = 0.5 d, a crescent-shaped concentration distribution area rapidly formed on the stoss-side of Layer 1. When t = 2 d, the crescent-shaped concentration distribution gradually expanded downwards, with most of the solute mass still concentrated in Layer 1, with only a small portion of solutes breaking through Layer 1 to enter Layer 2, and at this time, the depth of CMD had not yet gone through Layer 1. By t = 5 d, the area of the crescent-shaped solute distribution increased further, occupying nearly one-third of the bedform. At this point, Figure 8 also shows that the depth of CMD had gone through Layer 1 and entered into Layer 2. When 10 < t < 30 d, the boundary of crescent-shaped solute concentration distribution gradually blurred, and over these 20 days, the depth of CMD rapidly decreases by approximately 1.8 cm. When t > 60 d, the solutes gradually became uniform in the hyporheic zone, and the depth of CMD decreased very slowly. And when 60 < t < 300 d, it decreased by only about 0.4 cm (from −4.9 to −5.3 cm). Overall, the transport process of solutes in the streambed is as follows: Initially, solute penetrates in the streambed witnesses rapidly, with an average depth of 1.8 × 10⁻¹ cm per day during the first 30 days. However, over the subsequent 270 days, the average depth per day drops to only 6.3 × 10⁻³ cm. This phenomenon indicates that non-absorbable solutes can quickly penetrate the shallow layers of the streambed in the early stages, but the process of solutes entering deeper areas of the streambed gradually slows down in the later stages. This deceleration is attributed to changes in hydraulic conductivity and porosity within the bio-layer, caused by dynamic microbial clogging.

3.3. The Arrival and Penetrate Time of CMD in Streambed

Generally, the smaller hydraulic conductivity can induce longer penetration time of CMD. As shown in Table 2, the penetration times for Cases A, B, and C are 3.838, 3.839, and 3.936 days, respectively. Compared with Case A, Cases B and C exhibit delays in penetration time by 0.03% and 2.56%, respectively.

The arrival time (T_a) also conforms to this rule similarly. Figure 9 illustrates the differences (ΔT) in arrival times at different depths (y = −5, −4, −3, −2, −1, and 0 cm) for the CMD under various cases. The blue bars in Figure 9 represent the differences in arrival times between Cases A and B, while the red bars represent the differences between Case A and Case C. For the blue bars, it can be concluded that the deeper the location within the streambed, the greater the gap in arrival times between Cases A and B. A similar pattern is observed for the arrival times of Cases A and C (red bars). This is because a smaller hydraulic conductivity can prolong the arrival time of the CMD, and the deeper area in the streambed, the more pronounced this effect of prolonging the arrival time of the CMD. If we compare the red and blue bars, it can be seen that all the blue bars are higher than the red ones, this is because the hydraulic conductivity of Case C witnesses a slow, gradual decrease process. The patterns of Case C become closer to those of Case A at earlier times and closer to those of Case B at later times. Therefore, at y = 0 cm, the arrival times of Cases A and C are almost identical.

Based on the penetration time and arrival time patterns in Table 2 and Figure 9, this paper hypothesizes that as the hydraulic conductivity in Layer 1 becomes smaller, the flow velocity will decrease, i.e., the penetration time of CMD will be prolonged. To verify this hypothesis, this paper conducts multiple sets of simulations with different scaling factors for the hydraulic conductivity in Layer 1, with the porosity (n) also adjusted according to Equation (3). K* represents the scaling factor for K₀, that is, K* = K/K₀ (this paper selected seven sets of K*, which are 1.0, 0.75, 0.5, 0.25, 0.1, 0.05, and 0.01). Figure 10 shows the penetration times corresponding to different K*. As can be seen from Figure 10, when K* > 0.25, the penetration time indeed increases over time as the hydraulic conductivity coefficient decreases. Starting from the initial T = 3.838 d when K = K₀, it gradually decreases to T = 3.995 d when K = 0.25 K₀, with the penetration time increasing by approximately 4.09%. However, as K continues to decrease (K* < 0.25), the penetration time of CMD becomes positively correlated with K*. This is because as the hydraulic conductivity coefficient decreases, the porosity is also decreasing. Although the decrease in porosity does not affect Darcy’s flow velocity in porous media, it does increase the actual flow velocity (actual flow velocity v = u/n). Therefore, when the porosity decreases to a certain extent, the reduction in the hydraulic conductivity cannot resist the increase in actual flow velocity caused by the decrease in porosity, and thus, when K* is sufficiently small, the reduction in the hydraulic conductivity will actually accelerate the penetrating process of CMD in Layer 1.

3.4. The Effects of Microorganisms Growth in Anoxic Zone

To account for the conditions of actual hyporheic ecosystems, this study considers the growth of aerobic and anaerobic microorganisms in the shallow and deep layers of the streambed, respectively, and sets up Case D for comparative research. Figure 11a shows the variation in non-absorbable solute concentration in the overlying water during the process of microbial dynamic growth clogging the streambed, where Case C does not consider the growth of anaerobic microorganisms in Layer 2, while Case D does. Considering the dynamic growth of anaerobic microorganisms in Layer 2 would reduce the hydraulic conductivity of Layer 2, which would normally slow down the entry of solutes into the streambed. However, it can be seen from Figure 11a that the concentration curves of Case C and Case D almost overlap, indicating that non-absorbable solutes first enter Layer 1, and the resistance to the solute entry process caused by the clogging of Layer 2 is not very significant. This suggests that structural changes in the deep streambed (Layer 2) have little impact on the hyporheic exchange process at Surface 1. Combined with Table 2, it can be seen that if Layer 2 is considered as a growth zone for anaerobic microorganisms, T increases by 1.47%, indicating that the clogging caused by anaerobic microorganisms in Layer 2 would slow down the penetration time of solutes in Layer 1.

To investigate how the dynamic growth of anaerobic microorganisms in Layer 2 affects the solute penetration time, this study sets up multiple working conditions for analysis (Figure 11b). The impact of anaerobic microorganisms on hydraulic conductivity differs from that of aerobic microorganisms, and their clogging growth process may lead to a rapid decrease in hydraulic conductivity [39]. To analyze the influence of different variation processes of hydraulic conductivity in the streambed on the solute penetration time, this paper introduces the variable S*, which represents the multiple of the rate at which hydraulic conductivity decreases, i.e., the multiple of p₁ in Equation (6). If S* = 1, it means that the hydraulic conductivity in Layer 1 and Layer 2 decreases at the same rate, i.e., Case D; if S* = 0, it means that the hydraulic conductivity in Layer 2 remains unchanged, i.e., Case C. It can be seen from Figure 11b that S* is positively correlated with T. When S* < 1, the overall change in T is relatively slow, with a variation amplitude of about 1%. When S* > 1, the increase in T is more obvious. In particular, when S* = 100, T = 4.431d, with an increase of 10.94%. This indicates that a significant growth of anaerobic bacteria in Layer 2 would obviously affect the penetration time of solutes in the streambed.

3.5. The Limitations and Future Perspectives

This study provides insights into biofilm-induced dynamic layered clogging and its impacts on hyporheic exchange, but several limitations should be acknowledged, and future work can be expanded in the following directions:

(1)

Model Dimension and the Structure of Streambed

This study uses a two-dimensional (2D) model to simulate a single triangular bedform, failing to fully reflect the three-dimensional (3D) heterogeneity of natural streambeds. In real rivers, lateral undulations of the streambed, spatial variations in sediment particle distribution, and pore structures formed by bioturbation all significantly affect the spatial pattern of hyporheic exchange, which cannot be captured by 2D models [41]. In terms of the Future Improvement, a 3D coupled model should be developed, integrating realistic streambed morphologies (e.g., meanders, riffle-pool sequences) and layered sediment characteristics [42]. This model will simulate the non-uniform distribution of biofilm clogging in lateral and vertical directions, enabling more accurate predictions of dynamic hyporheic exchange in complex streambeds.

(2)

Improvement of Biofilm Systems

The biofilms are considered as a single physical clogging factor, ignoring the multi-species nature of natural biofilms. In actual hyporheic zones, biofilms consist of aerobic bacteria, anaerobic bacteria, and microalgae (e.g., diatoms), whose interactions (e.g., nutrient competition, oxygen transfer, and metabolic synergies) affect biofilm structure and clogging rates [43]. These biological interactions are not included in the current model. For future studies, the multi-species microbial dynamics should be integrated into the model, coupling metabolic processes of different species (e.g., aerobic respiration in surface biofilms and anaerobic denitrification in deep layers). Additionally, the regulation of biofilm growth by environmental factors (e.g., light, nutrients) should be considered to more realistically simulate biofilm-mediated clogging mechanisms.

4. Conclusions

This study systematically investigates the effects of biofilm-induced dynamic layered clogging on hyporheic exchange through a numerical modeling approach, yielding the following key conclusions:

(1)

Dynamic layered clogging significantly modulates hyporheic hydraulics: The total water flux entering the bio-layer decreases by 45.1%, and the flux penetrating to the deeper area (Layer 2) reduces by 28.6%. This flux reduction is attributed to progressive decreases in hydraulic conductivity (from 8.4 × 10⁻⁶ to 4.3 × 10⁻⁶ m/s) and porosity (from 0.40 to 0.34) induced by biofilm growth, which inhibits stream–streambed exchange processes.

(2)

Non-absorbable solute transport exhibits biphasic behavior: Initial rapid penetration (1.8 × 10⁻¹ cm/day over 30 days) transitions to slow diffusion (6.3×10⁻³ cm/day thereafter), driven by dynamic changes in bio-layer hydraulic properties. This temporal deceleration highlights the role of clogging in prolonging solute residence times in the hyporheic zone.

(3)

The penetration time of solute CMD correlates negatively with hydraulic conductivity under normal conditions, but this relationship reverses when hydraulic conductivity falls below a critical threshold (K* < 0.25). This reversal is attributed to the porosity-dependent increase in actual flow velocity (v = u/n), demonstrating the non-linear influence of clogging on subsurface transport.

(4)

The structural changes in the deep streambed (Layer 2) have little impact on hyporheic exchange at Surface 1, although anaerobic microbial clogging in Layer 2 slightly increases solute penetration time. The positive correlation between S* and penetration time shows that significant growth of anaerobic bacteria in Layer 2 (with S* > 1) would obviously affect the solute penetration time in the streambed.

These findings provide a theoretical framework for understanding the biofilm-clogging impacts on hyporheic exchange, with implications for river ecosystem protection. And this study holds potential applications in both academic research and environmental engineering technology. Academically, the established coupled model of biofilm dynamic clogging and hyporheic exchange can provide a theoretical framework for multi-scale simulations of biogeochemical processes in the hyporheic zone, facilitating a deeper understanding of material cycles (e.g., carbon and nitrogen transformation) and biotic interaction mechanisms in river ecosystems. In engineering applications, the results can guide river pollution control and ecological restoration practices, for instance, by predicting the impact of biofilm clogging on the migration and transformation of pollutants (e.g., nutrients, heavy metals) in the hyporheic zone to optimize pollution control strategies, or by providing parameter basis for artificially regulating streambed sediment structures to balance biofilm growth and hyporheic exchange efficiency, thereby enhancing river self-purification capacity and ecosystem stability.