Modeling Microplastic Dispersion in the Salado Estuary Using Computational Fluid Dynamics

Abstract

Microplastics (MPs) have emerged as a major pollutant in aquatic ecosystems, primarily originating from industrial activities and plastic waste degradation. Understanding their transport dynamics is crucial for assessing environmental risks and developing mitigation strategies. This study employs Computational Fluid Dynamics (CFD) simulations to model the trajectory of MPs in section B of the Salado Estuary in the city of Guayaquil, Ecuador, using ANSYS FLUENT 2024 R2. The transient behavior of Polyethylene Terephthalate (PET) particles was analyzed using the Volume of Fluid (VOF) multiphase model, k-omega SST turbulence model, and Discrete Phase Model (DPM) under a continuous flow regime. Spherical PET particles (5 mm diameter, 1340 kg/m³ density) were used to establish a simplified baseline scenario. Two water velocities, 0.5 m/s and 1.25 m/s, were selected based on typical flow rates reported in similar estuarine systems. Density contour analysis facilitated the modeling of the air-water interface, while particle trajectory analysis revealed that at 0.5 m/s, particles traveled 18–22.5 m before sedimentation, whereas at 1.25 m/s, they traveled 50–60 m before reaching the bottom. These findings demonstrate that higher flow velocities enhance MP transport distances before deposition, emphasizing the role of hydrodynamics in microplastic dispersion. While limited to one particle type and idealized conditions, this study underscores the potential of CFD as a predictive tool for assessing MP behavior in aquatic environments, contributing to improved pollution control and remediation efforts.

1. Introduction

Microplastics (MPs) are particles with a diameter of less than 5 mm [1]. Marine ecosystems are particularly vulnerable to pollution due to various human and industrial activities, such as the dumping of plastic waste into oceans, seas, and rivers [2,3]. Over time, exposure to the sun’s rays causes these plastics to fragment into smaller particles, called MPs [4].

MPs can be classified into two types according to their origin: primary and secondary [5]. Primary MPs are deliberately manufactured for specific uses, such as microspheres and granules [6,7]. These microplastics are incorporated into consumer products such as cosmetics, cleaning products, paints, and scrubs, as they replace natural ingredients, which are often more expensive [8]. In addition, pellets are used in the manufacture of larger plastics, used in processes such as molding and extrusion, to create plastic objects by melting them into specific molds [9].

Secondary MPs, on the other hand, are the result of the breakdown of larger plastics, which fragment into small particles due to exposure to environmental factors [10,11]. In some cases, they can also be generated through biological processes, as certain plastics can biodegrade by the action of bacteria and fungi [12]. The main sources of secondary MPs include common plastic waste such as bottles, bags, and packaging [13]. In less developed countries, natural disasters, such as tsunamis, hurricanes, and high tides, also contribute to pollution, as large amounts of waste can reach the sea [14].

The plastics most commonly found in MPs include materials such as polyethylene terephthalate (PET), polyester (PES), low-density polyethylene (LDPE), high-density polyethylene (HDPE), polyvinyl chloride (PVC), polypropylene (PP), polyamide (PA), polystyrene (PS), acrylonitrile-butadiene-styrene (ABS), and polytetrafluoroethylene (PTFE) [15].

PET is a thermoplastic polyester that has two characteristics [16]: it acts as an amorphous plastic when cooled rapidly, however, when it behaves as a semi-crystalline plastic it cools slowly [17]. It is classified as one of the most widely used plastic materials in the industry due to its excellent physical and chemical properties. It has a transparent color and is used in the manufacture of bottles, food packaging, or in the textile industry as a synthetic fiber [18,19].

In a previous investigation, several types of MPs were detected in a water distribution network, but PET was among the most common with a concentration of 0.0189 microplastics per liter (MPs/L) [20]. Analyses of different consumer products reveal the wide distribution of PET. First, PET was detected in drinking water processed in Germany along with other polymers, with concentrations of these particles ranging from 0.001 to 0.197 particles per liter [21], highlighting the contamination of drinking water, derived from filtered systems or pipes. Secondly, in plastic bottles of mineral water in Germany, higher concentrations of PET were found, with values ranging from 2649 ± 2857 particles per liter [22], suggesting that prolonged contact of the liquid with the container favors the release of microplastics. Finally, in the beers analyzed in Mexico, PET particles were identified in sizes from 100 to 3000 μm with a concentration of 152 ± 50.97 particles per liter [23].

Plastic pollution has emerged as a persistent threat to aquatic ecosystems, where its long-term accumulation disrupts ecological balance and threatens biodiversity. Among the most pervasive forms of this pollution are MPs, typically smaller than 5 mm, which are especially concerning due to their high mobility and potential for bioaccumulation. MPs are generated from a variety of sources, including the breakdown of larger plastic debris, textile fibers, and industrial emissions. The ability of these particles to infiltrate riverine, estuarine, and marine environments poses challenges for ecosystem resilience and resource management.

CFD was applied in [24] using the VOF coupled with the DPM model for tracking the spatial distribution of MPs and showing that the size of the particles and their density are determinants in their mobility. The project was carried out in a wetland environment subjected to stormwater conditions, through which it was analyzed how various variables of MPs influence the movement and dispersion of particles. The simulations were carried out in 200 s, using two velocities for water 0.1 m/s and 0.3 m/s, and constant air velocity 2.5 m/s. The simulations showed that particles of greater size and density in spherical shape tended to concentrate near the inlet zone when the water velocity was low, due to their limited mobility and rapid sedimentation. In contrast, smaller particles, having less inertia, remained in suspension longer and were transported farther.

In [25], the progressive degradation of PET in marine environments was found to begin approximately after 15 years of exposure. Through ATR-FTIR spectrometry characterization, researchers identified structural changes in the recovered bottles, including the loss of native functional groups and the appearance of new compounds, indicating chemical modifications induced by environmental factors. This study was conducted in the Ionian Sea and the Saronic Gulf, providing crucial information on the longevity of PET.

In [26], numerical simulations were performed to study the effects of different variables on the distribution of MPs in a coastal marine environment. VOF wave models and the First Airy wave model coupled with DPM were used. PET (Polyethylene Terephthalate), PU (Polyurethane), and PP (Polypropylene) particles were dumped from the coast to investigate the type, size, and shape of MPs under two ocean water flow rates and different temperature conditions.

Reference [27] describes the implementation of a two-dimensional numerical wave channel that simulates intermediate waves with a weak current in a coastal area to investigate the behaviors of MPs corresponding to parameters such as particle size (0.2, 1, and 5 mm), particle density (900, 1000, and 1100 kg/m³), and a submerged artificial structure.

In [28], CFD was used to analyze how different types of breakers influence the dispersion and accumulation of MPs in a coastal area. The importance of the interaction between inertia and viscosity in the advection of particles was highlighted, showing that smaller MPs can move more easily due to an optimal balance between forces. The research emphasizes the potential for future studies in three-dimensional environments and with more complex shapes of MPs, allowing a more complete analysis of their behavior in the ocean.

In [29], numerical modeling was used to investigate the transport and retention of MPs in a hyporheic zone. Simulations of 1 μm MP particles in a sandy riverbed showed that the advection-diffusion equation can appropriately represent MP transport at the pore scale. To corroborate the model’s applicability, the experiment was repeated with 10 μm particles, revealing delayed infiltration and transport. The model effectively represented both the transport and retention of MPs in the hyporheic zone.

In [30], a study titled “Numerical Prediction of the Short-Term Path of PM Particles in Laizhou Bay” analyzed the pathways of PM particles released from four river mouths adjacent to Laizhou Bay using the Boltzmann network method and the Lagrangian particle tracking method, which includes particle and particle-wall collisions. The trajectories of particles from the four river mouths were tracked over thirty days.

In [31], the accumulation of MPs in the sediments of a stormwater pond was analyzed. Thirteen sediment samples containing MPs up to 10 μm in size were examined, showing an average abundance of 11.8 μg/kg by mass and 44,383 items/kg by count. The particles were unevenly distributed, with variations up to two orders of magnitude within the pond. Floating MPs accounted for 95.4% of the total mass and 83.5% of the total number, with polypropylene predominating, followed by polyethylene. A CFD model simulated the transport of MPs from water to sediment, revealing that advection and dispersion were the main mechanisms and that a fraction of particles became trapped in the bed, reducing their presence in the water column.

Therefore, this study focuses on a segment of Section B of the Salado Stuary, located in the city of Guayaquil. This area was selected due to its high level of contamination, evidenced by the accumulation of solid waste in its mangroves, including plastic bags, PET bottles, disposable cups, and other polluting materials [5]. It has been proposed to simulate the trajectory of MPs in this sector using the ANSYS FLUENT 2024 R2 software.

For the simulation, data were collected that allowed the initial parameters to be established. Subsequently, the appropriate models to address the problem were defined, based on literature reviews that support the use of CFD as an effective tool to analyze the trajectory and dispersion of MPs in water bodies [26].

The Salado Estuary of Guayaquil is an ecosystem where pollution by MPs is evident, mainly due to the accumulation of plastic waste. “Pollution is one of the main evils that afflict the estuaries of Guayaquil, and every day in the branches of the Salado estuary, tubs, garbage bags, and plastic bottles accumulate” [32]. The constant presence of this waste favors the generation of MPs since over time plastics degrade due to exposure to solar radiation and the action of mechanical processes [33]. In addition, the presence of these pollutants can affect the biodiversity of the estuary, affecting the development, reproduction, and survival of marine species, which represents a risk to the food chain [34].

CFD is a methodology that allows the behavior of fluids within a system to be analyzed by solving equations for the conservation of mass, amount of motion, and energy. This analysis is carried out with the help of computers, whose technological development has allowed the simulation of these phenomena both in space and in time [35,36]. Due to its capabilities, CFD has become an effective and versatile tool to improve product quality, energy efficiency, and process design [37] Its ability to graphically represent the characteristics of the flow in two and three dimensions, as well as in real time, contributes to minimizing the costs and times associated with complex experimental trials [38].

In this sense, the importance of modeling the trajectory of MPs in an aquatic ecosystem is raised, specifically in a section of Section B of the Estero Salado. To do this, CFD will be used to understand its dynamics, obtaining density contours and particle trajectories under an average value of water velocity.

To simulate a multiphase fluid system, it is essential to define the geometry of the domain, which will be subjected to a meshing process. The discretization of space is a key step to accurately capture the behavior of the flow, requiring in some cases local refinements in areas of high complexity. Then, since it is a multiphase system, the appropriate set of equations is selected for modeling. Subsequently, the physical properties of the system are defined, and the boundary and initial conditions are established, considering possible symmetries and the influence of external sources. Finally, the equations are solved by segregated or coupled methods, depending on factors such as the flow velocity and whether the regime is transient or stationary [39].

In order to complement the CFD studies referenced above, this work focuses specifically on the dispersion of PET microplastics within an estuarine setting that has not yet been simulated using this approach. The primary objectives are: (1) to simulate the transport and sedimentation of PET microplastic particles using CFD tools, (2) to compare particle behavior under two different flow velocities, and (3) to assess the effect of hydrodynamic forces on particle trajectories. The methodology employs a three-dimensional CFD model based on the Volume of Fluid (VOF) approach and the Discrete Phase Model (DPM), coupled with the k-omega SST turbulence model.

The purpose of this research is to accurately simulate the path of PET MPs to evaluate their behavior and displacement in a water body of great ecological importance, such as the Salado Estuary, using CFD. The findings obtained will not only contribute to a better understanding of the distribution of these pollutants but will also provide fundamental information for the development of strategies aimed at the mitigation and conservation of this ecosystem. The selected area for this study corresponds to a segment of section B of the Salado Estuary as can be seen in Figure 1.

This study acknowledges certain model limitations, such as idealized boundary conditions and simplified particle geometry, but its novelty lies in applying a detailed CFD-based multiphase simulation to the Salado Estuary in Guayaquil—an ecologically important and pollution-impacted region. The results contribute new insights into how PET MPs behave under hydrodynamic forces specific to tropical estuarine conditions.

2. Numerical Modelling

2.1. Geometric Model and Boundary Conditions

The computational domain represents a 100 m × 70 m rectangular segment of Section B of the Salado Estuary in Guayaquil, selected due to its reported high plastic contamination and accessibility for future sampling [32]. This section provides a confined estuarine environment suitable for detailed particle behavior analysis. The geometry and meshing were developed using SpaceClaim and Meshing within ANSYS Workbench 2024 R2. The total domain depth was set to 12.64 m, comprising a 9.5 m water column and a 3.14 m air region above the free surface to capture interactions between the water and air phases as shown in Figure 2. A uniform bottom surface was assumed for simplification.

Boundary conditions were defined as follows: the inlet and outlet were set with uniform velocity and pressure outlet conditions, respectively, while the bottom and side walls were treated as no-slip boundaries to replicate realistic interaction with the channel surfaces, as shown in Figure 3. The air-water-free surface was modeled with a pressure outlet condition and treated using a kinematic constraint for the VOF interface. A flat bottom profile was assumed for simplification, and bottom slope effects were not included in this version of the model.

The velocity inlet conditions for water and air were applied as constant velocity boundaries. At the outlet, a gauge pressure of 0 Pa was set, ensuring atmospheric pressure at this boundary. To account for air-water interaction, surface tension effects were included with a constant coefficient of 0.072 N/m, corresponding to water at room temperature. Additionally, the “Continuum Surface Force” model was implemented to enhance the accuracy of the phase interface representation.

Table 1. Boundary conditions.

Type	Description
Velocity Inlet	Water and air inlet: water depth of 9.5 m with velocities of 0.25 m/s (Simulation A) and 1.25 m/s (Simulation B), volumetric fraction = 1. Air enters at 3.3 m/s with a height of 3.14 m.
Pression Outlet	Water and air outlet, 0 Pa gauge pressure.
Wall	No-slip condition applied to the bottom and sidewalls.

summarizes the boundary conditions. The decision to model constant inlet velocities (0.5 m/s and 1.25 m/s) and a steady air velocity (3.3 m/s) was made to establish a baseline for hydrodynamic influence on MP dispersion and supported by the literature [40,41,42]. While we acknowledge that estuarine environments are influenced by tidal, seasonal, and wind-driven fluctuations, constant flow conditions were chosen to isolate the effect of velocity magnitude on particle transport in a controlled, computationally feasible setup. Future work will incorporate transient boundary conditions reflecting tidal cycles and wind stresses to better emulate real-world variability.

2.2. Mesh Independence Analysis

After constructing the geometric model, the next step was mesh generation, which involves discretizing the geometry to accurately capture the physical phenomena in the simulation. To determine an optimal mesh, four different resolutions were tested, containing 105,536, 172,044, 207,328, and 300,300 cells. The meshes were generated using structured hexahedral cells with local refinement near the surface and particle injection regions. Cell dimensions varied from 0.2 mm to 1.5 mm, depending on the region of interest. This resolution ensures that the 5 mm PET particles are adequately resolved within the Lagrangian DPM framework, maintaining a ratio of at least 3–5 cells across each particle trajectory path.

A mesh independence test was performed using coarse, medium, and fine meshes, and the mesh with 207,328 tetrahedral cells and 222,500 nodes was selected for the final simulations as shown in Figure 4, as it provided a balance between accuracy and computational efficiency.

2.2.1. Control Variable

To evaluate mesh selection, water velocity was measured at the reference point (x: 35 m, y: 9.4 m, z: 0 m), as shown in Figure 5. The results are summarized in

Table 2. Water velocity at the reference point for different mesh resolutions.

Parameter	Velocity [m/s]
Mesh 1	4.270
Mesh 2	2.539
Mesh 3	2.542
Mesh 4	2.177

.

As shown in Figure 6, the water velocity at (x: 35 m, y: 9.4 m, z: 0 m) differs by only 0.073% between Mesh 2 and Mesh 3, indicating a negligible variation. In contrast, Mesh 1 and Mesh 4 exhibit more significant deviations from these values.

2.2.2. Overall Quality

The quality of the element of the four generated meshes was studied, and the results are summarized in

Table 3. Mesh quality parameters for different mesh resolutions.

	Element Quality	Aspect Ratio	Obliquity	Orthogonal Quality
Mesh 1	0.65522	2.452	0.029495	0.9973
Mesh 2	0.65404	2.4633	0.018038	0.99946
Mesh 3	0.66812	2.4038	0.0013479	0.99948
Mesh 4	0.66207	2.4318	0.0063195	0.9999

:

The evaluation of the four generated meshes indicates that Mesh 3 is the most balanced and highest-quality option. It exhibits the highest element quality value (0.66812), signifying a more uniform geometry well-suited for numerical simulations. Additionally, it has the lowest aspect ratio (2.4038), meaning its elements are closer to the ideal shape, reducing potential numerical errors.

The obliquity, which quantifies the angular deviation of elements, is also minimal in Mesh 3 (0.0013479), further confirming its suitability for fluid dynamics calculations. While Mesh 4 achieves the highest orthogonal quality (0.9999)—an important factor for computational accuracy—its other parameters do not perform as well as those of Mesh 3. Given that element quality, aspect ratio, and obliquity are crucial for minimizing discretization errors and ensuring numerical stability, Mesh 3 presents the best overall balance.

Furthermore, these values align with the mesh quality criteria established in [43], reinforcing the robustness of the selected mesh.

2.3. SST Kω Turbulence Model

For the simulations, the k-omega shear stress transport (SST) turbulence model was employed, as it is particularly well-suited for Volume of Fluid (VOF) applications. This model is recognized for its ability to dampen turbulence in interfacial cells, which is crucial for accurately capturing interfacial instabilities [26].

In contrast, the k-ε turbulence model is widely used in engineering due to its robustness and computational efficiency, making it ideal for fully turbulent flows and industrial heat transfer simulations. However, it assumes that molecular viscosity effects are negligible, which limits its accuracy in cases involving adverse pressure gradients or flow separation phenomena. The SST k-ω model overcomes these limitations by combining the high boundary layer accuracy of the k-ω model near walls with the free-stream independence of the k-ε model in the far field.

Originally developed by [44], the SST k-ω model integrates several improvements. One of its key enhancements is the incorporation of a damped cross-diffusion term in the ω equation, which refines the prediction of turbulent viscosity. Additionally, it modifies the definition of turbulent viscosity to enhance the representation of shear stress transport, improving the model’s ability to capture complex flow dynamics. The model also includes adjusted modeling constants, ensuring greater accuracy across a wider range of flow conditions.

These improvements make the SST k-ω model significantly more reliable for simulations involving adverse pressure gradients, airfoils, and transonic shock waves, where the standard k-ω model often falls short. Given its ability to balance accuracy near solid boundaries with stability in free-stream regions, the SST k-ω model is an optimal choice for this study.

This model is based on a two-equation system [45], where Equation (1) governs the turbulent kinetic energy (k) and Equation (2) describes the specific turbulence dissipation rate (ω):

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(U_i\rho k\right)={\displaystyle \frac{\partial }{\partial x_j}}\left(\left(\mu +{\sigma }_k{\mu }_t\right){\displaystyle \frac{\partial }{\partial x_j}}k\right)+\widetilde{P_k}-{\beta }^{*}\rho \omega k,$$

(1)

$$\begin{array}{c}{\displaystyle \frac{\partial }{\partial t}}\left(\rho \mathsf{\omega }\right)+{\displaystyle \frac{\partial }{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left(\left(\mu +{\sigma }_{\mathsf{\omega }}{\mu }_t\right){\displaystyle \frac{\partial }{\partial x_j}}\mathsf{\omega }\right)+{\displaystyle \frac{\rho \gamma }{{\mu }_t}}{S}^2-\beta \rho {\omega }^2\\ +2\rho \left(1-F_1\right){\displaystyle \frac{1}{\omega }}{\displaystyle \frac{1}{\sigma \omega ,2}}{\displaystyle \frac{\partial }{\partial x_j}}k{\displaystyle \frac{\partial }{\partial x_j}}\omega ,\end{array}$$

(2)

2.4. Volume of Fluid Model

It is a numerical method used by CFD to solve problems involving the interaction between fluids, such as air and water. Its main objective is to analyze the volume fraction of fluid within a computational cell.

The volume fraction is represented by α, where a value of 0 indicates the absence of primary fluid in the cell, while a value of 1 indicates its presence [28].

The VOF model is based on the conservation of momentum and continuity, which are described by the Navier-Stokes equations (Equations (3) and (4)).

2.4.1. Navier-Stokes Equations

The Navier–Stokes equations are a set of mathematical expressions that describe the behavior of a Newtonian fluid, derived from the conservation principles of mechanics and thermodynamics applied to a fluid volume. In Computational Fluid Dynamics (CFD), these equations are solved numerically using computer-based methods. While a simplified one-dimensional form of the Navier–Stokes equation is presented for illustrative purposes in this study, the full three-dimensional equations were implemented in the CFD solver to simulate the fluid flow accurately.

The Navier–Stokes equations used to analyze the motion of a fluid are [46]:

• Continuity equation

$${\displaystyle \frac{\partial \mathsf{\rho }}{\partial \mathrm{t}}}+\nabla \ast \left(\mathsf{\rho }\overrightarrow{\mathrm{v}}\right)=0$$

(3)

where:

ρ = Fluid Density

$\overrightarrow{v}$ = Fluid velocity vector

∇ = Vector differential operator ${\displaystyle \frac{\partial }{\partial x}}i+{\displaystyle \frac{\partial }{\partial y}}j+{\displaystyle \frac{\partial }{\partial z}}k$

• Momentum equation

$$\rho {\displaystyle \frac{D\overrightarrow{v}}{Dt}}=\nabla {\mathsf{\tau }}_{ij}-\nabla \rho +\rho F$$

(4)

${\mathsf{\tau }}_{ij}$ = Viscous stress tensor

F = Force

2.4.2. Open Channel Flow

These flows are known as free-surface flows, as their surface is in direct contact with the atmosphere (e.g., rivers, seas, estuaries, and dams) [47]. They differ from flows in closed pipes due to the influence of pressure; In the case of an open channel, the free surface maintains the same pressure as the atmosphere.

In ANSYS software 2024 R2 it is possible to simulate flows in open channels using the VOF method together with the boundary conditions of the free surface [48] This type of model is defined by the Froude number (Equation (5)), a dimensionless parameter that relates the inertial force to the hydrostatic force.

Froude’s number equation is expressed as:

$$F_r={\displaystyle \frac{V}{\sqrt{gy}}}$$

(5)

where V represents velocity, g is the acceleration due to gravity, and length refers to the depth of the body of water being considered. From this equation, the velocity of the wave can also be calculated, which is defined by:

$$V_w=V\pm \sqrt{gy}$$

(6)

Flows in open channels are classified according to the number of Froude. Yes $F_r$ < 1, flow is considered subcritical; yes $F_r$ = 1, it is considered critical; what if $F_r$ > 1, The flow is supercritical.

In open-channel flows, there are two key factors in establishing the initial flow conditions:

• Pressure inlet
• Mass Flow rate

The pressure input is given by the following equation:

$$P_0=q+P_s$$

(7)

where:

q is dynamic pressure and is as follows $q={\displaystyle \frac{\rho -{\rho }_0}{2}}{V}^2$ (V, ρ, velocity and density respectively).

$P_s$ is the static pressure and is given as follows $P_s=(\rho -{\rho }_0)|\overrightarrow{g}|(\widehat{g}\ast (\overrightarrow{b}-\overrightarrow{a}))$ ($|\overrightarrow{g}|$, Gravity Unit Vector).

The mass flow rate for channel-to-open flows is represented by the following equation:

$$\dot{m}=\rho \ast Q$$

(8)

where:

ρ is the density and Q the Volumetric flow rate.

Boundary conditions of waves in open channels.

2.4.3. Airy Wave Model

The height of the waves (H) is determined as follows:

$$H=2A=A_t+A_c$$

(9)

where A indicates the amplitude of the wave, At is the amplitude at the minimum point and Ac is the amplitude of the wave at the maximum point.

The wave number k is:

$$k={\displaystyle \frac{2\pi }{\lambda }}$$

(10)

The vector wave number $\overrightarrow{k}$ is determined from the following equation:

$$\overrightarrow{k}=k_x\widehat{X}+k_y\widehat{Y}$$

where $\widehat{X}$ is the direction of propagation of the reference wave, $\widehat{Z}$ opposite direction to gravity, $\widehat{Y}$ indicates the normal direction between $\widehat{X}$ and $\widehat{Z}$.

Application of wave theory.

To choose the right wave, the following parameters must be followed:

Verification of the total wave regime within the wave break limit.

The relationship between the height of the wave and the depth of the water within the limit of rupture of the wave is established as:

$${\left[{\displaystyle \frac{H}{h}}\right]}_{max}=0.78$$

(11)

The relationship between the wave height and the depth of the wavelength within the breaking limit is established as:

$${\left[{\displaystyle \frac{H}{\lambda }}\right]}_{max}=0.142$$

(12)

The criterion based on wave theory considers the limit of stability and the breaking of the waves.

Linear waves are described by Airy’s wave theory, in which the equations are expressed as follows:

For shallow water, the ratio of wave height to depth to wavelength is set as:

$${\left[{\displaystyle \frac{H}{\lambda }}\right]}_{max}=0.085$$

(13)

To check the inclination of the waves, the following equation is established:

$${\left[{\displaystyle \frac{H}{\lambda }}\right]}_{max}=0.02tanh\left(2\pi {\displaystyle \frac{h}{\lambda }}\right)$$

(14)

The equation for checking the relative height of the waves is set as:

$${\left[{\displaystyle \frac{H}{h}}\right]}_{max}=0.1$$

(15)

The Ursell number is defined as:

$$Ur={\displaystyle \frac{H{\lambda }^2}{h^3}}$$

(16)

The stability criterion of the Ursell number for a linear wave is set as follows:

$${\left(Ur\right)}_{max}={\displaystyle \frac{32{\pi }^2}{3}}$$

(17)

2.5. Discrete Phase Model

The discrete phase model follows the Euler-Lagrange approach [49] in this method the fluid phase is considered continuous and its resolution is by the Navier-Stoke equations [50], while the discrete phase is solved by tracing the particles. This model is applied in multiphase simulations where it is desired to analyze the particle path or the interaction between phases.

PET particles were defined as shown in

Table 4. Properties of the MP particles used in the simulation.

Microplastic	$\mathbf{Density}[\mathbf{kg}/{\mathbf{m}}^3$]	Size [mm]
Polyethylene Terephthalate (PET)	1340	5

:

The PET particles were injected at two closely spaced locations within the simulation domain, specifically at X = 35 m (Injection 1) and X = 34 m (Injection 2), while maintaining the same coordinates in Y = 9.5 m and Z = 100 m. The injection velocity was set to −0.001 m/s in the Z direction, indicating a downward motion.

Each injection had a flow rate of 0.1 kg/s and a total duration of 450 s. The PET particle size was set to 5 mm, as this represents the maximum size-defining microplastics (MPs) [51]. The injections followed a single-type configuration and were introduced at two distinct points along the X-axis, allowing for a detailed evaluation of the particle trajectory from the inlet to the exit point at the water surface.

Governing Equations in the DPM Model

• Balance of forces between particles

The balance of forces equalizes the inertia of particles with the forces acting on it, and is posed as follows:

$$m_p{\displaystyle \frac{d{\overrightarrow{u}}_p}{dt}}=m_p{\displaystyle \frac{\overrightarrow{u}-{\overrightarrow{u}}_p}{{\tau }_r}}+m_p{\displaystyle \frac{\overrightarrow{g}({\rho }_p-\rho )}{{\rho }_p}}+\overrightarrow{F}$$

(18)

where $m_p$ is the particle mass, $\overrightarrow{u}$ is the phase velocity of the fluid, ${\overrightarrow{u}}_p$ is the particle velocity, ${\tau }_r$ is the particle relaxation time, ρ is the fluid density, ${\rho }_p$ is the particle density, $\overrightarrow{F}$ is an additional force.

• Discrete Random Walk (DRW) Model

The DRW model, also known as the eddy lifetime model, represents the interaction of particles with a series of discrete turbulent eddies idealized within the fluid phase [52]. Each eddy is characterized by a random velocity fluctuation, distributed in a Gaussian manner, and represented in the three spatial directions as u′, v′, and w′. This variability in velocity reflects the chaotic nature of turbulent flow. Additionally, the model incorporates the eddy time scale (τ_e), which determines the duration for which a particle remains trapped within an eddy before transitioning to a new one, influencing its trajectory within the turbulent flow.

The values of u′, v′, and w′ that prevail during the lifetime of the turbulent eddy are sampled assuming that they obey a Gaussian probability distribution, establishing as follows:

$$u^{\prime }=\zeta \sqrt{\overline{u^{\prime 2}}}$$

(19)

where ζ represents a random number with a normal distribution, and the rest of the expression on the right side corresponds to the local RMS value of the variations in velocity.

Since the turbulent kinetic energy is known at each point of the flow, it is possible to determine the values of the fluctuating RMS components, assuming that the flow is isotropic, by the following relationship:

$$\sqrt{\overline{u^{\prime 2}}}=\sqrt{\overline{v^{\prime 2}}}=\sqrt{\overline{w^{\prime 2}}}=\sqrt{2k/3}$$

(20)

For the model k-ε, the model k-ω and their variants. When the simple linear regression model is used, the non-isotropy of the stresses is included in the derivation of the velocity fluctuations.

The characteristic duration of the eddy is defined as a constant:

$${\tau }_e=2T_L$$

(21)

where $T_L$ is the integral time.

$${\tau }_e=-T_{L}ln\left(r\right)$$

(22)

$r$ is the random number greater than 0 and less than 1. The random calculation option of ${\tau }_e$ produces a more realistic description of the correlation function.

The particle swirl crossing time is defined as:

$$t_{cross}=-\tau ln\left[1-\left({\displaystyle \frac{L_e}{\tau \left|u-u_p\right|}}\right)\right]$$

(23)

where $\tau$ is the particle’s relaxation time, $L_e$ is the length scale of the eddy and $\left|u-u_p\right|$ is the magnitude of the relative velocity.

• Saffman’s Lift Force

In an investigation on the behavior of a small sphere immersed in a slow-shear flow, it was possible to describe how a moving sphere within a viscous fluid with velocity gradients experiences a lift force oriented perpendicular to the direction of the flow [53].

The mathematical expression that defines Saffman’s lifting force is presented as follows:

$$\overrightarrow{F}=m_p{\displaystyle \frac{2K{v}^{\frac{1}{2}}\rho d_{ij}}{{\rho }_p{d}_p{\left(d_{lk}\ast d_{kl}\right)}^{\frac{1}{4}}}}(\overrightarrow{u}-\overrightarrow{u}p)$$

(24)

where K = 2.594 and $d_{ij}$ is the strain tensor. This lift force is based on small Reynolds numbers.

The study area exhibits a stable flow with minimal turbulence, which facilitates the definition of initial simulation parameters such as water velocity, wave amplitude, wavelength, water depth, and air velocity, in accordance with previous studies [40,41,42]. Furthermore, the stability of the water indicates the absence of strong currents or significant wind interactions, ensuring consistent flow conditions for the analysis.

• Wave height: 0.01 m
• Wave length: 50 m
• Water depth: 9.5 m
• Water velocity: Simulation A: 0.5 m/s–Simulation B: 1.25 m/s
• Air velocity: 3.3 m/s

2.6. Computational Method

The numerical calculations were performed using Ansys Fluent 2024 R2. The simulation employed standard initialization, starting from the domain inlet. This approach was chosen because flow velocity, pressure, and temperature remain constant throughout the domain. The flat open channel initialization model was applied, as it enhances simulation accuracy in cases where velocity variations are negligible. Additionally, the volumetric fraction was set to 1 at the start, reflecting the presence of fluid in the channel from the beginning.

The simulation ran for 1000 iterations, with a time step of 0.5 s and a maximum of 10 iterations per time step, resulting in a total simulated time of 500 s. This duration was sufficient to track the trajectory of particles in the open channel flow. However, due to the complexity of the 3D simulation, the computational time averaged 14 h, significantly increasing the computational cost.

Although the Courant-Friedrichs-Lewy (CFL) number is primarily relevant for explicit methods, it can still serve as a reference for evaluating temporal behavior in implicit simulations. In this case, the CFL number did not significantly impact numerical stability, as implicit methods allow for larger time steps without substantial accuracy loss.

To ensure result accuracy, convergence criteria were established based on the residual values of the simulation. Convergence was considered achieved when residuals dropped below 10⁻⁴, indicating that the system had reached a stable and precise solution. This threshold ensured minimal variation between iterations, providing reliable results aligned with the study’s objectives.

3. Results

Two simulations were conducted to analyze particle dispersion under distinct flow conditions representative of those observed in estuarine environments. Simulation A used a water inlet velocity of 0.5 m/s, and Simulation B applied a higher inlet velocity of 1.25 m/s. These values were selected based on previously reported hydrodynamic data for similar tropical estuaries [40,41]. This approach enabled an evaluation of how variations in flow magnitude influence microplastic transport and sedimentation dynamics.

3.1. Water Velocity Streamlines, Simulation A

Figure 7 illustrates the velocity streamlines in the open channel over time, with a color scale representing speed in meters per second. Darker shades indicate higher velocities (10.83 m/s), while lighter shades correspond to lower velocities (0 m/s).

At 0 s (Figure 7a), the flow appears uniform and parallel, with no visible disturbances, indicating that the simulation begins under homogeneous conditions without significant phase interactions. By 100 s (Figure 7b), the streamlines maintain a similar pattern, though minor fluctuations start to emerge, possibly due to phase interactions or slight particle dispersion if considered in the study.

At 300 s (Figure 7c), the flow remains largely uniform, but subtle changes in velocity distribution suggest that particles, if present, may begin to move more noticeably or settle. By 500 s (Figure 7d), the flow pattern is more developed, with potential variations in particle velocity and distribution, influenced by fluid viscosity, emerging turbulence, or sedimentation.

Overall, the analysis confirms that the flow remains stable throughout the domain, with no significant eddies or abrupt disturbances.

These results confirm the accuracy of the simulation in representing the expected behavior of the phases under the given conditions, demonstrating a successful numerical reproduction of open-channel flow stability. However, the lack of turbulence or shear effects limits the ability to model more complex dispersion mechanisms. Future simulations should incorporate transient and tidal components to better reflect real estuarine dynamics.

3.2. Water Velocity Streamlines, Simulation B

Figure 8 illustrates the flow evolution considering a water inlet velocity of 1.25 m/s. The highest velocities, around 4.16 m/s, are shown in dark tones, while the lowest, near 0 m/s, appear in lighter shades.

At the initial time step (Figure 8a), the flow is uniform and well-aligned, indicating homogeneous initial conditions with no significant phase interactions. By the second stage (Figure 8b), minor variations in the streamlines emerge, potentially due to phase interactions or the initial stages of particle dispersion, if applicable.

In Figure 8c, the flow remains predominantly stable, though slight changes in velocity distribution suggest gradual particle displacement or the onset of sedimentation. By the final stage (Figure 8d), more noticeable modifications in the flow pattern appear, including velocity variations and possible turbulence or sedimentation effects influenced by fluid viscosity.

Overall, the flow remains stable within the simulation domain, with no abrupt disturbances or large eddy formations. These results validate the accuracy of Simulation B in capturing the expected fluid phase behavior under higher flow conditions, confirming the model’s ability to reproduce stable open-channel flow at elevated velocities. Nonetheless, the absence of transient features, turbulence fluctuations, or shear layers limits the representation of more complex dispersion phenomena. To enhance realism, future simulations should incorporate tidal variability, unsteady flow conditions, and enhanced turbulence modeling.

3.3. Density Contours

Throughout the simulated time intervals, the interface between water and air remains stable and uniform across the entire computational domain. Figure 9a–c illustrates this consistency, with a clear distinction between the two phases. The density scale highlights these differences, where blue tones represent higher-density regions corresponding to water, while red tones indicate lower-density areas associated with air.

The flow behavior aligns with the characteristics of a calm, open-channel system, with minimal disturbances and velocity fluctuations in both phases. This stability reinforces the accuracy of the simulation in capturing the intended hydrodynamic behavior, serving as a successful numerical validation of open-channel flow under idealized estuarine conditions.

3.4. Pressure Contours

Figure 10 illustrates the pressure stability characteristics of estuaries and open channels. Across the entire domain, air pressure remains constant until it reaches the liquid’s bottom, where the highest pressure values are recorded. This pressure distribution remains consistent in all analyzed instances, specifically at 0 s, 100 s, 300 s, and 500 s.

Although visual differences between time steps may appear minimal, this uniformity is an anticipated outcome given the steady flow regime applied in the model. The simulation’s ability to maintain pressure stability over time confirms the accuracy and reliability of the numerical setup for modeling quiescent hydrodynamic conditions in estuarine systems.

3.5. Air-Water Interface

Figure 11 shows the isosurface of volume fraction at 500 s, revealing a generally stable air-water interface throughout the domain. The dominant blue coloration indicates a predominance of the aqueous phase, confirming that the interface lies just below the surface and corresponds to a typical estuarine stratification. The volume fraction in the central interface region remains close to 0.5, consistent with the expected transition zone between air and water in multiphase VOF simulations. Minor surface disturbances, particularly near the lateral boundaries, are attributed to Kelvin–Helmholtz instabilities arising from velocity shear at the interface. These low-amplitude fluctuations, with vertical displacements not exceeding 1 cm, are characteristic of shallow wave formation in low-turbulence environments. Overall, the interface maintains a thickness of approximately 3–5 mm and reflects a stable flow regime representative of salt estuary conditions under steady inflow conditions.

3.6. Particle Dispersal

Likewise, two simulations were carried out with a change in velocity, Simulation A was performed with a water inlet velocity of 0.5 m/s, while Simulation B used a higher inlet velocity of 1.25 m/s. The following results were obtained:

3.6.1. Particle Dispersal for Water Inlet Velocity of 0.5 m/s

In the analysis of PET particle tracking during Simulation A, the particles exhibit distinct behavior throughout the process. Initially, as shown in Figure 12a–c, the injection begins and the particles follow a linear trajectory, indicating that they fall into the water shortly after injection. As observed in Figure 12d, the particles reach the bottom of the computational domain and continue to move along the bottom surface, influenced by drag forces.

Figure 12e shows that the particles maintain the same trajectory, progressing toward the end of the domain. By Figure 12f, the particles exit the computational domain, signaling the completion of the tracking process at approximately 175 s.

In the subsequent time steps, the particles continue along their established path without significant deviations. By Figure 12g, it is evident that the particle injection process is complete, as the predefined injection time of 450 s has elapsed. Finally, in Figure 12h, the particles continue to move within the domain, consistently guided by drag forces, indicating the persistence of the flow dynamics over time.

In the analysis of Simulation A, as shown in Figure 13, the particle trajectories exhibit minimal variation across the different evaluated scenarios. This indicates that the flow velocity remains consistent, maintaining predictable behavior throughout the domain. The particles follow an inclined path from the injection point, gradually descending due to gravity until they settle at the bottom of the domain. They reach a depth between 18 and 22.5 m along the z-direction, suggesting that the sedimentation process is gradual and steady under the defined conditions. The time required for the PET particles to travel the entire length of the domain is approximately 200 s, further supporting the notion of a stable flow velocity that remains constant over both time and space. This indicates a controlled flow pattern with no significant fluctuations.

The uniformity in the particle trajectories suggests the absence of significant turbulence or unexpected phase interactions, pointing to a stable multiphase flow in controlled equilibrium.

3.6.2. Particle Dispersal for Water Inlet Velocity of 1.25 m/s

Figure 14a,b illustrate the initial stages of PET particle tracking in Simulation B, viewed isometrically. Shortly after injection, the particles enter the water and begin to drift. In Figure 14c, the particles reach the bottom of the computational domain at approximately half of their length. As shown in Figure 14d, they continue to advance through the domain, driven by drag forces. Figure 14e demonstrates that the PET particles reach the end of the domain after 100 s.

In the subsequent time steps, the particles maintain their motion with no significant changes. By Figure 14f, the completion of particle injection is confirmed, as the injection time was set at 450 s. Finally, Figure 14g shows a decrease in the number of particles within the domain, which is attributed to their velocity.

Figure 15 shows the evolution of the PET particle trajectories in simulation B, from their injection into the water body at a depth of approximately 9.5 m. As the particles move through the domain, they exhibit a steady, gradual descent until reaching the bottom of the computational domain, which occurs between 50 and 60 m along the z-axis. This continuous descent pattern suggests a progressive sedimentation process, with no abrupt changes or irregular deviations in the particle trajectories. The observed stability can be attributed to the conditions within the estuary, where turbulence is minimal, fostering a stable flow environment. The low turbulence allows the particles to maintain a consistent motion, unaffected by random forces that might otherwise disrupt their paths.

Regarding the transit time, it is estimated that a PET particle takes approximately 80 s to travel 100 m along the domain. This time is consistent with a controlled flow, where the particles maintain a constant velocity from injection to exit. The combination of the gradual descent and consistent travel time further supports the idea of a flow environment with low dynamic complexity.

4. Discussion

4.1. Influence of Water Velocity on Particle Dispersal

This section begins with an acknowledgment of key model limitations. First, the exclusive use of spherical PET particles does not reflect the diversity of microplastics found in natural estuarine systems, which include a range of sizes, shapes, and polymer densities. This was a deliberate simplification to focus on hydrodynamic behavior under idealized conditions. Second, the simulations used a fixed continuous flow regime, which does not capture the tidal fluctuations typical of estuarine environments. Third, environmental factors such as temperature gradients, salinity stratification, and sediment interactions were not included but are recognized as relevant for future extensions of this work.

Although validation using field or experimental data was outside the scope of this initial numerical study, it remains a critical step to corroborate the model’s predictive accuracy. We recommend techniques such as sediment traps, in-situ particle sampling, or dye tracing to validate flow behavior and microplastic deposition. These tools will support the calibration of CFD models and improve their ecological relevance.

A comparison of Simulations A and B reveals key differences in the behavior of PET particles in the Salado Estuary, particularly in terms of sedimentation distances and particle trajectories. These differences highlight the influence of flow conditions and domain properties on particle behavior.

In simulation A (Figure 13), PET particles settle at the bottom of the estuary between 18 and 22.5 m from their injection point. In contrast, in Simulation B (Figure 15), particles reach the bottom between 50 and 60 m along the longitudinal axis of the estuary. This difference suggests that horizontal transport plays a more significant role in Simulation B, allowing particles to travel a greater distance before settling. This is attributed to the higher water flow velocity in Simulation B.

Despite these differences in sedimentation distances, both simulations show uniform particle trajectories with minimal variations, owing to the low turbulence in the estuary. The stable flow conditions facilitate controlled particle transport, ensuring that the particles follow a predictable path from injection to bottom sedimentation.

Regarding domain exit time, a PET particle in Simulation A takes approximately 200 s to exit the domain, whereas in Simulation B, it takes just 80 s. This difference supports the hypothesis that higher water velocities accelerate the transport of MPs, reducing their residence time in the aquatic environment and potentially influencing their accumulation further from the emission point.

A Pearson correlation analysis was conducted to assess the relationship between water velocity and the distance traveled by MPs before reaching the domain’s bottom. The analysis reveals a strong positive correlation (r = 0.97) [54], indicating that as water velocity increases, MPs travel greater distances before settling.

To visually support the comparative findings of this study,

Table 5. Summary of sedimentation distances based on flow velocity.

Simulation	Flow Velocity [m/s]	Distance [m]
A	0.50	18.0–22.5
B	1.25	50.0–60.0

has been added to summarize the sedimentation distances observed under the two simulated flow velocities. This table illustrates how increased velocity leads to extended horizontal transport of PET particles before settling.

These results highlight the hydrodynamic influence on microplastic transport and provide a clear illustration of the velocity-dependence of PET particle dispersal.

Furthermore, findings specific to PET should not be extrapolated to all MPs. Due to PET’s density (1340 kg/m³) and spherical shape, it exhibits distinct behavior in flow. Other polymers such as polypropylene (PP) or polyethylene (PE), which are lighter, would remain buoyant under similar conditions. This specificity must be considered when interpreting the results.

These findings emphasize the need for further studies that consider factors such as variations in MP density, interactions with biofilms, and degradation processes, all of which could significantly affect MP behavior in the aquatic environment. Additionally, future research could focus on more complex turbulence models and experimental validations under real-world conditions to better represent these dynamics.

4.2. Comparison with Previous Studies

The results of the present research can be compared to similar studies involving simulations and experimental measurements of particle dispersion in aquatic systems. Previous research has shown that particle dispersion is influenced not only by the water flow velocity but also by dynamic conditions such as waves, eddy formation, wind-induced turbulence, and interactions with natural or man-made structures.

In [27], it was emphasized that the physical properties of particles, including size and density, significantly affect their dispersion in the presence of artificial structures. Small particles (0.2 mm) exhibit high dispersion due to vertical mixing, while larger, denser particles tend to sink rapidly without being suspended. In contrast to their findings, the present study shows that the particles maintain a uniform flow pattern, with limited interaction between particles and the flow, due to the absence of velocity gradients generated by structures.

Reference [28] investigated the effects of different types of coastal breaks on the behavior of MPs. Lighter particles experience forward advection in the surface layer, while neutral and heavier particles move toward the bottom or inshore, influenced by larger wave sizes than those considered in the present study. In contrast, the present simulation does not account for such variations in size and density, as dynamic conditions such as waves or undertows are not included.

In [26], the impact of water velocity, particle size, and density on the distribution of particulate matter in coastal environments was analyzed. Their findings show that PET particles tend to settle on the bottom in low-velocity waters, similar to the behavior observed in the current study, where PET particles travel along the domain before reaching the estuary’s bottom. Denser particles, like PET and PU, tend to sink in slow-moving water, while lighter particles, such as PP, remain at the surface and are transported to shore. It was also noted that as water velocity increases, lighter particles travel greater distances, underscoring the importance of velocity in dispersion.

In [24], it was observed that water velocity directly influences the moment particles reach the bottom of the domain. At velocities of 0.1 m/s and 0.3 m/s, larger and denser particles tend to settle near the entrance, while smaller particles remain suspended longer and are transported further. In contrast, the present study, with water velocities of 0.5 m/s and 1.25 m/s in the Estero Salado, shows that MPs travel greater distances before settling. This indicates that in bodies of water with minimal wave activity, increased water velocity results in longer transport distances before deposition. These differences can be attributed to the specific hydrodynamic conditions and the nature of the water body studied, emphasizing the importance of considering environmental characteristics when analyzing MP dispersion.

The current simulations provide a controlled environment that allows for the observation of basic patterns in MP transport and sedimentation. In contrast, the studies reviewed incorporate additional factors such as artificial structures, waves, and velocity variations, leading to more dynamic and diverse particle behaviors. This research complements the present analysis by offering a broader perspective on the processes influencing the dispersion and accumulation of MPs in different aquatic environments.

5. Conclusions

The literature review provided valuable insights into how key characteristics of MP particles, such as size and density, influence their transport and sedimentation in aquatic environments. This understanding was essential for configuring and analyzing the simulations conducted in the study.

Based on this theoretical framework, the geometry and meshing of Section B of the Salado Estuary were designed, reflecting its specific conditions, including a depth of 9.5 m, a length of 100 m, and a width of 70 m.

During the simulation analysis, density contours and particle trajectories were employed to visualize the distribution and movement of PET particles throughout the flow. Density contours helped identify particle concentrations in various areas, while particle traces illustrated individual movements, facilitating a better understanding of MP dispersion and deposition within the estuary.

The primary factor influencing the simulation results was the water inflow velocity. As the velocity increased, particles traveled greater distances from the injection point before settling, delaying sedimentation. In Simulation A, with lower flow velocity, particles descended more quickly due to reduced horizontal drag forces. In contrast, Simulation B, with a higher flow velocity, demonstrated more dominant horizontal transport, which slowed sedimentation. This highlights the critical role of water velocity in the transport and distribution of MPs in the Salado Estuary.

This study is limited by the uniformity of particle characteristics and the idealized hydrodynamic conditions. Nonetheless, it provides a foundation for future work that should integrate environmental variables, a variety of MP types, and transient flow conditions. A sensitivity analysis of model parameters and experimental validation will be crucial to strengthen the applicability of these findings. Ultimately, this work aims to inform mitigation strategies and environmental management practices in estuarine systems affected by plastic pollution.

To refine the analysis, future simulations should vary the average water velocity and incorporate additional environmental and operational factors, such as water turbidity and channel geometry. This would allow for a more comprehensive evaluation of MP dispersion, transport, and deposition. A sensitivity analysis could also help identify the most influential factors affecting MP dispersion, further optimizing the model and enhancing the understanding of MP behavior in riverine environments.

This study contributes valuable knowledge on MP trajectory and sedimentation, emphasizing the impact of water velocity on MP behavior in estuarine environments. It also advances the understanding of MP dynamics in the Salado Estuary, aiding in future environmental assessments and mitigation strategies in the inner and outer estuary of the Gulf of Guayaquil due to its importance for the fishing and aquaculture sector. However, there are limitations, particularly the need for experimental validation to corroborate simulation results. Future research could expand on this work by investigating the behavior of smaller MP particles, incorporating wind effects, and tidal flows, and evaluating the impact of different particle shapes and compositions. Comparing numerical simulations with field data would also improve the model’s accuracy and applicability to real-world estuarine systems.