Long-time behaviour of a porous medium model with degenerate hysteresis.

Hysteresis in the pressure-saturation relation in unsaturated porous media, owing to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. As an extension of previous existence and uniqueness results, we prove that under physically admissible initial conditions and without mass exchange with the exterior, the unique global solution of the fluid diffusion problem exists and asymptotically converges as time tends to infinity to a possibly non-homogeneous mass distribution and an a priori unknown constant pressure.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Implementation of temporal moments to elucidate the reactive transport of metformin and erythromycin in the saturated porous media.

This study investigates the fate and transport dynamics of metformin (MTN) and erythromycin (ETM), both classified as pharmaceutical and personal care products (PPCPs), in a saturated sandy soil column using temporal moment analysis (TMA). The key flow and transport parameters, including Darcy velocity, longitudinal dispersivity, adsorption, and degradation coefficients, were analyzed. The results reveal that MTN, a highly mobile contaminant, is eliminated from the column in approximately 40 days, while ETM shows significant adsorption due to its hydrophobic and adsorptive nature. Darcy velocity significantly affects PPCP transport; a one-order magnitude change alters contaminant mass recovery at the column outlet by 88% for MTN and 39-fold for ETM. Longitudinal dispersivity has minimal impact on the transport of PPCPs. However adsorption primarily governs the fate of PPCPs with high adsorption coefficients (Kd), and degradation rates control the fate of low-sorbing PPCPs. A one-order magnitude change in Kd results in a 55% change in the zeroth temporal moment (ZTM) of MTN and a 30-fold change in the case of ETM. Additionally, a one-order magnitude change in the degradation coefficient leads to a 60% variation in MTN's ZTM and a 5% variation in ETM's ZTM. Thus, TMA is a valuable tool for understanding PPCP dynamics in subsurface environments, providing critical insights for managing their increasing concentrations.

Microbial nitrogen bubble formation in porous media.

Microbially induced nitrogen (N2) gas bubbles can desaturate subsurface areas and thus have been considered as an alternative ground improvement technique for mitigating soil liquefaction potential caused by earthquakes. However, the detailed mechanisms of subsurface N2 bubbles are not well understood and remain a subject of ongoing research. In this study, a transparent microfluidic device was utilized to mimic biological N2 gas bubble formation by nitrate-reducing bacteria and to visually characterize the entire process. During N2 gas formation, a limited number of bubble nucleation sites were identified, which gradually expanded upward through the preferential pore channels. N2 gas bubbles tended to create interconnected gas pockets rather than existing as evenly distributed small gas cavities. The degree of water saturation gradually reduced over a week as the bubbles were produced. The gas ganglia repeatedly grew until they reached the top boundary, which triggered a drastic expulsion of bubbles by ebullition. Despite fluctuations in saturation level, the residual saturation was maintained at around 73 %. Comparative experimental case studies of CO2 gas bubble formation were conducted to identify contrasting gas formation mechanisms. CO2 gas bubbles were generated via the abiotic decompression of a supersaturated CO2 solution under two distinct rates of pressure reduction. Rapid CO2 bubble formation led to uniform nucleation and 41 % residual saturation, while slower formation yielded 35 % due to stable liquid displacement by the gas front. This study highlights the potential of the microfluidic device as an experimental tool for visualizing subsurface gas formation mechanisms. The insights gained could further enhance and optimize geotechnical applications involving gas formation in highly saturated soils.

Quantifying local and global mass balance errors in physics-informed neural networks.

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN's ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN's solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN's local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN's hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

Harnessing elastic instabilities for enhanced mixing and reaction kinetics in porous media.

Turbulent flows have been used for millennia to mix solutes; a familiar example is stirring cream into coffee. However, many energy, environmental, and industrial processes rely on the mixing of solutes in porous media where confinement suppresses inertial turbulence. As a result, mixing is drastically hindered, requiring fluid to permeate long distances for appreciable mixing and introducing additional steps to drive mixing that can be expensive and environmentally harmful. Here, we demonstrate that this limitation can be overcome just by adding dilute amounts of flexible polymers to the fluid. Flow-driven stretching of the polymers generates an elastic instability, driving turbulent-like chaotic flow fluctuations, despite the pore-scale confinement that prohibits typical inertial turbulence. Using in situ imaging, we show that these fluctuations stretch and fold the fluid within the pores along thin layers ("lamellae") characterized by sharp solute concentration gradients, driving mixing by diffusion in the pores. This process results in a [Formula: see text] reduction in the required mixing length, a [Formula: see text] increase in solute transverse dispersivity, and can be harnessed to increase the rate at which chemical compounds react by [Formula: see text]-enhancements that we rationalize using turbulence-inspired modeling of the underlying transport processes. Our work thereby establishes a simple, robust, versatile, and predictive way to mix solutes in porous media, with potential applications ranging from large-scale chemical production to environmental remediation.

Calorimetric investigation on heat release during the disintegration process of pharmaceutical tablets.

The compendial USP〈701〉 disintegration test method offers a crucial pass/fail assessment for immediate release tablet disintegration. However, its single end-point approach provides limited insight into underlying mechanisms. This study introduces a novel calorimetric approach, aimed at providing comprehensive process profiles beyond binary outcomes. We developed a novel disintegration reaction calorimeter to monitor the heat release throughout the disintegration process and successfully obtained enthalpy change profiles of placebo tablets with various porosities. The formulation comprised microcrystalline cellulose (MCC), anhydrous lactose, croscarmellose sodium (CCS), and magnesium stearate (MgSt). An abrupt temperature rise was observed after introducing the disintegration medium to tablets, and the relationship between the heat rise time and the tablet's porosity was investigated. The calorimeter's sensitivity was sufficient to discern distinct heat changes among individual tablets, and the analysis revealed a direct correlation between the two. Higher porosity corresponded to shorter heat rise time, indicating faster disintegration rates. Additionally, the analysis identified a concurrent endothermic process alongside the anticipated exothermic phenomenon, potentially associated with the dissolution of anhydrous lactose. Since lactose is the only soluble excipient within the blend composition, the endothermic process can be attributed to the absorption of heat as lactose molecules dissolve in water. The findings from this study underscore the potential of utilising calorimetric methods to quantify the wettability of complex compounds and, ultimately, optimise tablet formulations.

Effects of fluid composition in fluid injection experiments in porous media.

Experiments on fluid flow in porous media, using fluids loaded with solids of various grain sizes, have been conducted in a modified Hele-Shaw setup. This setup utilised weakly cemented porous media with specific hydraulic and mechanical properties. Fluid injection in coarse granular media with clean or low-concentration fine particles, results in infiltration only, with pressure close to the material tensile strength, while injection in finer granular material causes damage alongside infiltration, with the fluid pressure still close to the material tensile strength. When larger particle sizes or higher particle concentrations are used in the mixture, the fluid travels further within the porous medium, primarily influenced by the grain size of the granular medium. In the latter case, the Darcy flow equation with an effective permeability term can be employed to determine the pressure differential. For the largest particle sizes included in the fluid, the equation is still applicable, but the effective permeability requires adjustment for particle size within the fluid rather than the granular medium. This is crucial when the injection point is locally clogged. The experiments show that fracturing conditions are controlled by different mechanisms. Dimensional and statistical analysis was used to classify the injection pressures to regimes predicted by fracturing theory or by Darcy law with modified effective permeabilities. The findings show that both the material properties and fluid composition are important designing parameters.

Natural mineral colloids facilitated transport of EE2 in saturated porous media: Effects of humic acid and conjugate form.

Steroid estrogens have posed significant ecological risks to aquatic organisms due to their potent endocrine-disrupting effects. The role of natural mineral colloids in facilitating the transport of hydrophobic organic pollutants in the environment has been confirmed, but the control mechanisms of colloids on 17α-Ethinylestradiol (EE2) migration in the subsurface environment are often still not well understood. This study combined the batch sorption equilibrium experiments and dynamic transport simulations to reveal the interface interactions and co-transport characteristics between illite colloids and EE2 at both macroscopic and microscopic levels. The existing form changes of EE2 and the influence of coexisting humic acid (HA) during transport in porous media were also specifically investigated. The batch experiments demonstrated that the primary mechanisms governing EE2 sorption onto illite colloids involved surface sorption and hydrogen bonding. The coexistence of HA could load onto the surface of illite colloids, thereby enhancing the colloidal sorption capacity for EE2. Transport experiments demonstrated that the migratory ability of EE2 in silty clay was limited, but illite colloids could significantly promote its penetration, with the peak penetration content (Ct/C0) increasing from 0.64 to 0.77. In the absence of HA, EE2 primarily transported in a dissolved form, accounting for 62.86% of the total concentrations. When HA concentrations were increased to 10 mg/L and 20 mg/L, the proportion of colloidal conjugate EE2 in the effluents reached 52.13% and 54.49%, respectively. The enhanced transport of EE2 by HA was primarily attributed to the improved migration ability of illite colloids and the increased proportion of illite-EE2 conjugate, resulting in a maximum Ct/C0 value of 0.94. The validity of these results was further confirmed by employing calculations based on the Derjaguin-Landau-Verwey-Overbeek and Colloidal Filtration Theory. This study provides new insights of understanding the transport of EE2 in subsurface environment.

A Novel Finite Element-Based Method for Predicting the Permeability of Heterogeneous and Anisotropic Porous Microstructures.

Permeability is a fundamental property of porous media. It quantifies the ease with which a fluid can flow under the effect of a pressure gradient in a network of connected pores. Porous materials can be natural, such as soil and rocks, or synthetic, such as a densified network of fibres or open-cell foams. The measurement of permeability is difficult and time-consuming in heterogeneous and anisotropic porous media; thus, a numerical approach based on the calculation of the tensor components on a 3D image of the material can be very advantageous. For this type of microstructure, it is important to perform calculations on large samples using boundary conditions that do not suppress the transverse flows that occur when flow is forced out of the principal directions. Since these are not necessarily known in complex media, the permeability determination method must not introduce bias by generating non-physical flows. A new finite element-based method proposed in this study allows us to solve very high-dimensional flow problems while limiting the biases associated with boundary conditions and the small size of the numerical samples addressed. This method includes a new boundary condition, full permeability tensor identification based on the multiscale homogenization approach, and an optimized solver to handle flow problems with a large number of degrees of freedom. The method is first validated against academic test cases and against the results of a recent permeability benchmark exercise. The results underline the suitability of the proposed approach for heterogeneous and anisotropic microstructures.

Nanoengineering-Enhanced Capillary Cooling Achieves Sustained Thermal Protection for Ultra-High Heat Flux and Temperature.

Extreme thermal conditions with heat flux densities exceeding 1 MW·m-2 or temperatures reaching up to 1000 °C are prevalent in various situations. However, the ability of thermal protection either depends on specialized materials or is currently limited with existing cooling schemes. Herein, we propose an innovative cooling scheme that relies on evaporation-driven capillary flow enhanced by nanoengineering-designed porous structures with common materials. Experimentally-obtained capillary flow cooling curve identifies critical heat flux corresponding to evaporation-driven flow stage, where coolants cool the surface and subsequent vapor impedes heat transfer from thermal boundaries. Nanoengineering provides opportunities for enhanced capillary flow, which proves to endow bronze, TC4, and Al2O3 with thermal protection ability 50%-180% higher than that without nanoengineering-designed. Our scheme achieves critical heat flux up to 2.0-3.1 MW·m-2, and performs thermal dissipation capacity almost twice higher than inherent latent heat of coolant. Furthermore, in a supersonic wind tunnel with total temperature reaching up to 1792 K, our scheme effectively protects surfaces by cooling them to surface temperatures below 500 K. Nanoengineering-enhanced capillary cooling gives access to the application of common materials for high-temperature and high-heat-flux environments and paves the way for the development of lightweight, long-lasting, and large-scale solutions for thermal protection. This article is protected by copyright. All rights reserved.

Facilitated transport of ferrihydrite with phosphate under saturated flow conditions.

With increasing phosphate (P) entering the environment during agricultural application, the subsurface flow of particular P has been recently discussed as a vital P transport pathway. Iron (oxyhydr)oxide colloid-facilitated P transport is critical for iron and P biogeochemical processes in the subsurface. This study investigated the ferrihydrite colloid-facilitated P transport through adsorption and column experiments under different P concentrations and three pH conditions. Increased P loading on ferrihydrite colloids decreased the transport of ferrihydrite colloids (< 8.0%) under acid conditions through pore straining and irreversible attachment. Under neutral and alkaline conditions, ferrihydrite colloids exhibited more negative surfaces and smaller diameters with increasing P, which further enhanced ferrihydrite colloid transport (maximum to 95.6%). Ferrihydrite colloid-facilitated P transport was limited under acid conditions, and it was 10% - 57% enhancement under neutral and alkaline conditions with increasing P adsorption. Under neutral conditions, ferrihydrite colloid-facilitated P transport was strongest (maximum to 68.84%) because of its stronger ferrihydrite colloid transport than under acid conditions and larger P adsorption capacity than under alkaline conditions. Our findings indicate that the facilitated transport of ferrihydrite colloids in the presence of P may be appreciable in iron and phosphate-rich soil and subsurface systems, which is essential for evaluating the fate of iron and iron-facilitated P and potential environmental risks of P transport in the subsurface.

Fractal geometry of fingering front morphologies of water and NAPL flow in homogeneous porous media: A comparison study.

Fingering front morphologies for water and non-aqueous phase liquids (NAPLs) infiltrating into homogeneous unsaturated porous media were quantitatively described based on the fractal assumption. Correlations of fractal dimensions with physical properties of the fluids were studied. The implications of fractal dimensions for environmental systems are further discussed. Fingering front morphologies had fractal properties, and diesels which with high capillary numbers experienced high fractal dimensions than water. Fractal dimension was suggested as an indicator for dye coverage and infiltration depth, which represent pollution area and depth, respectively. The pollution areas showed positive correlations with fractal dimensions while the infiltration depths showed negative correlations. This information is useful for contaminated soil risk management and important in the effective design of recovery and remediation schemes.

Unveiling the Role of PTFE Surface Coverage on Controlling Gas Diffusion Layer Water Content.

Gas diffusion layers (GDLs) are usually coated with a hydrophobic agent to achieve a delicate balance between liquid and gas phases to maximize mass transport. Yet, most GDL numerical models to date have assumed an average contact angle for all materials, thereby eliminating the possibility of studying the role of the polytetrafluoroethylene (PTFE) content. This study introduces two mixed wettability algorithms to predict the mixed wetting behavior of GDLs composed of multiple materials. The algorithms employ contact angle and distance to solid materials to determine the critical capillary pressure for each pore voxel. The application of the algorithms to the estimation of capillary pressure vs saturation curves for two GDLs, namely, a micro-computed tomography (µ-CT) reconstructed SGL 39BA GDL and a stochastically reconstructed Toray 120C GDL, showed that, in agreement with experimental data, the addition of PTFE resulted in a decrease in saturation at a given capillary pressure. For Toray-120C, the mixed wettability model was capable of reproducing experimentally observed features in the intrusion curve at low saturation that could not be reproduced with a single wettability model, providing a clear link between PTFE coverage and intrusion at low saturation. Numerical results also predicted an increased breakthrough pressure and a decrease in saturation with increasing PTFE, in agreement with experimental observations. The decreased saturation at breakthrough improves gas transport through the layer while maintaining the layer's ability to remove water. Diffusivity simulations confirm the increase in diffusivity at breakthrough with increasing PTFE, thereby providing a rationale for the addition of PTFE, as well as for the optimal amount. This study emphasizes the importance of multimaterial wetting models and calls for more detailed investigations into PTFE and ionomer distributions in GDLs and catalyst layers, respectively.

Use of recycled construction and demolition waste as substrate in constructed wetlands for the wastewater treatment of cheese production.

Recycled building debris has recently emerged as a suitable wetland infill substrate due to its low density, exceptional water absorption capabilities, and high porosity. This study investigated, for the first time, the use of construction demolition wastes (CDW), and rock processing residues (RPR) as substrate materials in vertical-horizontal flow hybrid constructed wetlands for the treatment of cheese production wastewater. Results showed that the use of both CDW as well as RPR, as substrate material, provided an equal or even better quality of treated wastewater compared to the conventional use of gravel as a substrate. High removal efficiencies were recorded for turbidity (CDW: 91-92%, RPR: 97%), solids (CDW: 85-88%, RPR: 96-97%), organic matter (CDW: 79-84%, RPR: 96-98%), and total phosphorus (CDW: 72-76%, RPR: 87%) for both examined recycled materials. During the experiment, different loadings rates (HLR) were tested: 25 mm d-1 and 37.5 mm d-1. Radiological measurements indicate that, their use did not cause toxic effects on the environment, as the amounts of radioactivity found in the effluent of the systems are not significant. Increasing the hydraulic loading rate appeared to have no negative effect on pollutant removal, as the systems and plants were fully acclimated and mature. This approach offers several advantages, including the use of readily available and abundant waste material, potential cost savings, and the environmental benefits of recycling CDW and RPR instead of disposing of them in landfills.

Research on the Migration and Adsorption Mechanism Applied to Microplastics in Porous Media: A Review.

In recent years, microplastics (MPs) have emerged as a significant environmental pollutant, garnering substantial attention for their migration and transformation behaviors in natural environments. MPs frequently infiltrate natural porous media such as soil, sediment, and rock through various pathways, posing potential threats to ecological systems and human health. Consequently, the migration and adsorption mechanisms applied to MPs in porous media have been extensively studied. This paper aims to elucidate the migration mechanisms of MPs in porous media and their influencing factors through a systematic review. The review encompasses the characteristics of MPs, the physical properties of porous media, and hydrodynamic factors. Additionally, the paper further clarifies the adsorption mechanisms of MPs in porous media to provide theoretical support for understanding their environmental behavior and fate. Furthermore, the current mainstream detection techniques for MPs are reviewed, with an analysis of the advantages, disadvantages, and applications of each technique. Finally, the paper identifies the limitations and shortcomings of current research and envisions future research directions.

A two-phase flow model simulating water penetration into pharmaceutical tablets.

The purpose of the study is introduce a two-phase flow model to simulate water penetration into pharmaceutical tablets. This model was built by integrating Darcy's law with the continuity principle, on the premise that water penetration was driven by capillary actions. Notably, this model concerned both the ingress of water (wetting phase) and simultaneous displacement of air (non-wetting phase). Due to the interference of the two fluids, the relative permeability and capillary pressure vary during water penetration. Evolution of these parameters was incorporated in the model. Calibration of the model by water penetration experiments of the microcrystalline cellulose (MCC) tablet yielded an average pore radius of 42 nm. This derived result was corroborated by FIB-SEM analysis revealing the presence of extensive microporosity within MCC particles with an average radius of ∼30 nm. Further validation was achieved through close resemblance between the simulated and experimental water penetration profiles of MCC tablets possessing different porosities. Overall, this study underscored the advantage of the two-phase flow model over single-phase flow models, by capturing the dependence of permeability and capillary pressure on water saturation. Therefore it holds promise for an enhanced description of water penetration into tablets.

The bimolecular reactive transport in heterogeneous porous media: Sub-diffusion in interpretation of laboratory experiment.

This present work consists of investigating the effects of particle size heterogeneity and flow rates on transport-reaction kinetics of CuSO4 and Na2EDTA2- in porous media, via the combination of a bimolecular reaction experiment and model simulations. In the early stages of transport, a peak is observed in the concentration breakthrough curve of the reactant CuSO4, related to the delayed mixing and reaction of the reactants. The numerical results show that an increase in flow rate promotes the mixing processes between the reactants, resulting in a larger peak concentration and a slighter tail of breakthrough curves, while an increase in medium heterogeneity leads to a more significant heavy tail. The apparent anomalous diffusion and heavy-tailing behavior can be effectively quantified by a novel truncated fractional derivative bimolecular reaction model. The truncated fractional-order model, taking into account the incomplete mixing, offers a satisfactory reproduction of the experimental data.

Bacterial surface properties and transport behavior actively respond to an extracellular polymeric substance gradient in saturated porous media.

The transport and retention of bacteria in porous media, such as aquifer, are governed by the solid-liquid interface characteristics and bacterial mobility. The secretion of extracellular polymeric substance (EPS) by bacteria modifies their surface property, and thereby has effects on their adhesion to surface. The role of EPS in bacterial mobility within saturated quartz sand media is uncertain, as both promoting and inhibitory effects have been reported, and underlying mechanisms remain unclear. In this study, the effects of EPS on bacterial transport behavior and possible underlying mechanism were investigated at 4 concentrations (0 mg L-1, 50 mg L-1, 200 mg L-1 and 1000 mg L-1) using laboratory simulation experiments in conjunction with Extend Derjaguin-Landau-Verweu-Overbeek (XDLVO) modeling. The results showed that EPS facilitated bacterial mobility at all tested concentrations. It could be partially explained by the increased energy barrier between bacterial cells and quartz sand surface in the presence of EPS. The XDLVO sphere-plate model predicted that EPS induced a higher electrostatic double layer (EDL) repulsive force, Lewis acid-base (AB) and steric stabilization (ST), as well as a lower Lifshitz-van der Waals (LW) attractive force. However, at the highest EPS concentration (1000 mg L-1), the promotion of EPS on bacterial mobility weakened as a result of lower repulsive interactions between cells, which was supported by observed enhanced bacterial aggregation. Consequently, the increased aggregation led to greater bio-colloidal straining and ripening in the sand column, weakening the positive impact of EPS on bacterial transport. These findings suggested that EPS exhibited concentration-dependent effects on bacterial surface properties and transport behavior and revealed non-intuitive dual effects of EPS on those processes.

Influence of salinity gradients on the diffusion of water and ionic species in dual porosity clay samples.

Most of the available data on diffusion in natural clayey rocks consider tracer diffusion in the absence of a salinity gradient despite the fact that such gradients are frequently found in natural and engineered subsurface environments. To assess the role of such gradients on the diffusion properties of clayey materials, through-diffusion experiments were carried out in the presence and absence of a salinity gradient using salt-diffusion and radioisotope tracer techniques. The experiments were carried out with vermiculite samples that contained equal proportions of interparticle and interlayer porosities so as to assess also the role played by the two types of porosities on the diffusion of water and ions. Data were interpreted using both a classical Fickian diffusion model and with a reactive transport code, CrunchClay that can handle multi-porosity diffusion processes in the presence of charged surfaces. By combining experimental and simulated data, we demonstrated that (i) the flux of water diffusing through vermiculite interlayer porosity was minor compared to that diffusing through the interparticle porosity, and (ii) a model considering at least three types of porous volumes (interlayer, interparticle diffuse layer, and bulk interparticle) was necessary to reproduce consistently the variations of neutral and charged species diffusion as a function of salinity gradient conditions.

Three-dimensional modeling for colloid-facilitated contaminant transport with the effect of mobile and immobile sorbents.

A conceptual equilibrium-based mathematical model for colloid-associated contaminant transport has been developed to study the impact of the subsurface environment on contaminant transport through a three-dimensional, saturated, and homogeneous groundwater flow system with uniform flow. The kinetic model's critical limitation is dealing with the more significant number of parameters utilized upon application to larger scales in three-dimensional regions when a series of transport mechanisms are incorporated. Therefore, the present study is the first attempt to study the equilibrium approach in three-dimensional regions to avoid complexities in the model. The current study, however, shows that the mere existence of colloids does not indicate that contaminants will move more quickly; rather, it also depends on how the aqueous phase interacts with the static solid matrix, captured colloid particles, and mobile colloids as well as how colloids interact with stationary solid matrix phase. We noticed that the affinity of contaminants to immobile sorbents (stationary solid matrix and captured colloids) can reduce the transport even in the presence of colloids. Three-dimensional numerical experiments reveal that contaminants infiltrate more in the downward direction in the absence of colloids and can be distributed more in the longitudinal direction and less in the downward direction when colloids are present. The dual nature of colloids is espied here: first, colloids can remove pollutants from a specific area more quickly, and second, in a similar manner, colloids can pollute a specific region more quickly.