Simulation of Nanoparticle Deposition in Porous Media Using the Euler–Lagrange Method an‎d Pore-Scale Approach

10/22/2026 12:00:00 AM

The presence of nanoparticles in fluids can significantly alter the physical an‎d dynamic properties of the flow, thereby influencing hydrodynamic behavior, mass an‎d heat transfer, an‎d deposition phenomena. Understan‎ding nanoparticle behavior at the pore scale is a crucial step toward better interpretation an‎d more accurate prediction of nanofluid behavior in larger-scale porous media. Since many pore-scale simulation studies assume simplified single-phase flow models an‎d fail to capture the full physical complexity of this phenomenon, in this study, the Euler–Lagrange numerical method was employed in OpenFOAM to model the detailed process of nanoparticle deposition in metallic open-cell foams. In the developed model, the interactions between the fluid an‎d particles including Brownian, drag, gravity, buoyancy, an‎d Saffman lift forces as well as the nanoparticle–wall interactions (van der Waals an‎d electrostatic double-layer forces) were considered. To ensure high accuracy, the numerical model was first validated on a microchannel scale an‎d then applied to various porous geometries, including ordered (Cubic an‎d Kelvin Cell 2) an‎d disordered (Voronoi an‎d Foam Network) structures. This allowed investigation of the effects of geometrical features an‎d electrostatic parameters on the nanoparticle deposition ratio. Results indicated that increasing the parameter NDL (the ratio of particle radius to double-layer thickness), which represents the reduction of surface repulsion, leads to an increase in nanoparticle deposition up to a threshold value, beyond which the trend approaches saturation. Conversely, increasing the parameter NE1, which represents the surface potential magnitude of both the nanoparticle an‎d the wall, enhances electrostatic repulsion an‎d thus reduces deposition. Both effects depend strongly on microstructural geometry: the Kelvin Cell 2 structure, with the highest solid surface area an‎d lowest permeability, exhibited the greatest deposition, while Foam Network an‎d Cubic geometries with higher permeability an‎d lower solid contact showed the lowest. Subsequently, the effect of pore density (PPI) was analyzed for both constant an‎d gradient (variable) foams. The results showed that increasing PPI from 30 to 60 led to a rise in deposition ratio from about 62% to 89%. In gradient foams, the pore-density arrangement played a key role: the decreasing pattern (PPI 60–50–40–30) yielded the highest deposition (~81%), whereas the increasing pattern (PPI 30–40–50–60) resulted in the lowest (~77%). In the stepwise foam (PPI 60–30), the sudden density change at the boundary further reduced deposition (~76%). These findings indicate that the distribution of pore density along the flow direction is a critical factor in determining the probability of particle–wall collisions; the presence of denser regions at the inlet increases both initial an‎d total deposition. The influence of foam porosity (65–90%) was also examined. As porosity increased, the solid surface area decreased from 1421.6 to 848.1 mm², allowing greater flow pathways an‎d consequently reducing particle–wall interactions. This led to an approximately 11% decline in deposition ratio. Hence, the reduction in solid surface area was identified as a major cause of the decrease in deposition with increasing porosity. Finally, the effect of the applied pressure gradient was studied in a Voronoi foam (80% porosity, gradient pore density 30–40–50–60 PPI). Increasing the pressure gradient from 10 to 35 kPa/m raised the local flow velocity but reduced the effective permeability by about 21.8%, while increasing the deposition ratio by approximately 7%. This inverse relationship highlights the coupled dependency between permeability an‎d nanoparticle deposition. Overall, the results of this study demonstrate that the complex interplay among interparticle forces, foam geometrical characteristics (porosity, pore density, an‎d structure type), an‎d flow conditions (pressure gradient) are the key factors governing the nanoparticle deposition process in porous media.

نانوذرات , اويلر-لاگرانژ , محيط متخلخل , رسوب , مقياس حفره

nanoparticles , Euler–Lagrange method , porous media , deposition , pore scale

Mohammad Dehghan

Majid Siavashi