Commentary - (2025) Volume 16, Issue 6
Received: 01-Nov-2025, Manuscript No. jpm-26-179482;
Editor assigned: 03-Nov-2025, Pre QC No. P-179482;
Reviewed: 17-Nov-2025, QC No. Q-179482;
Revised: 24-Nov-2025, Manuscript No. R-179482;
Published:
29-Nov-2025
, DOI: 10.37421/2090-0902.2025.16.566
Citation: Rossi, Valentina. ”Pore-Scale Modeling of Fluid Flow in Porous Media.” J Phys Math 16 (2025):566.
Copyright: © 2025 Rossi V. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.
The study of fluid flow and solute transport within porous geological formations is a cornerstone of many scientific and engineering disciplines. Understanding these complex phenomena is critical for effective resource management, environmental protection, and subsurface infrastructure development. Recent advancements have focused on developing sophisticated mathematical frameworks to accurately model these processes, accounting for the inherent heterogeneities and dynamic conditions present in natural systems. One significant area of research involves integrating fundamental physical laws with advanced computational techniques to capture the intricate behaviors of fluids and dissolved substances in porous media. The interplay between fluid rheology and transport properties is another vital aspect being investigated. Non-Newtonian fluids, which exhibit flow behavior that deviates from Newtonian principles, are prevalent in various industrial and biological applications. Research in this area aims to precisely quantify how shear-thinning or shear-thickening characteristics influence dispersion and velocity profiles within porous structures, offering more realistic models for complex fluid systems. Furthermore, the coupled nature of heat and mass transfer in porous materials is of paramount importance for technologies such as geothermal energy extraction and carbon sequestration. Robust numerical schemes are being developed to solve governing equations that encompass buoyancy-driven convection and phase changes. This allows for the accurate simulation of thermal-hydraulic-mechanical couplings, revealing crucial feedback loops that dictate the long-term performance and stability of underground systems. Diffusion processes in nanoporous materials, particularly those with complex pore structures, represent a significant challenge. Advanced simulation methods like the Lattice Boltzmann method are being employed to model molecular diffusion and derive effective diffusion coefficients. The development of generalized correlations between pore network topology and diffusion rates is crucial for understanding transport in emerging advanced materials. The dynamics of multiphase flow in porous media, especially concerning interface capturing and wetting phenomena, are being explored through novel modeling approaches. Phase-field methods, when coupled with Darcy-Brinkman models, offer the capability to simulate complex scenarios such as capillary trapping and fingering, providing deeper insights into fluid displacement processes. Anomalous transport, which deviates from standard advection-dispersion behavior, occurs in many disordered porous media. The application of fractional calculus provides a powerful tool to develop models that capture long-range correlations and memory effects, leading to more accurate descriptions of solute spreading in complex geological structures and enhanced environmental risk assessments. Pore-scale roughness and wettability significantly influence capillary-driven imbibition. Investigations combining pore-network simulations with experimental validation are elucidating how surface heterogeneities affect invasion patterns and fluid saturation. This research refines our understanding of capillary forces at the pore scale, with direct implications for enhanced oil recovery and natural fluid migration. The integration of pore-scale reaction kinetics with macroscopic continuum equations is essential for modeling reactive transport. Novel coupling strategies are being developed to account for flow heterogeneity's influence on reaction rates. These studies demonstrate that pore-scale flow variations can profoundly alter reaction efficiency and product distribution, a critical factor in biogeochemical processes and contaminant degradation. The direct impact of pore-scale heterogeneity on dispersion coefficients is a subject of ongoing research. Advanced imaging techniques and numerical simulations are being used to link tortuosity and pore network connectivity to the effective dispersion tensor. This provides a crucial bridge between microscopic pore structure and macroscopic transport properties, vital for accurate groundwater and contaminant transport modeling. Finally, continuum models for porous media with dynamic pore structures are being advanced. The development of stress-dependent permeability models, coupled with transport equations, allows for the simulation of how structural changes, such as swelling or compaction, affect fluid flow paths and solute migration, with applications in geotechnical engineering and agricultural science.
The complex interplay of fluid flow and solute transport within porous geological formations is a subject of intense multidisciplinary research. A novel mathematical framework that integrates Darcy's law with advection-dispersion equations, specifically addressing heterogeneous permeability and variable fluid properties, has been presented. This work highlights a multi-scale approach to capture pore-scale phenomena that influence macroscopic transport behavior, leading to more accurate predictions for contaminant migration and resource recovery applications [1].
Further investigations into the influence of pore structure on non-Newtonian fluid flow and its subsequent impact on chemical transport in porous media have been conducted. By employing pore-scale simulations coupled with continuum modeling, researchers have illustrated how shear-thinning or shear-thickening behaviors modify dispersion characteristics and velocity profiles. A significant contribution is the quantification of the effective dispersion tensor as a function of fluid rheology and pore geometry, offering improved models for applications involving complex fluids like polymers or biological suspensions [2].
Modeling coupled heat and mass transfer in porous materials is of critical importance for applications such as geothermal energy extraction and carbon sequestration. A robust numerical scheme has been introduced for solving the governing partial differential equations that account for buoyancy-driven convection and phase changes. The primary outcome is the accurate simulation of thermal-hydraulic-mechanical coupling, revealing critical feedback loops that influence the long-term performance and stability of underground systems [3].
The impact of pore-scale connectivity and tortuosity on macroscopic diffusion processes in nanoporous materials is being explored. Lattice Boltzmann methods are utilized to simulate molecular diffusion and derive effective diffusion coefficients. A key finding is the development of a generalized correlation between pore network topology parameters and the effective diffusion rate, which is crucial for understanding transport in advanced materials like membranes and catalysts [4].
A phase-field approach has been developed to model the dynamics of multiphase flow in porous media, with a particular focus on interface capturing and wetting phenomena. The novelty lies in the consistent coupling of phase-field equations with a Darcy-Brinkman model. This enables the simulation of complex scenarios such as capillary trapping and fingering, providing a more detailed understanding of fluid displacement processes in oil recovery and groundwater hydrology [5].
The modeling of anomalous transport in disordered porous media, moving beyond standard advection-dispersion formulations, has been addressed. By employing fractional calculus, a model has been developed to capture the long-range correlations and memory effects inherent in such systems. The significance lies in providing a more accurate description of solute spreading in complex geological structures, which is crucial for environmental risk assessment and resource exploration [6].
The influence of pore-scale roughness and wettability on capillary-driven imbibition in porous media has been investigated. Utilizing pore-network simulations and experimental validation, researchers have elucidated how surface heterogeneities affect invasion patterns and fluid saturation. The key contribution is a refined understanding of capillary forces at the pore scale, with direct implications for the design of enhanced oil recovery techniques and the understanding of natural fluid migration in rocks [7].
Multiscale modeling of reactive transport in porous media, integrating pore-scale reaction kinetics with macroscopic continuum equations, has been presented. A novel coupling strategy has been developed that accounts for the influence of flow heterogeneity on reaction rates. The primary insight is the demonstration that pore-scale variations in flow can significantly alter the overall reaction efficiency and the spatial distribution of reaction products, a critical factor in biogeochemical processes and contaminant degradation [8].
The effects of pore-scale heterogeneity on dispersion coefficients in porous media are being investigated using advanced imaging techniques and numerical simulations. It has been demonstrated how the tortuosity and connectivity of the pore network directly influence the effective dispersion tensor. This work provides a crucial link between microscopic pore structure and macroscopic transport properties, essential for accurate modeling in groundwater flow and contaminant transport studies [9].
Continuum models for fluid flow and transport in porous media with dynamic pore structures, such as those undergoing swelling or compaction, are being developed. A key innovation is the introduction of a stress-dependent permeability model that is coupled with transport equations. The findings reveal how changes in the porous medium's structure can significantly alter fluid flow paths and solute migration, impacting applications in geotechnical engineering and agricultural science [10].
This collection of research explores advanced modeling techniques for fluid flow and solute transport in porous media. It highlights the critical role of pore-scale characteristics, such as heterogeneity, roughness, and connectivity, in influencing macroscopic transport phenomena. Studies utilize multi-scale approaches, integrating Darcy's law with advection-dispersion equations, phase-field methods, and fractional calculus to capture complex behaviors like non-Newtonian fluid flow, reactive transport, and anomalous diffusion. The research emphasizes the development of accurate predictive models for applications ranging from environmental remediation and resource recovery to geothermal energy and material science, providing deeper insights into the relationship between microscopic structure and macroscopic transport properties.
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