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Limitations of two-dimensional models and experiments in a three-dimensional world


Understanding flow and transport processes in the unsaturated zone remains a central challenge in hydrogeology, owing to the complex coupling between multiphase flow, pore-scale geometry, and spatial heterogeneity. These processes are often investigated using two-dimensional (2D) models and experiments, which provide high resolution and experimental control, but inherently simplify the physics of flow in three-dimensional (3D) porous media.

Recent pore-scale simulations highlight that dimensionality plays a fundamental role in controlling key transport mechanisms. In partially saturated systems, 3D flow fields exhibit fundamentally different phase connectivity, velocity distributions, and streamline organization compared to their 2D counterparts. In particular, the additional degree of freedom in 3D enhances connectivity and enables flow to bypass occlusions, reducing the prevalence of dead-end regions and altering residence time distributions and mixing dynamics.

These structural differences lead to distinct macroscopic behavior. For instance, while 2D systems typically predict a monotonic increase in mixing and reaction efficiency with decreasing saturation, 3D simulations reveal a non-monotonic dependence, with peak mixing and reactivity occurring at intermediate saturations. This behavior emerges from the interplay between velocity variance, correlation length, and fluid-filled pore volume, which are all strongly controlled by dimensionality.

The results demonstrate that both 2D models and microfluidic experiments can systematically overestimate mixing enhancement and reactive transport under unsaturated conditions. More broadly, they underscore that conclusions drawn from 2D systems are not always directly transferable to real porous media. These findings highlight the need for computational and experimental approaches that explicitly account for three-dimensional effects, or for careful reinterpretation of 2D results when applied to field-scale problems.