Researchers Develop Theory Linking Flow Distributions in Porous Media to Topological Properties
Researchers have developed a pore-network model that predicts flow rate distributions in disordered two-dimensional porous media, finding that flow across pore bodies follows a Gamma distribution. The model improves on prior mean-field approaches by incorporating local flow correlations — specifically how flow splits and merges at pore junctions. These findings could improve predictions of fluid transport in geophysical and engineered porous systems using minimal geometric information.
A study submitted to the Journal of Fluid Mechanics presents a theoretical framework for understanding how fluid flows through disordered porous media composed of two-dimensional arrays of circular obstacles under steady Stokes flow conditions. The authors show that flow rate distributions across pore bodies follow a Gamma distribution, and that flow rates through pore throats are fully determined by this distribution. Crucially, the Gamma distribution parameters can be linked to simple geometric properties — specifically the coefficient of variation of pore throat widths — making the model practical to apply with limited structural data. The theory outperforms earlier mean-field models by explicitly accounting for local flow correlations arising from the splitting and merging of flow at pore junctions. Predictions from the model show close agreement with computational fluid dynamics simulations across the ensemble of disordered geometries studied. The work spans fluid dynamics, soft condensed matter, and geophysics, suggesting broad applicability to problems such as groundwater flow, filtration, and transport in biological tissues.
What's missing
The study is a preprint and has not yet undergone peer review. The model is validated only for two-dimensional systems with circular obstacles under Stokes (low Reynolds number) flow; its applicability to three-dimensional, non-circular, or inertial-flow regimes is not established.
What different sources said
- arXiv physicsCenter
Topological origin of flow distributions in disordered porous media
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