2024/05/20 by Mirko Residori, Residori, Mirko, Suvendu Mandal +5 · 1 citation
Engineering · #Enhanced Oil Recovery Techniques #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Heat and Mass Transfer in Porous Media #Lattice Boltzmann Simulation Studies #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2405.12381
openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study low-Reynolds-number fluid flow through a two-dimensional porous medium modeled as a Lorentz gas. Using extensive finite element simulations we fully resolve the flow fields for packing fractions approaching the percolation threshold. Near the percolation transition, we find a power-law scaling of the flow rate versus the pressure drop with an exponent of ≈ 5/2, which has been predicted earlier by mapping the macroscopic flow to a discrete flow network [Phys. Rev. Lett. 54, 1985]. Importantly, we observe a rounding of the scaling behavior at small system sizes, which can be rationalized via a finite-size scaling ansatz. Finally, we show that the distribution of the kinetic energy exhibits a power-law scaling over several decades at small energies, originating from collections of self-similar, viscous eddies in the dead-end-channels. Our results lay the foundation for unraveling critical behavior of complex fluids omnipresent in biological and geophysical systems.