2003/10/09 by Grunde Lovoll, Grunde Løvoll, Yves Méheust +5 · 132 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Boundary value problem #Capillary action #Capillary number #Capillary pressure #Displacement (psychology) #Flow (mathematics) #Geology #Geometry #Geotechnical engineering #Hele-Shaw flow #Lattice Boltzmann Simulation Studies #Material Dynamics and Properties #Mathematical analysis #Mathematics #Mechanics #Open-channel flow #Physics #Porosity #Porous medium #Power law #Pressure gradient #Scaling #Theoretical and Computational Physics #Thermodynamics #Viscosity #Viscous fingering #Wetting #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1103/physreve.70.026301
published in Physical Review E 70(2), 026301 (American Physical Society) · 11 pages 10 figures
arxiv created 2003/10/09 · openalex publication_date 2004/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present in this paper an experimental study of the invasion activity during unstable drainage in a two-dimensional random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (nonwetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length lambda from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance z to the latter tip and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure is then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.