Deformable porous media

Objective

Understand the variety of patterns that form under the combined action of Coulomb friction, capillary- and viscous forces and make contact with non-equilibrium statistical mechanics on the theoretical and field observations on the empirical side, as well as hydrofracture processes where the solid matrix breaks down locally.

 

Figure 1. Left: Labyrinthine pattern of air fingers in a fluid-solid mixture forming as the fluid is drained through the hole in the center [Sandnes 2007]. Right: Evolution of the labyrinthine pattern at the top. At the bottom, we show our computer

These processes are studied both in simple table top-models and by algorithmic models that reproduce the many patterns observed in the laboratory. There are also some geological realizations of these patterns. As the deformation rates increase, different forces come into play. First, viscous forces will qualitatively change the displacement patterns by gradually de-mobilizing the Coulomb friction. Then inertial forces will enter the picture along with a stick-slip dynamics. The corresponding numerical models, which take these forces into account, become more challenging as the forces become less local. These models are built, from the simple to the more complex. Apart from verifying quantitative agreement with corresponding experiments, thereby establishing the key mechanisms at work, the simulations will be used to explore a minimum power principle. This principle is already established in the simplest simulations that only include pressure, capillary and Coulomb friction.

Figure 2. Phase diagram of different shapes that are created when changing the solid filling fraction, and the injection rate [Sandnes 2011]. We find capillary fingering and viscous fingering which well-known patterns in immiscible two-phase in flow porous media, hydraulic are fracturing – in addition to a host of patterns never seen before.

Are patterns relevant to biological tissue also in this diagram?

Selected articles before center launch

  1. Dumazer G., Sandnes B, Ayaz M., Måløy K.J., Flekkøy E., Frictional Fluid Dynamics and Plug Formation in Multiphase Millifluidic Flow, Phys. Rev. Lett., 117, 028002 (2016)
  2. M. Niebling, R. Toussaint, E.G. Flekkøy and K.J. Måløy, Dynamic aerofracture of dense granular packings, Phys. Rev. E 86 (2015)
  3. J.A. Eriksen and E.G. Flekkøy Numerical approach to frictional fingers, Phys. Rev. E 92 (2015)
  4. L. Laurson, X. Illa, S. Santucci, K.T. Tallakstad, K.J. Måløy, and M. Allava, The average avalanche shape: universality beyond the mean field. Nat. Commun. 4:2927 doi: 10.1038/ncomms3927 (2013)
  5. K.T. Tallakstad, R. Toussaint, S. Santucci, K.J. Måløy, Non-Gaussian Nature of Fracture and Survival of Fat-Tail Exponenets, Phys. Rev. Lett, 110, 145501 (2013)
  6. B. Sandnes, E.G. Flekkøy, H.A. Knudsen, K.J. Måløy, and H. See Patterns and flow in frictional fluid dynamics, Nature Comm. 2 doi:10.1038/ncomms1289 (2011)
  7. J. L. Vinningland, Ø. Johnsen, E.G. Flekkøy, R. Toussaint and K.J. Måløy, Granular Rayleigh- Taylor instability: experiment and simulation, Phys. Rev. Lett. 99 048001 (2007)

Selected articles from 2017