Self-affine fractal interfaces from immiscible displacement in porous media

Abstract

Wetting immiscible displacement of one ffuid by another in a porous medium yields self-affine (anisotropic) fractal interfaces between the two ffuids. Water-air interfaces are characterized experimentally by a scale-dependent roughness w(L) ALs, with p 0.73+'0.03, independent of the capillary number Ca, and A cx:Ca a47-. The exponent p is related to the "box" and "divider' dimensions by Dt, 2-P and Dd 1/P, respectively.

Deblocking of interacting particle assemblies: from pinning to jamming

“…This is clearly illustrated nowadays by the large variety of studies dealing with front invasion where roughening processes take place such as flow through porous media [16][17][18] or imbibition [19], flame propagation [20,21], deposition processes [14,15], and flux penetration in superconducting materials [32,33,45,46]. From a macroscopic point of view, the development of modeling techniques for the description of these dynamical systems has been generally based on the traditional approach to transport phenomena, where the governing expressions are usually differential equations representing local balances of the quantity of interest (e.g., mass, momentum, flux of superconducting vortices, etc.)…”

Variety of stylolites' morphologies and statistical characterization of the amount of heterogeneities in the rock

“…various geological examples such as erosion patterns (Dunne, 1980;Cerasi et al, 1995), 39 multiphase fluid percolation in porous rocks (Rubio et al, 1989), fractures (Schmittbuhl et 40 al., 1993), or stylolites . In these studies, the scaling behavior of 41 various data sets was investigated, showing that the statistics at one scale could be 42 extrapolated to another scale using a power law relationship.…”

Fluid Invasion in Porous Media: Viscous Gradient Percolation

“…(7), we obtain κ e ≃ 0.46 in good agreement with the value 0.47(2) directly measured from our simulations and 0.48 from imbibition experiments in Refs. [10,11].…”