Self-affine fractal interfaces from immiscible displacement in porous media

Wetting immiscible displacement of one fluid by another in a porous medium yields self-affine (anisotropic) fractal interfaces between the two fluids. Water-air interfaces are characterized experimentally by a scale-dependent roughness w(L)=${\mathrm{AL}}^{\beta }$, with β=0.73±0.03, independent of the capillary number Ca, and A∝${\mathrm{Ca}}^{\mathrm{-}0.47\pm 0.06}$. The exponent β is related to the ‘‘box’’ and ‘‘divider’’ dimensions by $D_b$=2-β and $D_d$=1/β, respectively.