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)=AL^β, with {β}=0.73±{}0.03, independent of the capillary number Ca, and A{∝}Ca^-0.47±0.06. The exponent {β} is related to the ``box'' and ``divider'' dimensions by Db=2-{β} and Dd=1/{β}, respectively.