  We report experiments on spontaneous imbibition of a viscous fluid by a model
porous medium in the absence of gravity. The average position of the interface
satisfies Washburn's law. Scaling of the interface fluctuations provides a
dynamic exponent z \simeq 3, indicative of global dynamics driven by capillary
forces. The complete set of exponents clearly shows that interfaces are not
self-affine, exhibiting distinct local and global scaling, both for time
(b=0.64\pm 0.02, b* =0.33 \pm 0.03) and space (a=1.94 \pm 0.20, a_loc=0.94 \pm
0.10). These values are compatible with an intrinsic anomalous scaling
scenario.
