  We present a theoretical study of spontaneous imbibition of liquid 4He in
silica aerogels focusing on the effect of porosity on the fluid dynamical
behavior. We adopt a coarse-grained three-dimensional lattice-gas description
like in previous studies of gas adsorption and capillary condensation, and use
a dynamical mean-field theory, assuming that capillary disorder predominates
over permeability disorder as in recent phase-field models of spontaneous
imbibition. Our results reveal a remarkable connection between imbibition and
adsorption as also suggested by recent experiments. The imbibition front is
always preceded by a precursor film and the classical Lucas-Washburn scaling
law is generally recovered, although some deviations may exist at large
porosity. Moreover, the interface roughening is modified by wetting and
confinement effects. Our results suggest that the interpretation of the recent
experiments should be revised.
