  We describe the imbibition process from a point source into a homogeneous
semi-infinite porous material. When body forces are negligible, the advance of
the wetting front is driven by capillary pressure and resisted by viscous
forces. With the assumption that the wetting front assumes a hemispherical
shape, our analytical results show that the absorbed volume flow rate is
approximately constant with respect to time, and that the radius of the wetting
evolves in time as r \approx t^(1/3). This cube-root law for the long-time
dynamics is confirmed by experiments using a packed cell of glass microspheres
with average diameter of 42 {\mu}m. This result complements the classical
one-dimensional imbibition result where the imbibition length l \approx
t^(1/2), and studies in axisymmetric porous cones with small opening angles
where l \approx t^(1/4) at long times.
