  A new approach to the modelling of wetting fronts in porous media on the
Darcy scale is developed, based on considering the types (modes) of motion the
menisci go through on the pore scale. This approach is illustrated using a
simple model case of imbibition of a viscous incompressible liquid into an
isotropic porous matrix with two modes of motion for the menisci, the wetting
mode and the threshold mode. The latter makes it necessary to introduce an
essentially new technique of conjugate problems that allows one to link
threshold phenomena on the pore scale with the motion on the Darcy scale. The
developed approach (a) makes room for incorporating the actual physics of
wetting on the pore scale, (b) brings in the physics associated with pore-scale
thresholds, which determine when sections of the wetting front will be brought
to a halt (pinned), and, importantly, (c) provides a regular framework for
constructing models of increasing complexity.
