In this paper the free boundary problem for groundwater phreatic surface is represented in the form of a variational principle. It is proved that the flow domain Ω that solves the problem is a minimizer of some functional Λ(Ω). Weak solutions are introduced as minimizers of the lower semi-continuous regularization of Λ(⋅). Within this approach the existence of weak solutions is proved for a wide class of input data.

Water flow in plant tissues takes place in two different physical domains separated bysemipermeable membranes: cell insides and cell walls. The assembly of all cell insides andcell walls are termed symplast and apoplast,respectively. Water transport is pressure driven in both, where osmosis plays an essentialrole in membrane crossing. In this paper, a microscopic model of water flow and transportof an osmotically active solute in a plant tissue is considered. The model is posed on thescale of a single cell and the tissue is assumed to be composed of periodicallydistributed cells. The flow in the symplast can be regarded as a viscous Stokes flow,while Darcy’s law applies in the porous apoplast. Transmission conditions at the interface(semipermeable membrane) are obtained by balancing the mass fluxes through the interfaceand by describing the protein mediated transport as a surface reaction. Applyinghomogenization techniques, macroscopic equations for water and solute transport in a planttissue are derived. The macroscopic problem is given by a Darcy law with a force termproportional to the difference in concentrations of the osmotically active solute in thesymplast and apoplast; i.e. the flow is also driven by the local concentration differenceand its direction can be different than the one prescribed by the pressure gradient.