Water flow in plant tissues takes place in two different physical domains separated by
semipermeable membranes: cell insides and cell walls. The assembly of all cell insides and
cell walls are termed symplast and apoplast,
respectively. Water transport is pressure driven in both, where osmosis plays an essential
role in membrane crossing. In this paper, a microscopic model of water flow and transport
of an osmotically active solute in a plant tissue is considered. The model is posed on the
scale of a single cell and the tissue is assumed to be composed of periodically
distributed 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 interface
and by describing the protein mediated transport as a surface reaction. Applying
homogenization techniques, macroscopic equations for water and solute transport in a plant
tissue are derived. The macroscopic problem is given by a Darcy law with a force term
proportional to the difference in concentrations of the osmotically active solute in the
symplast and apoplast; i.e. the flow is also driven by the local concentration difference
and its direction can be different than the one prescribed by the pressure gradient.