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.Comment: 31 page
