2013/05/25 by Andrés Chavarría‐Krauser, Chavarría-Krauser, Andrés, Mariya Ptashnyk +1 · 1 citation
Computer Science · #35B27 #35K61 #74Qxx #76D07 #76M50 #76S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.1305.5949
openalex publication_date 2013/05/25 · openalex created_date 2025/11/01 · openalex updated_date 2026/07/28
Water flow in plant tissues takes place in two different physical domains\nseparated by semipermeable membranes: cell insides and cell walls. The assembly\nof all cell insides and cell walls are termed symplast and apoplast,\nrespectively. Water transport is pressure driven in both, where osmosis plays\nan essential role in membrane crossing. In this paper, a microscopic model of\nwater flow and transport of an osmotically active solute in a plant tissue is\nconsidered. The model is posed on the scale of a single cell and the tissue is\nassumed to be composed of periodically distributed cells. The flow in the\nsymplast can be regarded as a viscous Stokes flow, while Darcy's law applies in\nthe porous apoplast. Transmission conditions at the interface (semipermeable\nmembrane) are obtained by balancing the mass fluxes through the interface and\nby describing the protein mediated transport as a surface reaction. Applying\nhomogenization techniques, macroscopic equations for water and solute transport\nin a plant tissue are derived. The macroscopic problem is given by a Darcy law\nwith a force term proportional to the difference in concentrations of the\nosmotically active solute in the symplast and apoplast; i.e. the flow is also\ndriven by the local concentration difference and its direction can be different\nthan the one prescribed by the pressure gradient.\n