Modeling xylem and phloem water flows in trees according to cohesion theory and Munch hypothesis

Water and solute flows in the coupled system of xylem and phloem were modeled together with predictions for xylem and whole stem diameter changes. With the model we could produce water circulation between xylem and phloem as presented by the Munch hypothesis. Viscosity was modeled as an explicit function of solute concentration and this was found to vary the resistance of the phloem sap flow by many orders of magnitude in the possible physiological range of sap concentrations. Also, the sensitivity of the predicted phloem translocation to changes in the boundary conditions and parameters such as sugar loading, transpiration, and hydraulic conductivity were studied. The system was found to be quite sensitive to the sugar-loading rate, as too high sugar concentration, (approximately 7 MPa) would cause phloem translocation to be irreversibly hindered and soon totally blocked due to accumulation of sugar at the top of the phloem and the consequent rise in the viscosity of the phloem sap. Too low sugar loading rate, on the other hand, would not induce a sufficient axial water pressure gradient. The model also revealed the existence of Munch "counter flow", i.e., xylem water flow in the absence of transpiration resulting from water circulation between the xylem and phloem. Modeled diameter changes of the stem were found to be compatible with actual stem diameter measurements from earlier studies. The diurnal diameter variation of the whole stem was approximately 0.1 mm of which the xylem constituted approximately one-third.