Thermodynamic analysis of the interaction of the xylem water and phloem sugar solution and its significance for the cohesion theory

Abstract

The cohesion theory explains water transport in trees by the evaporation of water in the leaves (transpiration), which in turn generates the tension required for sap ascent, i.e. the flow of pure water from the soil through the root system and the non-living cells of the tree (xylem tracheids) up to the leaves. Only a small part of this water flow entering the leaves is used in photosynthesis to produce sugar solution, which is transported from the leaves through the living cells (phloem) to everywhere in the tree where it is needed and used. The phloem sieves are connected to the xylem tracheids by water transparent membranes, which means that the upflow of pure water and downflow of sugar solution interact with each other, causing the osmotic pressure in the sugar solution (Münch model). In this paper we analyse this interaction with a thermodynamic approach and we show that some open questions in the cohesion theory can then perhaps be better understood. For example, why under a quite high tension the water can flow in the xylem mostly without any notable cavitation, and how the suction force itself depends on the cavitation. Minimizing Gibbs energy of the system of xylem and phloem, we derive extended vapor pressure and osmotic pressure equations, which include gas bubbles in the xylem conduits as well as the cellulose-air-water interface term. With the aid of the vapor pressure equation derived here, we estimate the suction force that the cavitation controlled by the phloem sugar solution can generate at high moisture contents. We also estimate the suction force that the transpiration can generate by moisture gradient at low moisture contents. From the general osmotic pressure equation we derive an equation for calculating the degree of cavitation with different sugar solution concentrations and we show the conditions under which the cavitation in the xylem is totally avoided. Using recent field measurement results for a Scotch pine, the theory is demonstrated by showing its predictions for possible amounts of cavitation or embolism from morning hours to late afternoon.