A model of the variation of water potential and diameter within a woody axis cross-section under transpiration conditions

The spatio-temporal variation of water potential and the corresponding changes in diameter in a woody axis cross-section have been modelled. The two-dimensional space model is based on the assumption that the water flux is regulated by Darcy's law which leads to a diffusion type equation. This equation takes into account the water movements to and from the xylem vessels in space and time. The water potential of the vessels being given, a numerical solution provided the values of the water potential variations of the wood and peripheral elastic tissues in the woody axis cross-section throughout the day. By specifying that the predawn water potential equilibrates throughout the whole section, this study enabled us to determine a range of satisfactory values of parameters. A first validation was given by an application of the model to a peach-tree. It was performed by comparing the calculated variations in diameter of a trunk to those which were measured. In conclusion we discuss some physiological consequences of the model.