Modelling the isotope enrichment of leaf water

Farquhar and Gan [10] have proposed a model for the spatial variation in the isotopic enrichment of H₂ ¹⁸O across a leaf, which is specifically formulated for monocotyledoneous leaves. The model is based on the interaction between mass fluxes longitudinally within the xylem, and fluxes laterally through veinlets into the lamina mesophyll, where moisture leaves the leaf through transpiration. The lighter, more abundant, molecule H₂ ¹⁶O escapes preferentially with the evaporating water, resulting in the enrichment of H₂ ¹⁸O at these sites. Enriched water diffuses throughout the leaf, and it is this spatial distribution of enriched water which the model seeks to capture. In this paper we present a general formulation of the model in terms of mass flux, extending it to include variable transpiration rates across the leaf surface, as well as a tapering xylem. Solutions are developed for the general case and, since the solutions present in the form of Kummer functions, properties are established as well as methods for estimating the solutions under certain conditions relevant to the biology. The model output is compared with Gan's data ([14, 15]) collected from maize plants.