A theoretical model of hydraulic conductivity recovery from embolism with comparison to experimental data on Acer saccharum

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Abstract
A theoretical model of bubble dissolution in xylem conduits of stems was designed using the finite differential method and iterative calculations via computer. The model was based on Fick's, Henry's and Charles' laws and the capillary equation. The model predicted the tempo of recovery from embolism in small diameter branches of woody plants with various xylem structures under different xylem water pressures. The model predicted the time required to recover conductivity in any position in the stem. Repeated iterative solution of the model for different situations yielded an empirical formula to calculate the time for complete recovery of conductivity in stems from a fully embolised initial state. The time, tp, is given by: image where α is a temperature coefficient; D is the coefficient of diffusion of air in wood at 25°C; rcs is the ratio of the area of total conduit cross section to the stem cross section; Ψxp is the stem xylem pressure potential (Pa, where 0 Pa equals atmospheric pressure); τ is solution surface tension (0.072 N m−1); and Dc and Ds are diameters of the conduits and the stem, respectively (m). The equation is valid only when Ψxp > –4τ/Dc. The model predicts no recovery of conductivity when Ψxp≤–4τ/Dc. The model agreed with experiments.