A careful physical analysis of gas bubble dynamics in xylem

Many studies have confirmed that cavitation in xylem is caused by air bubbles. Recently Shen et al. (Tree Physiol. 22 (2002) R655), analysed the expansion of a pre-existent bubble in xylem and one formed by air seeding. The present paper makes a further analysis of bubble expansion by the equilibrium criterion of the Helmholtz function. It has been proved that when xylem pressure Pl′ decreases to a special value Pl′∗ from a value higher than, or equal to, or lower than −Po (Po is atmospheric pressure), an air bubble in xylem can grow up steadily, corresponding to minimums of the Helmholtz function F(r). As soon as Pl′ is lower than Pl′∗, since F(r) will be a decreasing function when Pl′<Pl′∗, resulting in non-equilibrium of the bubble, it will break inducing a cavitation event. The analysis is consistent with the results of mechanism. Given Pl′⩾−3Po, if an air bubble could enter a conduit, it would be in a stable equilibrium. When Pl′<−3Po an air bubble entering a conduit will be in an unstable equilibrium. As the water further vaporizes, it will break at once. This is the case to which the former published formula Pl′=−2σ/rp is applicable.