Physical analysis of the process of cavitation in xylem sap

Recent studies have confirmed that cavitation in xylem is caused by air bubbles. We analyzed expansion of a preexistent bubble adhering to a crack in a conduit wall and a bubble formed by the passage of air through a pore of a pit membrane, a process known as air seeding. We consider that there are two equilibrium states for a very small air bubble in the xylem: one is temporarily stable with a bubble radius r(1) at point s(1) on the curve P(r) relating pressure within the bubble (P) with bubble radius (r); the other is unstable with a bubble radius r(2) at point s(2) on P(r) (where r(1) < r(2)). In each equilibrium state, the bubble collapse pressure (2sigma/r, where sigma is surface tension of water) is balanced by the pressure difference across its surface. In the case of a bubble from a crack in a conduit wall, which is initially at point s(1), expansion will occur steadily as water potential decreases. The bubble will burst only if the xylem pressure drops below a threshold value. A formula giving the threshold pressure for bubble bursting is proposed. In the case of an air seed entering a xylem conduit through a pore in a pit membrane, its initial radius may be r(2) (i.e., the radius of the pore by which the air seed entered the vessel) at point s(2) on P(r). Because the bubble is in an unstable equilibrium when entering the conduit, it can either expand or contract to point si. As water vaporizes into the air bubble at s(2), P rises until it exceeds the gas pressure that keeps the bubble in equilibrium, at which point the bubble will burst and induce a cavitation event in accordance with the air-seeding hypothesis. However, other possible perturbations could make the air-seeded bubble contract to s(1), in which case the bubble will burst at a threshold pressure proposed for a bubble expanding from a crack in a conduit wall. For this reason some cavitation events may take place at a xylem threshold pressure (P'(1)*) other than that determined by the formula, P'(1p)* = -2sigma/r(p), proposed by Sperry and Tyree (1988), which is applicable only to air-seeded bubbles at s(2). The more general formula we propose for calculating the threshold pressure for bubble breaking is consistent with the results of published experiments.