Negative Pressure and Cavitation Dynamics in Plant-like Structures

TL;DR

Negative pressure in plant-like water-filled, porous cells is analyzed through a confined cavitation framework that extends classical nucleation theory to include liquid compressibility and cell elasticity, yielding predictions for the critical radius $R^\ast$, energy barrier $\Delta F^\ast$, and equilibrium bubble volume $V_\mathrm{b}$. The theory is combined with experiments in artificial, plant-mlike cells to reveal ultra-fast nucleation, MHz inertial oscillations, and complex propagation patterns arising from poroelastic coupling, including both positive and negative interactions between neighboring cells. These results illuminate how xylem embolism and spore-ejection mechanisms operate under tension and offer blueprints for biomimetic devices that exploit water under negative pressure for actuation and transport. Overall, the work integrates thermodynamics, fluid mechanics, and experimental biomimicry to map the rich dynamics of cavitation in closed, elastic, plant-like structures under dehydration-driven negative pressure.

Abstract

It is well known that a solid (e.g. wood or rubber) can be put under tensile stress by pulling on it. Once a critical stress is overcome, the solid breaks, leaving an empty space. Similarly, due to internal cohesion, a liquid can withstand tension (i.e. negative pressure), up to a critical point where a large bubble spontaneously forms, releasing the tension and leaving a void (the bubble). This process is known as cavitation. While water at negative pressure is metastable, such a state can be long-lived. In fact, water under tension is found routinely in the plant kingdom, as a direct effect of dehydration, e.g. by evaporation. In this chapter, we provide a brief overview of occurrences of water stress and cavitation in plants, then use a simple thermodynamic and fluid mechanical framework to describe the basic physics of water stress and cavitation. We focus specifically on situations close to those in plants, that is water at negative pressure nested within a structure that is solid, but porous and potentially deformable. We also discuss insights from these simple models as well as from experiments with artificial structures mimicking some essential aspects of the structures found within plants.

Figures (9)

• Figure 1: (a) A liquid at positive pressure exerts an outward force on the walls of a container, while (b) a liquid at negative pressure is in a tensile state and exerts an inward force on the walls. The walls are represented as being deformable, to illustrate the force applied by the fluid. (c) The tensile state as in (b) not only "pulls" on the walls but also on other interfaces; in particular, this tends to make sufficiently large bubbles grow, resulting in cavitation.
• Figure 2: (a) Birth and growth of a cavitation bubble in a dehydrating slice of vascular tissue (xylem) of a pine tree. (b) In-vivo observation of the resulting embolism using X-ray microtomography (transverse and longitudinal cross-sections on left and right, respectively); black areas are gas-filled. (c) Simultaneous cavitation in neighboring cells of a fern sporangium, at the basis of a catapult-like spore ejection mechanism. (d) Another cavitation-based spore ejection mechanism in a fungus. (e) Cavitation induced by osmotic dehydration in fungal spores. Panels (a) and (c) republished with permission of the Royal Society, from Ponomarenko2014 and Llorens2016 respectively; permission conveyed through Copyright Clearance Center, Inc. Panels (b) and (d) reproduced from Choat2016 and Meredith1963 respectively, by permission of Oxford University Press. Panel (e) reproduced from Milburn1970 by permission of Wiley, © New Phytologist Trust.
• Figure 3: Schematic Pressure-Temperature phase diagram of water. $P_\mathrm{sat}(T)$ is the saturation vapor pressure, which represents the coexistence line between the zones of stability of the liquid and vapor phases. When a liquid (point a) is heated up (path 1), vapor can become the stable phase (beyond point b): vapor bubbles can spontaneously nucleate, corresponding to boiling. When pressure is decreased from point a (path 2), vapor can also become the stable phase (below point c) and the nucleation of vapor bubbles is called cavitation in this case.
• Figure 4: Mechanics of negative pressure generation by dehydration of a cell containing liquid water. (a) If the confining cell is infinitely rigid, withdrawing a volume $\Delta V$ of the liquid stretches the liquid by the same amount, which makes the pressure drop (see Equation \ref{['eq:DehydrationMechanicsRigid']}). (b) If the cell is deformable, the same process both stretches the liquid and makes the cell shrink. More liquid volume needs to be removed to produce a similar drop in pressure (see Equation \ref{['eq:DehydrationMechanicsGeneral']}). Red arrows represent the force exerted by the liquid on the walls; lighter blue color indicates a less dense liquid.
• Figure 5: Thermodynamics of negative pressure originating from dehydration. (a) Evaporation in a subsaturated vapor dehydrates the cell until the negative pressure in the cell balances the negative water potential of the external water vapor (see Equation \ref{['eq:Kelvin']}). Equilibrium between the liquid and vapor at different pressures can be mediated through the formation of curved liquid-vapor menisci (inset). (b) Dehydration in an osmotic solution produces the same effect; equilibrium is reached when the negative pressure in the cell balances the external osmotic pressure (see text).