Osmosis at constant volume and water uptake in tall trees

TL;DR

This paper models water movement and cavitation repair in tall trees using a thermodynamic approach of osmosis at constant volume, explaining how negative pressures are maintained and cavitations are repaired in xylem vessels.

Contribution

It introduces a thermodynamic model linking osmosis, elastic energy, and cavitation repair in tall trees, providing new insights into water transport and cavitation dynamics.

Findings

Oscillations between tensile and coexisting vapor-liquid states in solvent.

Negative pressure in xylem is sustained by osmosis and elastic energy.

Cavitation repair is facilitated by elastic energy stored in cell walls.

Abstract

We consider a thermodynamic state of a solvent and solution separated with an elastic semipermeable membrane in a box with a constant volume and the relevance of this simple model for the water uptake in tall trees. Under moderate concentrations of a solute, the solution and solvent are under the positive and negative pressure, respectively. In the case of the soft membrane the pressure difference between the compartments with the solvent and solution is given by van't Hoff equation. A state of the negative pressure is not stable and after some time cavitations transform the solvent into the state of coexisting liquid and bubbles of saturated vapor. The pressure difference between the solvent and solution decreases and the membrane relaxes restoring the liquid phase in the compartment with solvent. In this way the solvent oscillates between the tensile state and the coexisting state of liquid and bubbles of saturated vapor. The xylem and phloem, the main vascular systems in trees, are coupled with ray cells. Assuming that a sap in these systems is kept under the constant volume the osmosis between the xylem and phloem with ray cells sustains the negative pressure of the xylem sap. Due to the osmosis elastic energy stored in walls of tracheary element could repair cavitations. In this way both water transport in tall trees and cavitations repair in tracheary elements are related to the osmosis under constant volume. A possible explanation of two long standing problems in tree physiology, water uptake in tall trees and cavitations repair, are offered within this model.