Long-distance water transport in trees using Korteweg capillarity and microfluidic wave mechanics

The height to which water ascends in trees can reach values, which are above those expected from classical hydraulic formulae by at least one order of magnitude. This problem requires a fluid-mechanical approach to long-distance water transport and capillarity in tree xylems beyond the Navier–Stokes approximation. In the leading-order approximation, such transport is described as a logarithmically nonlinear wave-mechanical many-body model isomorphic to the multiphase fluid with Korteweg-type capillarity and the ideal equation of state. This model indicates a significant reduction in the effective dynamic viscosity and predicts the existence of nonlinear, dispersive, non-dissipative waves of the Korteweg-de Vries type. The wave-mechanical duality suggests that the water molecules in the capillary do form a collective microfluidic state previously conjectured in Dixon–Joly's cohesion theory. The approach reveals the versatile role of transpiration in trees: aside from the vacuum pumping of water from roots to canopy, it creates temperature conditions, which suppress cavitation and thus sustain higher tension values. It is also responsible for creating and maintaining variations of temperature and density, which facilitates control of the direction and magnitude of the effective wave-mechanical force acting upon the flow. By regulating the temperature and density of the sap circulating via their xylem and phloem tissues, plants can adjust this force with respect to the force of gravity, making the long-distance transport of water and dissolved nutrients more efficient.