Session: 10-09-01: Multiphase Flows and Applications

Paper Number: 120206

120206 - Transpiration of Water in a 100-M Tall Simulated Tree 

Stomatal transpiration in trees is theorized to generate the required pressure difference to passively drive water from the soil to the leaves. Trees self-regulate the size of stomata pore opening which can range between micrometers to a few nanometers. In tall trees such as redwoods which are 100 m high, a pressure difference of more than 10 times the atmospheric pressure is required to pull water against gravity over the entire height. Thus, assuming water in the soil is at 1 atm, absolute negative pressure of more than -10 atm is supposed to occur in stomata pores. The overall process involves evaporation of water at the liquid meniscus in stomatal opening potentially generating such a large pressure difference. Thus, comprehension of absolute negative pressure in the liquid and passive propagation of water in the nanoscale pores is crucial to gain a fundamental understanding of the process. Understanding and modeling of the transpiration process has mostly been limited to 1D models, such as the soil-plant-atmosphere continuum (SPAC) model, comprehensive whole-tree model, Ball-Berry stomatal conductance model, supply-demand model, etc. where the transport of water is modeled through a set of resistances driven by differences in water potential. 2D models of transpiration, such as soil-tree-atmosphere continuum (STAC) model, have also been proposed. All such models require fitting parameters and/or external inputs. Further, they do not provide insight into the physics of passive flow, especially on the origin of absolute negative pressure which has been experimentally shown to occur in nanoscale conduits. A published literature, using continuum simulations, attained negative pressure in nanochannels but did not include disjoining pressure which has recently been shown to be dominant in hydrophilic channels of height <100 nm; also, transpiration process was not the focus of the simulation study. Thus, no current literature exists which has coupled absolute negative pressure to transpiration process in a continuum simulation. This work uses 3D CFD simulations to mimic the stomata-xylem-soil pathway in a 100 m tall tree. In nanoscale conduits of height <100 nm, disjoining pressure has been found to play a significant role in determining the liquid water pressure. Thus, to capture the proper physics of water transport in a nanopore, disjoining pressure model is developed and implemented into the simulations, followed by which the transpiration simulations are performed. Disjoining pressure is found to be capable of inducing absolute negative pressures as high as -23.5 atm at the nanopore meniscus during evaporation, thus presenting a sufficient stand-alone explanation of the transpiration mechanism. It is also observed that for very high evaporation rates (5000 kg/m2s in our study), the disjoining pressure driven supply of water cannot balance the evaporation at the meniscus resulting in complete dewetting of meniscus from the nanopore and thus the possible failure of transpiration mechanism. The numerical investigation is supplemented with an analysis based on kinetic theory which dictates a limit on the maximum mass transfer at the liquid meniscus, thus demonstrating the existence of an upper limit to height of trees. The present work lays a foundation for future continuum studies of physical phenomenon where nanoscale liquid films are prominent.

Presenting Author: Shalabh Maroo Syracuse University

Presenting Author Biography: ---

Authors:

Sajag Poudel Syracuse University
An Zou Syracuse University
Shalabh Maroo Syracuse University