  We present an investigation of transpiration of water in a 100 m tall tree
using continuum simulations. Disjoining pressure is found to induce absolute
negative pressures as high as -23.5 atm at the liquid-vapor meniscus during
evaporation, thus presenting a sufficient stand-alone explanation of the
transpiration mechanism. In this work, we begin by first developing an
expression of disjoining pressure in a water film as a function of distance
from the surface from prior experimental findings. The expression is then
implemented in a commercial computational fluid dynamics solver and the
disjoining pressure effect on water wicking in nanochannels of height varying
from 59 nm to 1 micron is simulated. The simulation results are in excellent
agreement with experimental data, thus demonstrating and validating that
near-surface molecular interactions can be integrated in continuum numerical
simulations through the disjoining pressure term. Following the implementation,
we simulate the transpiration process of passive water transport over a height
of 100 m by using a domain comprising of nanopore connected to a tube with a
ground-based water tank, thus mimicking the stomata-xylem-soil pathway in
trees. By varying the evaporation rate from liquid-vapor interface in the
nanopore, effects on naturally-created pressure difference and liquid flow
velocity are estimated. Further, kinetic theory analysis is performed to study
the combined effect of absolute negative liquid-film pressure and accommodation
coefficient on the maximum mass flux feasible during transpiration. Continuum
simulations coupled with kinetic theory reiterate the existence of an upper
limit to height of trees. The numerical model developed here is adept to be
employed to design and advance several other nanofluidics-based natural and
engineering systems.
