  Sap exudation is the process whereby trees such as sugar (Acer saccharum) and
red maple (Acer rubrum) generate unusually high positive stem pressure in
response to repeated cycles of freeze and thaw. This elevated xylem pressure
permits the sap to be harvested over a period of several weeks and hence is a
major factor in the viability of the maple syrup industry. The extensive
literature on sap exudation documents competing hypotheses regarding the
physical and biological mechanisms that drive positive pressure generation in
maple, but to date relatively little effort has been expended on devising
mathematical models for the exudation process. In this paper, we utilize an
existing model of Graf et al. [J. Roy. Soc. Interface 12:20150665, 2015] that
describes heat and mass transport within the multiphase gas-liquid-ice mixture
in the porous xylem tissue. The model captures the inherent multiscale nature
of xylem transport by including phase change and osmotic transport in wood
cells on the microscale, which is coupled to heat transport through the tree
stem on the macroscale. A parametric study based on simulations with synthetic
temperature data identifies the model parameters that have greatest impact on
stem pressure build-up. Measured daily temperature fluctuations are then used
as model inputs and the resulting simulated pressures are compared directly
with experimental measurements taken from mature red and sugar maple stems
during the sap harvest season. The results demonstrate that our multiscale
freeze-thaw model reproduces realistic exudation behavior, thereby providing
novel insights into the specific physical mechanisms that dominate positive
pressure generation in maple trees.
