Experimental and computational comparison of freeze-thaw-induced pressure generation in red and sugar maple

Sap exudation is the process whereby trees such as sugar (Acer saccharum Marsh.) and red maple (Acer rubrum L.) 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.