Experimental and computational comparison of freeze-thaw induced pressure generation in red and sugar maple
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Sap exudation is the process whereby trees such as sugar (Acer saccharum) and red maple (A. rubrum) generate high positive stem pressure in response to repeated freeze-thaw cycles. This elevated xylem pressure permits 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 various competing hypotheses regarding the physical and biological mechanisms driving positive pressure generation in maple, but to date relatively little effort has been expended on devising detailed 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 within the porous xylem tissue. The model captures the inherent multiscale nature of xylem transport by including phase change and osmotic transport within wood cells on the microscale, which is coupled to heat transport through the tree stem on the macroscale. We extend this model by incorporating a root reflection coefficient that introduces an asymmetry in root water flux and hence permits a more realistic accumulation of stem pressure. A parametric study based on simulations with synthetic temperature data singles out the essential 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.
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