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.

翻译：汁液泌出是指糖枫（Acer saccharum）和红枫（Acer rubrum）等树木在反复冻融循环作用下产生异常高的正茎压的过程。这种升高的木质部压力使树汁能在数周内持续采集，因此是枫糖浆产业可行性的关键因素。关于汁液泌出的大量文献记录了驱动枫树正压生成的物理与生物机制的竞争性假说，但迄今为止在建立泌出过程的数学模型方面投入的努力相对较少。本文采用Graf等人[《英国皇家学会界面杂志》12:20150665, 2015]的现有模型，该模型描述了多孔木质部组织中气-液-冰多相混合物内的热质传递过程。模型通过纳入微观尺度上木材细胞内的相变与渗透输运过程，捕捉了木质部输运固有的多尺度特性，并与宏观尺度上贯穿树干的热传递过程相耦合。基于合成温度数据模拟的参数化研究识别了对茎压积累影响最大的模型参数。随后以实测日温度波动作为模型输入，将模拟压力结果直接与成熟红枫和糖枫在树汁采收季节的实测数据进行对比。结果表明，本文提出的多尺度冻融模型能够再现真实的泌出行为，从而为揭示主导枫树正压生成的具体物理机制提供了新见解。