School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA.
J Theor Biol. 2014 Jan 7;340:267-84. doi: 10.1016/j.jtbi.2013.08.027. Epub 2013 Sep 4.
Current models of leaf hydration employ an Ohm's law analogy of the leaf as an ideal capacitor, neglecting the resistance to flow between cells, or treat the leaf as a plane sheet with a source of water at fixed potential filling the mid-plane, neglecting the discrete placement of veins as well as their resistance. We develop a model of leaf hydration that considers the average conductance of the vascular network to a representative areole (region bounded by the vascular network), and represent the volume of tissue within the areole as a poroelastic composite of cells and air spaces. Solutions to the 3D flow problem are found by numerical simulation, and these results are then compared to 1D models with exact solutions for a range of leaf geometries, based on a survey of temperate woody plants. We then show that the hydration times given by these solutions are well approximated by a sum of the ideal capacitor and plane sheet times, representing the time for transport through the vasculature and tissue respectively. We then develop scaling factors relating this approximate solution to the 3D model, and examine the dependence of these scaling factors on leaf geometry. Finally, we apply a similar strategy to reduce the dimensions of the steady state problem, in the context of peristomatal transpiration, and consider the relation of transpirational gradients to equilibrium leaf water potential measurements.
当前的叶片水合模型采用了叶片的欧姆定律类比，将其视为理想电容器，忽略了细胞间的流动阻力，或者将叶片视为具有固定电势的水源填充中平面的平面薄片，忽略了叶脉的离散位置及其阻力。我们开发了一种叶片水合模型，该模型考虑了代表性气腔（由叶脉包围的区域）的血管网络的平均电导率，并将气腔内部的组织体积表示为细胞和空气空间的多孔弹性复合材料。通过数值模拟找到了 3D 流动问题的解，然后将这些结果与具有精确解的 1D 模型进行比较，范围涵盖了温带木本植物。然后我们表明，这些解给出的水合时间可以很好地由理想电容器和平面薄片时间的和来近似，分别代表通过脉管系统和组织的传输时间。然后，我们开发了将此近似解与 3D 模型相关联的比例因子，并研究了这些比例因子对叶片几何形状的依赖性。最后，我们在唇形孔蒸腾的背景下应用了类似的策略来降低稳态问题的维度，并考虑了蒸腾梯度与平衡叶片水势测量之间的关系。
