Severino Gerardo, Tartakovsky Daniel M
Division of Water Resources Management and Bio-System Engineering, University of Naples, Federico II via Universitá 100, 80055 , Portici, Naples, Italy,
J Math Biol. 2015 Jun;70(7):1645-68. doi: 10.1007/s00285-014-0813-8. Epub 2014 Jul 10.
Transpiration, a process by which plants extract water from soil and transmit it to the atmosphere, is a vital (yet least quantified) component of the hydrological cycle. We propose a root-scale model of water uptake, which is based on first principles, i.e. employs the generally accepted Richards equation to describe water flow in partially saturated porous media (both in a root and the ambient soil) and makes no assumptions about the kinematic structure of flow in a root-soil continuum. Using the Gardner (exponential) constitutive relation to represent the relative hydraulic conductivities in the Richards equations and treating the root as a cylinder, we use a matched asymptotic expansion technique to derive approximate solutions for transpiration rate and the size of a plant capture zone. These solutions are valid for roots whose size is larger than the macroscopic capillary length of a host soil. For given hydraulic properties, the perturbation parameter used in our analysis relates a root's size to the macroscopic capillary length of the ambient soil. This parameter determines the width of a boundary layer surrounding the soil-root interface, within which flow is strictly horizontal (perpendicular to the root). Our analysis provides a theoretical justification for the standard root-scale cylindrical flow model of plant transpiration that imposes a number of kinematic constraints on water flow in a root-soil continuum.
蒸腾作用是植物从土壤中提取水分并将其传输到大气中的过程，是水文循环的一个重要（但量化程度最低）组成部分。我们提出了一个基于第一原理的根系尺度水分吸收模型，即采用普遍接受的理查兹方程来描述部分饱和多孔介质（包括根系和周围土壤）中的水流，并且不对根 - 土连续体中的流动运动结构做任何假设。利用加德纳（指数）本构关系来表示理查兹方程中的相对水力传导率，并将根系视为圆柱体，我们使用匹配渐近展开技术来推导蒸腾速率和植物捕获区大小的近似解。这些解对于尺寸大于宿主土壤宏观毛细管长度的根系是有效的。对于给定的水力特性，我们分析中使用的摄动参数将根系大小与周围土壤的宏观毛细管长度联系起来。这个参数决定了围绕土壤 - 根界面的边界层宽度，在该边界层内水流严格水平（垂直于根系）。我们的分析为植物蒸腾作用的标准根系尺度圆柱流模型提供了理论依据，该模型对根 - 土连续体中的水流施加了一些运动学约束。
