title: A boundary-layer solution for flow at the soil-root interface.
abstract: 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.
authors.affiliation: Division of Water Resources Management and Bio-System Engineering, University of Naples, Federico II via Universitá 100, 80055 , Portici, Naples, Italy, severino@unina.it.
authors.forename: Gerardo
authors.initials: G
authors.lastname: Severino
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Tartakovsky
mesh_terms: D001693:Biological Transport, Active; D055641:Mathematical Concepts; D008954:Models, Biological; D018517:Plant Roots / Q000502:physiology*; D018526:Plant Transpiration / Q000502:physiology*; D012987:Soil; D014867:Water / Q000378:metabolism; D052584:Xylem / Q000502:physiology
chemical_list: D012987:Soil; D014867:Water