University of California, San Diego
Campus Directory| Search
Daniel TartakovskyPublications › severino-2015-boundary
› Publications › Teaching › Research group › Useful links

Cite Details

G. Severino and D. M. Tartakovsky, "A boundary-layer solution for flow at the soil-root interface", J. Math. Biol., vol. 70, no. 7, doi:10.1007/s00285-014-0813-8, pp. 1645-1668, 2015


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.

BibTeX Entry

author = {G. Severino and D. M. Tartakovsky},
title = {A boundary-layer solution for flow at the soil-root interface},
year = {2015},
urlpdf = {},
journal = {J. Math. Biol.},
volume = {70},
number = {7},
doi = {10.1007/s00285-014-0813-8},
pages = {1645-1668}