Department of Mechanical and Aerospace Engineering

Daniel Tartakovsky › Publications › severino-2015-boundary

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.

@article{severino-2015-boundary,

author = {G. Severino and D. M. Tartakovsky},

title = {A boundary-layer solution for flow at the soil-root interface},

year = {2015},

urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/severino-2015-boundary.pdf},

journal = {J. Math. Biol.},

volume = {70},

number = {7},

doi = {10.1007/s00285-014-0813-8},

pages = {1645-1668}

}