Root growth: homogenization in domains with time dependent partial perforations

Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, UK
capdeboscq@maths.ox.ac.uk
Department of Mathematics I, RWTH Aachen University, Wüllnerstr. 5b, 52056 Aachen, Germany
ptashnyk@math1.rwth-aachen.de

Received: 28 October 2010
Revised: 27 June 2011

Abstract

In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for the nutrient density.