In this article the process of nutrient uptake by a single branch of a root is studied. We consider diffusion and active transport of nutrients dissolved in water. The uptake of nutrients happens on the surface of thin root hairs distributed periodically and orthogonal to the root surface. Water velocity is defined by the Stokes equations. Macroscopic model for nutrient uptake by a hairy root is derived. The macroscopic model consists of a reaction-diffusion equation in the domain with hairs, and diffusion-convection equation in the domain without hairs. The macroscopic water velocity is described by the Stokes system in the domain without hairs, with no-slip condition on the boundary between domains with hairs and of free fluid.
|Faculties / Institutes:||The Faculty of Mathematics and Computer Science > Department of Applied Mathematics|
|Controlled Keywords:||Mehrskalenanalyse, Homogenisierung <Mathematik>, Reaktions-Diffusionsgleichung, Stokes-Gleichung|
|Uncontrolled Keywords:||two-scale convergence , partially perforated domain|