Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: Nonstandard scaling

TL;DR

This paper develops a multiscale analytical framework for understanding nutrient uptake by plant root hairs with sparse distribution, combining asymptotic methods and numerical validation to derive effective macroscopic equations.

Contribution

It introduces a novel multiscale analysis approach for nutrient absorption in plant roots with sparse hairs, including rigorous derivation of macroscopic models and validation via simulations.

Findings

Derived effective macroscopic equations for nutrient uptake

Identified higher order correctors for improved accuracy

Validated asymptotic results with numerical simulations

Abstract

In this paper we undertake a multiscale analysis of nutrient uptake by plant root hairs, considering different scale relations between the radius of hairs and the distance between them. We combine the method of formal asymptotic expansions and rigorous derivation of macroscopic equations. The former prompt us to study a distinguished limit (which yields a distinct effective equation), allow us to determine higher order correctors and provide motivation for the construction of correctors essential for rigorous derivation of macroscopic equations. In the final section, we validate the results of our asymptotic analysis by direct comparison with full-geometry numerical simulations.