  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.
