SIAM Journal on Applied Mathematics, Volume 81, Issue 4, Page 1361-1388, January 2021.
In this paper we undertake a multiscale analysis of nutrient uptake by plant roots by considering different scale relations between the radius of root 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. The results of our asymptotic analysis are validated by direct comparison with full-geometry numerical simulations.

中文翻译：

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根毛稀疏分布的植物根系养分吸收的多尺度分析：非标准缩放

SIAM Journal on Applied Mathematics，第 81 卷，第 4 期，第 1361-1388 页，2021
年1 月。在本文中，我们通过考虑根毛半径和它们之间的距离之间的不同尺度关系，对植物根部的养分吸收进行了多尺度分析. 我们结合了形式渐近展开的方法和宏观方程的严格推导。前者促使我们研究一个显着的极限（它产生一个独特的有效方程），使我们能够确定高阶校正器，并为构建对宏观方程的严格推导必不可少的校正器提供动力。我们的渐近分析的结果通过与全几何数值模拟的直接比较得到验证。