• 研究论文 •

### 根表面养分吸收通量和根围溶质浓度的近似解析解

1. 1 福建师范大学数学与信息学院, 福州 350117
2 福建省分析数学及其应用重点实验室, 福州 350117
• 收稿日期:2018-05-17 出版日期:2018-10-20 发布日期:2019-01-30
• 通讯作者: 欧忠辉
• 基金资助:
国家自然科学基金(11671085);国家自然科学基金(11771082);福建省引导性项目(2015Y0054)

### Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations

Hui-Ping ZHANG1,Shu-Yue WANG1,Zhong-Hui OU1,2,*()

1. 1 College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China
2 Fujian Key Laboratory of Mathematical Analysis and Applications, Fuzhou 350117, China
• Received:2018-05-17 Online:2018-10-20 Published:2019-01-30
• Contact: Zhong-Hui OU
• Supported by:
Supported by the National Natural Science Foundation of China(11671085);Supported by the National Natural Science Foundation of China(11771082);the Fujian Province Guiding Project(2015Y0054)

Abstract:

Aims We use the Nye-Tinker-Barber model to obtain approximate analytical solutions of the root surface nutrient uptake flux and the rhizosphere solute concentrations.
Methods The rhizosphere is divided into the distant field and the close-range field. The outer solution is obtained by the similarity variable method, and the inner solution is obtained by the rescaling method. Expanding the outer solution from root surface and matching it with the inner solution, we finally obtain the approximate analytical solutions of the root surface nutrient uptake flux and rhizosphere solute concentrations based on Nye-Tinker-Barber model. Numerical simulations are performed on the uptake fluxes of six elements (N, K, P, Mg, S and Ca) and the solute concentrations of two elements (N and K). Comparisons are made among the Nye- Tinker-Barber model approximate analytical solutions, Roose’s analytical solutions and the numerical solutions.
Important findings The approximate analytical solutions of the root surface uptake fluxes based on the diffusion Nye-Tinker-Barber model are similar to those of the Roose's analytical solutions; both approaches produced higher values than the numerical solutions. The approximate analytical solutions of the rhizosphere N and K concentrations based on the diffusion Nye-Tinker-Barber model are similar to the Roose’s analytical solutions and coincide with the trend of changes in the numerical solutions. The approximate analytical solutions of all elements but N, of the root surface, uptake fluxes based on the convection-diffusion Nye-Tinker-Barber model are more similar to the numerical solutions than the Roose’s analytical solutions, and the approximate analytical solutions of the rhizosphere N and K concentrations are coincide with the trend of changes in the numerical solutions.