根表面养分吸收通量和根围溶质浓度的近似解析解

doi:10.17521/cjpe.2018.0117

摘要/Abstract

摘要：

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。

关键词: 解析解, 养分吸收通量, Nye-Tinker-Barber模型, 溶质浓度全局解

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.

Key words: analytical solution, nutrient absorption flux, the Nye-Tinker-Barber model, global solution of solute concentration

张慧萍, 王淑月, 欧忠辉. 根表面养分吸收通量和根围溶质浓度的近似解析解. 植物生态学报, 2018, 42(10): 1043-1049. DOI: 10.17521/cjpe.2018.0117

Hui-Ping ZHANG, Shu-Yue WANG, Zhong-Hui OU. Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations. Chinese Journal of Plant Ecology, 2018, 42(10): 1043-1049. DOI: 10.17521/cjpe.2018.0117

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链接本文: https://www.plant-ecology.com/CN/10.17521/cjpe.2018.0117

https://www.plant-ecology.com/CN/Y2018/V42/I10/1043

图/表 6

图1 扩散方程中6种元素通量随时间的变化趋势。c∝是初始浓度, 6种元素的初始浓度分别为5、0.046、0.1、0.0029、0.001、0.008 μmol·cm-3; Ftot(t)是养分吸收通量; t是时间, 以25天为例。

Fig. 1 Changes in the fluxes of six elements with time in diffusion Nye-Tinker-Barber model. c∝ is the initial concentration, with given values of 5, 0.046, 0.1, 0.0029, 0.001, 0.008 μmol·cm-3 for the six elements; Ftot(t) is the element uptake flux; t is time, with a duration of 25 days as an example.

图2 对流扩散方程中6种元素通量随时间的变化趋势。c∝是初始浓度, 6种元素的初始浓度分别为5、0.046、0.1、0.0029、0.001、0.008 μmol·cm-3; Ftot(t)是养分吸收通量; t是时间, 以25天为例。

Fig. 2 Changes in the fluxes of six elements with time in convection-diffusion Nye-Tinker-Barber model. c∝ is the initial concentration, with given values of 5, 0.046, 0.1, 0.0029, 0.001, 0.008 μmol·cm-3 for the six elements; Ftot(t) is the element uptake flux; t is time, with a duration of 25 days as an example.

图3 扩散方程中1、7、13、19天钾浓度随距离的变化趋势。c(t)是养分浓度; c∝是养分初始浓度, 钾的初始浓度为0.046 μmol·cm-3; r是到根表面的距离。

Fig. 3 Changes in potassium concentration with distance for 1, 7, 13 and 19 in diffusion Nye-Tinker- Barber model. c(t) is the nutrient concentration; c∝ is the initial concentration, with a given value of 0.046 μmol·cm-3 for potassium, r is the distance to the root surface.

图4 对流扩散方程中1、7、13、19天钾液态浓度随距离的变化趋势。c(t)是养分浓度; c∝是养分初始浓度, 钾的初始浓度为0.046 μmol·cm-3; r是到根表面的距离。

Fig. 4 Changes in potassium concentration with distance for 1, 7, 13 and 19 in convection-diffusion Nye-Tinker- Barber model. c(t) is the nutrient concentration; c∝ is the initial concentration, with a given value of 0.046 μmol·cm-3 for potassium; r is the distance to the root surface.

图5 扩散方程中1、7、13、19天氮浓度随距离的变化趋势。c(t)是养分浓度; c∝是养分初始浓度, 氮的初始浓度为5 μmol·cm-3; r是根表面的距离。

Fig. 5 Changes in nitrogen concentration with distance for 1, 7, 13 and 19 d in diffusion Nye-Tinker- Barber model. c(t) is the nutrient concentration; c∝ is the initial concentration, with a given value of 5 μmol·cm-3 for nitrogen; r is the distance to the root surface.

图6 对流扩散方程中1、7、13、19天氮液态浓度随距离的变化趋势。c(t)是养分浓度; c∝是养分初始浓度, 氮的初始浓度为5 μmol·cm-3; r是根表面的距离。

Fig. 6 Changes in nitrogen concentration with distance for 1, 7, 13 and 19 d in convection-diffusion Nye- Tinker-Barber model. c(t) is the nutrient concentration; c∝ is the initial concentration, with a given value of 5 μmol·cm-3; r is the distance to the root surface.

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