Volume 5, Issue 2
Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots

Wenting Lin, Xin Ning, Jianhe Shen & Zhonghui Ou

J. Nonl. Mod. Anal., 5 (2023), pp. 336-353.

Published online: 2023-08

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  • Abstract

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.

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3502

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@Article{JNMA-5-336, author = {Lin , WentingNing , XinShen , Jianhe and Ou , Zhonghui}, title = {Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {2}, pages = {336--353}, abstract = {

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.336}, url = {http://global-sci.org/intro/article_detail/jnma/21929.html} }
TY - JOUR T1 - Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots AU - Lin , Wenting AU - Ning , Xin AU - Shen , Jianhe AU - Ou , Zhonghui JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 336 EP - 353 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.336 UR - https://global-sci.org/intro/article_detail/jnma/21929.html KW - Cadmium, complex, uptake, boundary condition. AB -

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.

Wenting Lin, Xin Ning, Jianhe Shen & Zhonghui Ou. (2023). Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots. Journal of Nonlinear Modeling and Analysis. 5 (2). 336-353. doi:10.12150/jnma.2023.336
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