Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots (Journal of Nonlinear Modeling and Analysis, 2024)
The concentration distribution of cadmium ion in soil is studied bythe phytoavailability model. According to the states of the cadmium complex:fully inert, fully labile and partially labile, we establish three correspondingcadmium uptake sub-models, and derive respective global analytical solutionsat steady state. In particular, when the complex is partially labile, we givethe steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex andfully inert complex in planar geometry and fully inert complex in cylindricalgeometry, that is, the ration approximation method. In this paper, the globalanalytical solutions are compared with the results of literature and numericalsimulations. Therefore, the double check is realized to ensure the rationalityof the analytical method. The global concentration profile of cadmium ionsin the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from theroot surface and finally reaches the initial value; the change rate of cadmiumion concentration is the largest when the complex is fully labile; whatever thestate 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 reasonableto take the fixed right boundary, and plant roots can uptake cadmium ions ina wider range.