Transient And Steady State Solutions Of Nutrient Uptake Model By Plant Roots

Plants need to absorb 13 different nutrients from soil in the process of growth and development.The main nutrients include nitrogen,phosphorus,sulfur,potassium,magnesium and calcium,which exist in soil solution as forms of ions.Plants absorb nutrients in soil through three ways: convection,diffusion and mass flow.Nutrient uptake models of plant roots not only help us better understand the complex absorption mechanism,but also predict the concentration and flux of nutrients absorbed by roots,and realize the quantification of demand and supply under stress conditions.This paper studies the nutrient uptake models of plant roots under different nutrient absorption mechanisms,discusses the plant root exudates,the stability of metal complexes and the influence of root microorganisms,and builds analytical methods to obtain the transient-state solutions,steady-state solutions and numerical solutions.These studies play a key role in increasing the yield of crops,producing the organic food,reducing the production costs and protecting environment.This paper mainly contains three parts as follows:In the first part,we use the Kirk model to study the effect of organic acid exudation from plant roots on the rock phosphate solubilization and the phosphate desorption reaction in rhizosphere,and quantify the bioavailability of phosphate in soil.We solve the Kirk model in order to study the promotion of organic acid on the solubilization and desorption of phosphate with the analytical solutions.The semicoupled Kirk model can be divided into the citrate and the phosphate sub-models.Their analytical solutions are successively obtained by using the Laplace and the inverse Laplace transforms realized by the residue theorem.The profiles of the analytical and numerical solutions are highly matched in the rhizosphere except on the right boundary,and it demonstrates that the analytical solution can be directly used to calculate and predict concentration and uptake of phosphate.In the second part,we use the cadmium uptake model by plant roots to predict the cadmium ion concentration of cadmium complex in the soil solution.According to the instability of cadmium complex,namely fully inert,fully labile and partially labile,we use corresponding sub-models to deduce the analytical solutions of cadmium ion concentration.Particularly,when cadmium complex is partially labile,we multiply the ratio of the solutions of partial lability and full inertness in the planar coordinates with the solution of full inertness in the cylindrical coordinate,to obtain the solution of partial lability in the cylindrical coordinate.This analytical method can give the expressions of concentrations and fluxes both at the root surface and in the rhizosphere,and the distribution of cadmium ion in soil.When the cadmium ion concentration is higher at the root surface,the dissociation of cadmium complex will increase the cadmium ion uptake by root,and it demonstrates that initial concentration of cadmium ion is an crucial factor to control the cadmium ion uptake.In the third part,we use the nitrogen absorption model by plant roots to study the concentration of nitrogen in rhizosphere in Cartesian and cylindrical coordinates.If the nutrient uptake equation is transformed into modified Bessel equation,the steady-state solution can be obtained;If solving the Sturm-Liouville problem and using integral transformation,the transient-state solution can be obtained in the Cartesian coordinates.