Analytical Solution And Numerical Analysis Of Plant Nutrient Uptake Model

Roots are the vegetative organs of plants. Roots take up water and nutrients to sustain growth and metabolism. In the process of plant growth, the plants need to absorb 17 kinds of essential nutrients. Roots need enough nitrogen, phosphorus, potassium, magnesium, calcium and sulfur. When the nutrient concentration is low in the soil, root exudation can promote nutrients uptake. For example, cluster roots exudate organic acids. The quantitative research for plant nutrient uptake is important for plant growth, rational fertilization, environmental protection and soil nutrient management. This article uses the numerical simulation to study the effects of the parameters of different nutrient elements on the nutrient concentration and the influx of nutrient upta.ke. The perturbation method is applied to get the approximate analytical solution of the nutrient concentration and the influx of nutrient uptake. The article consists of the following three parts.The first part, the potassium, phosphorus, nitrogen, magnesium, calcium and sulfur are necessary for the plant growth. These nutrients have different migration patterns in the soil and then can lead to different nutrient concentration in the soil and the influx of nutrient uptake. The diffusion coefficient impacts on the migration rate of nutrients and then can have an impact on the nutrient concentration and the influx of nutrient uptake. We consider the convection and the diffusion terms in the Roose model[34]and use numerical simulation to study the nutrient uptake of maize root. The simulation results show that the potassium, phosphorus, nitrogen, sulfur and magnesium dissipate on the root surface, while the calcium accumulates on the root surface. These are consistent with the experimental rcsults[42]. For phospho-rus, potassium, nitrogen and magnesium, the nutrient concentration increases with diffusion coefficient and barely changes in the far root zone. The influx of nutrient uptake decreases with time and barely changes in the far root zone.The second part, we divide rhizosphere zone into root surface zone (near field) and far root zone (far field), and then use the perturbation method to get the global approximate analytic solution. We get the inner solution by introducing a small per-turbation parameter and using perturbation expansion, and get the outer solution by using expansion of Taylor, and then match the inner and the outer solutions in the overlap area. The global approximate analytic solution has three dimensionless parameters:uptake coefficient, farfield scaled concentration and Peclet number. We compare the numerical solution, the approximate analytic solution of Roose mod-e1[34,35] with the global approximate analytic solution under different parameter values. The results show that the global approximate analytic solution is closer to the numerical solution than the approximate analytic solution of Roose model[34,35]. For the different values of Peclet number, the global approximate analytic solution is consistent with the numerical solution. But when the Peclet number is relatively large, the approximate analytic solution of Roose model[34,35] will deviate from the numerical solution.In the third part, proteaceae plants and part of the leguminous plants will produce cluster roots under low phosphorus condition. The cluster roots can exudate citrate to promote the phosphate uptake of roots. Based on cluster roots model developed by Zygalakis[33], we transform the matrix equations for the numerical calculation. The rhizosphere zone is divided into cluster roots zone and without cluster roots zone. The numerical results show that in the two days of cluster roots growth, cluster roots do not exudate citrate. The phosphate and the citrate concentration barely change. Two days later, cluster roots begins to exudate citrate, and the citrate concentration reaches the maximum value on root surface and then decreases. The phosphate concentration increases in the cluster roots zone and reaches the maximum value. Four days later, the citrate concentration changes little, and the phosphate concentration reaches the maximum value near the cluster roots zone and then reduces.