Analytical study of the effects of some soil and plant parameters on root growth due to absorption of one mobile ion: A free-boundary model

The object of our study is: a model for root growth through a free-boundary problem and the effects resulting from differences in nutrient availability and transport of only one mobile nutrient between the root surface and the rhizosphere produced by an absorption Michaelis-Menten for low and high concentrations. The model equations are solved by two methods: the quasi-stationary method and the balance integral method. The numerical solutions are used to compute radial root growth. Curves of nutrient concentration at the root-soil interface, curve as a function of root radius as well as curves representing root radius as a function of time are plotted. The parameters which are varied are the root absorption power, flux velocity at the root surface, efflux, rhizosphere radius, diffusion coefficient, buffer power, and maximum influx. The two methods show the theoretical results for radial root growth in the range of low and high concentrations. The balance integral method provides more detailed information.