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We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic boundary conditions are considered at the individual root surfaces within a root system. As an example, we compare the three-dimensional simulation results of phosphate uptake by a young maize root system to the corresponding effective solution. We show that the two solutions are similar concerning phosphate uptake and the size of the depletion zones. The presented approach makes it possible to verify simplifications that are made in the development of effective models. Furthermore, it is possible to extend existing models by including spatial heterogeneities that will increase our understanding of rhizosphere processes. [ABSTRACT FROM AUTHOR]