The solution of convection–diffusion equations for solute transport to plant roots

To help develop models of solute uptake that are computationally efficient and suitable for up-scaling to whole root systems, we provide three alternative analytical solutions of equations for transport to absorbing roots by convection and diffusion, and we compare their performance with a numerical solution over the range of plant and soil conditions found in practice. We point out an important pitfall in commonly used methods to solve convection–diffusion equations numerically and show how it can be avoided. We identify a simple analytical solution that is valid for all realistic combinations of parameter values, and show that for most purposes it performs as well as a complete, but more complex, analytical solution allowing fully for both convection and diffusion. We conclude that this solution is suitable for use in general solute uptake models.