Minimizing hydraulic resistance of a plant root by shape optimization

• For a given root volume there is an optimum structure that minimizes a root hydraulic resistance.
• The optimum root structure is characterized by the dimensionless stele conductivity.
• The optimum dimensionless stele conductivity is a constant depending on stele-root radius ratio.

Optimum plant root structure that minimizes a single root’s hydraulic resistance to water-uptake is studied in this paper with the constraint of constant root volume. Hydraulic resistances under the slender body approximation and without such a limitation are considered. It is found that for large stele-to-cortex permeability ratio, there exists an optimum root length-to-base-radius ratio that minimizes the hydraulic resistance. A remarkable feature of the optimum root structure is that the optimum dimensionless stele conductivity depends only on a single geometrical parameter, the stele-to-root base-radius ratio. Once the stele-to-root base-radius ratio and the stele-to-cortex permeability ratio are given, the optimum root length-to-radius ratio can be found. While these findings remain to be verified by experiments for real plant roots, they offer theoretical guidance for the design of bio-inspired structures that minimize the hydraulic resistance for fluid production from porous media.