Minimizing hydraulic resistance of a plant root by shape optimization |
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Affiliation: | 1. PhysioSign Laboratory, 91040, USA;2. Dept. of Cardiology, Baotou Central Hospital, Baotou, Inner Mongolia 014040, China;3. Dept. of Electrophysiology, Xiangtan Center Hospital, Medical College, Central-South Univ., Hunan 411100, China;4. Dept. of Electrophysiology, Wuhan Asia Heart Hospital, Hubei 430022, China |
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Abstract: | 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. |
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Keywords: | Porous media flow Root water uptake Hydraulic resistance Optimum root structure |
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