Optimal design of water transport systems
In its simplest form the transport system in pine needles can be described as a porous pipe with uniform wall suction – a well-studied flow configuration with application from evaporative coolers to rocket engines. Despite the simplicity of such a one-dimensional design, the pine needle’s vascular system can be modified axially such that the energy loss expressed as pressure drop due to viscous drag associated with fluid movement is minimized along the length of the needle. We have developed a non-trivial solution for the optimum distribution of axial permeability based on an idealized one-dimensional model of water flow in a system driven by uniform wall suction (evaporation) subject to the physical constraints of cellular packing. Energy loss (pressure drop) within the needle’s transport system, however, must be consistent with biological and physical functions, which require that (i) the pressure at the tip remains above a physiological minimum and (ii) water flux is able to meet the evaporative demand. These two criteria set the ultimate needle length and allow us to test to what degree biological systems can optimize their hydraulic design within the geometrical constraints posed by needle development. Our analysis of their hydraulic properties demonstrates excellent agreement between the predicted optimum permeability distribution and measured values. This finding adds another level to our understanding of the importance of optimization in naturally made materials.
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