Optimal vein density in artificial and real leaves

doi:10.1073/pnas.0709194105

Optimal vein density in artificial and real leaves

*Department of Organismic and Evolutionary Biology,
^§School of Engineering and Applied Sciences, and
^¶Arnold Arboretum, Harvard University, Cambridge, MA 02138; and
^†Laboratoire de Physique de la Matière Condensée, Centre National de la Recherche Scientifique–Unité Mixte de Recherche 6622, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France

Edited by Karl J. Niklas, Cornell University, Ithaca, NY, and accepted by the Editorial Board March 31, 2008 (received for review September 27, 2007)

Abstract

The long evolution of vascular plants has resulted in a tremendous variety of natural networks responsible for the evaporatively driven transport of water. Nevertheless, little is known about the physical principles that constrain vascular architecture. Inspired by plant leaves, we used microfluidic devices consisting of simple parallel channel networks in a polymeric material layer, permeable to water, to study the mechanisms of and the limits to evaporation-driven flow. We show that the flow rate through our biomimetic leaves increases linearly with channel density (1/d) until the distance between channels (d) is comparable with the thickness of the polymer layer (δ), above which the flow rate saturates. A comparison with the plant vascular networks shows that the same optimization criterion can be used to describe the placement of veins in leaves. These scaling relations for evaporatively driven flow through simple networks reveal basic design principles for the engineering of evaporation–permeation-driven devices, and highlight the role of physical constraints on the biological design of leaves.

Footnotes

^‡To whom correspondence should be addressed. E-mail: xavier.noblin{at}unice.fr
Author contributions: X.N., L.M., D.A.W., N.M.H., and M.A.Z. designed research; X.N., L.M., I.A.C., N.M.H., and M.A.Z. performed research; X.N., L.M., N.M.H., and M.A.Z. analyzed data; and X.N., L.M., N.M.H., and M.A.Z. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. K.J.N. is a guest editor invited by the Editorial Board.
↵ ‖ In this reference, qualitative correlation is made between vein density and tissue proportions, which is not necessarily related to δ.