X. Noblin1, L. Mahadevan 2, I.A. Coomaraswamy 2, D.A. Weitz2 , N.M. Holbrook 3, M. A. Zwieniecki 4

1 Laboratoire de Physique de la Matiuere Condens'ee, UNSA, Parc Valrose, 06108 Nice Cedex 2, France.
2 School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138 USA.
3 Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, 02138 USA.
4 Arnold Arboretum of Harvard University, Harvard University, Cambridge, MA, 02138 USA.
*e-mail: xavier.noblin@unice.fr

Abstract

Vascular architecture in leaves shows a great diversity, but a few basic physical principles of evaporatively driven transport of water play a general role to better understand it. 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, 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.