Optimal Vein Density in Artificial and Real Leaves
Original Entry by Ryan Truby
AP 225 - Introduction to Soft Matter
September 16, 2012
Authors: X. Noblin, L. Mahadevan, I. A. Coomaraswamy, D. A. Weitz, N. M. Holbrook, M. A. Zwienieki
Citation: X. Noblin, et al. Optimal Vein Density in Artificial and Real Leaves. PNAS. 2008, 105, 9140-9144.
Keywords (from Ref.): water transport, microfluidics, biomimetics, leaf hydraulic properties, evaporative pump
Related Course Keywords: diffusion, osmotic pressure
Background and Introduction
Stoma are pore-like structures found in the leaves of plants that are vital to two important mechanisms in plant physiology: photosynthesis and transpiration. Photosynthesis is the reaction by which plants use water and the energy of incident photons emitted from the Sun to convert carbon dioxide to glucose, a sugar the plant then uses as a source of chemical energy. When stoma are open, carbon dioxide diffuses into the leaves of plants and on into organelles called chloroplasts where photosynthesis takes place, while the oxygen produced from photosynthesis is released from the plant as it diffuses through these open pores. Consequently, precious water can diffuse from the plant too as water vapor while these stoma are open. This loss of water from the plant is called transpiration, and plants have evolved to use transpiration to their benefit. By careful control of these stoma, plants use transpiration as a means for regulating the osmotic pressures of their cells and their internal temperatures, as well for driving water upward against gravity by capillary action from the soil to their leaves.
The authors of this article employed multi-channeled microfluidic devices as artificial leaves in order to model the transpiration-mediated evaporation of water from real leaves and better understand leaves' role in water transport in plants. Through various experimental trials and the development of a numerical model derived from both Fick's law and Darcy's law, the authors were able to elucidate a scaling relation correlating the artificial leaves' ideal channel density with their thicknesses. Interestingly, this scaling relation agreed with an analysis of the distances separating higher-order veins from both each other and the leaf's surface in leaves from 32 different plant species, revealing that leaves vascularize themselves with a network characterized by an ideal vein density.
The artificial leaves designed by the authors were microfluidic devices fabricated from PDMS and fixed to glass substrates. The devices possessed N parallel channels (of length = L, width = ω, height = h) separated by a distance d. The channels were fixed between the glass substrate and a layer of PDMS with thickness δ.
Discussion and Relevance to Soft Matter
 X. Noblin, et al. Optimal Vein Density in Artificial and Real Leaves. PNAS. 2008, 105, 9140-9144.