Gigantic floating leaves occupy a large surface area at an economical material cost

Abstract

The giant Amazonian waterlily (genus Victoria) produces the largest floating leaves in the plant kingdom. The leaves' notable vasculature has inspired artists, engineers, and architects for centuries. Despite the aesthetic appeal and scale of this botanical enigma, little is known about the mechanics of these extraordinary leaves. For example, how do these leaves achieve gigantic proportions? We show that the geometric form of the leaf is structurally more efficient than those of other smaller species of waterlily. In particular, the spatially varying thickness and regular branching of the primary veins ensures the structural integrity necessary for extensive coverage of the water surface, enabling optimal light capture despite a relatively low leaf biomass. Leaf gigantism in waterlilies may have been driven by selection pressures favoring a large surface area at an economical material cost, for outcompeting other plants in fast-drying ephemeral pools.

Fig. 1.. Giant Amazonian waterlily (V. cruziana).

(A) Giant floating leaves can support the weight of a small child. (B) Underside of the leaf showing the vascular network and the petiolar attachment (PA), midrib (MR), and sinuses (S) in the upturned margin. (C and D) Sinuses and stomatodes (yellow arrow) function as part of a rainwater drainage system. (E) The complex vascular network is composed of a radiating series of thick girders (white arrow) and thinner, orthoradial connective anastomoses (blue arrow). (F) Relative size of waterlily leaves: (i), Victoria, (ii) Euryale, (iii) Nymphaea, (iv) Nuphar, and (v) Barclaya. In the five genera that make up the family Nymphaeaceae, gigantism is restricted to the sister genera Victora and Euryale.

Fig. 2.. Mechanical stiffness of giant waterlily leaves.

(A) Force, F, measured as a function of indentation distance, δ, for different species of waterlily: V. cruziana (circles), Nymphaea cultivar “Black Princess” (squares), and N. lotus (triangles). Tests performed on different leaves are represented by different color markers. Inset: Scaling the force by the measured stiffness collapses the data onto one curve. (B) Vasculature thickness of V. cruziana, as a function of radial distance from the petiole attachment (markers) and a line of best fit. Dashed lines represent the mean radial position at which branching occurs; x_i indicates the position at which the ith bifurcation.

Fig. 3.. Modeling the vasculature architecture.

(A) Schematic view of one-eighth of the waterlily model constructed with branching length b = 12 cm and branching angle θ = 16^∘. The width of the first generation of branches w = 20 mm; following generations have w/2, w/4, and w/8. The first anastomose (orthoradial branch) is located a distance a₀ = 10 cm from the center; subsequent anastomoses are separated by a distance a = 5 cm, and their widths are w_a = 1.5 mm. (B) Side view of vasculature (blue) and lamina (gray). The vascular thickness decreases from H₀ = 5 cm at the center to H_L = 1.5 mm at the leaf edge, and the lamina is a uniform sheet of thickness H_L. (C) Finite element simulations of the structure shown in (A), indented by 10 cm, incorporating the leaf vasculature, different Young’s moduli for lamina and vasculature and the buoyancy of the underlying liquid. (D) Comparing experimental force-indentation relations for V. cruziana (circles) and computed force-displacement curves for a circular disk of uniform thickness (pink region); a disk with linearly decreasing thickness (orange region), the vasculature only (green region), and the full waterlily model (the black line), comprising vasculature and lamina. All four structures have the same volume, equal to that of the leaves of V. cruziana on which the experiments were performed, and force-displacement curves are bounded by the range of measured Young’s moduli (i.e., E = 0.6 to 2.7 MPa), except the full waterlily model that explicitly uses E_vein = 0.6 MPa and E_lamina = 2.7 MPa. (E) Thickness profiles used in simulations for the four scenarios from (D) (gray surfaces) and resulting indentation profiles (colors); colors correspond to surface von Mises stress (color bar). The indentation axis is scaled by a factor of 2 for visual clarity.

Fig. 4.. Biomimetric load-bearing structures.

(A) Leaf-like structures, with a thickness profile that mimicked that of Victoria (left) and with a uniform thickness (right), were three-dimensionally printed from an equal amount of plastic. (B) The vascularized structure (left) and plate-like structure (right) supporting 500 and 50 g weights, respectively. (C) Deflection profiles of the vascularized (solid curves) and uniform (dashed lines) platforms measured for increasing weight, W, of applied load (color bar).