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Water Affects Morphogenesis of Growing Aquatic Plant Leaves

Fan Xu's picture

Lotus leaves floating on water usually experience short-wavelength edge wrinkling that decays toward the center, while the leaves growing above water normally morph into a global bending cone shape with long rippled waves near the edge. Observations suggest that the underlying water (liquid substrate) significantly affects the morphogenesis of leaves. To understand the biophysical mechanism under such phenomena, we develop mathematical models that can effectively account for inhomogeneous differential growth of floating and freestanding leaves to quantitatively predict formation and evolution of their morphology. We find, both theoretically and experimentally, that the short-wavelength buckled configuration is energetically favorable for growing membranes lying on liquid, while the global buckling shape is more preferable for suspended ones. Other influencing factors such as the stem or vein, heterogeneity, and dimension are also investigated. Our results provide a fundamental insight into a variety of plant morphogenesis affected by water foundation and suggest that such surface instabilities can be harnessed for morphology control of biomimetic deployable structures using substrate or edge actuation.

Phys. Rev. Lett., 124, 038003, 2020.

This work has been selected for a Focus (Explaining the Ruffles of Lotus Leaves) in Physics, highlighted by Nature (Rubber ‘leaves’ reveal the physics of the floating lotus), featured in Physics Buzz (How water can shape lotus leaves) and PhysOrg (Improved mathematical model helps explain different lotus leaf types).


Dear Xu Fan,

Congratulations on your excellent work! It is a very well designed study and I find the experimental re-creation of the phenomena using WSR very interesting. These soft active materials can be very nice platforms to study morphological growth phenomena.

I was wondering whether, in very high R/h, you observe crumpling type behavior? In our study on instabilities in dielectric elastomers, when the membrane get thinner (through stretching), the instability mode changes from buckling to wrinkling to crumpling. I am adding a link to this work below. Thank you.

Best regards,





Fan Xu's picture

Dear Hareesh,

Thank you so much for your interest in our work and sharing your excellent work on prestretch-determined pattern selection among buckling, wrinkling and crumpling! Both in our computation and experiment without prestreth (stress-free state), we did not observe the crumpling type response (that may occur upon very large prestrething deformation λ>5.5?), even when R/h reaches ~200. In our case, the onset of instability patterns usually appears upon moderate growth strain ~10-2 (max<0.2). Moreover, the different boudnary condtion (clamped in your case and free boudnary in our case) would be another influencing factor. I hope this helps:)

Best wishes,


Dear Xu Fan,

Thank you very much for your response. You have summed up well the various factors that would play into the instability modes. It would indeed be interesting to look more closely at how the boundary conditions affect the stresses in the membrane and the resultant instability modes.

Best regards,




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