When Fan Xu needs a break from his mechanics of soft materials research at Fudan University, he likes to visit the campus’s lotus pool for a calming breath of fresh air. When you’re a physicist, though, sometimes a short break can backfire—in Xu’s case, leading to an 18-month study of thin biological tissue.
It all started when he observed something curious in the growth of the lotus plants. “I noticed that the leaves had different shapes depending on whether they had a water foundation,” he says. “The lotus leaves floating on the water had a flat shape with wrinkles around the margin, while for leaves growing up above the water they have a global deformation, like a cone shape.” While there are a host of factors influencing the growth of a lotus leaf, including genes, Xu wondered what effect the water substrate had on leaf growth and whether he could explain the various shapes from a physics perspective.
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| Figure 1. The Xi Garden at Fudan University boasts a number of water lilies and lotuses. Image credit: Fudan School of Management |
“The basic idea is very simple,” he says of their work, recently published in Physical Review Letters. He and his students developed a series of partial differential equations to describe the support that water lends growing leaves, then solved the nonlinear equations to find multiple solutions requiring the least amount of energy on the plant’s part. “The principle is quite straightforward: you describe the energy, you do the minimization of the energy, and you have different shapes,” he explains —though the actual derivations require over one-hundred lines of equations* so maybe straightforward isn’t quite the right term.
His theoretical predictions matched well with his observations in nature—shockingly well. Solving for a variety of leaf sizes and shapes growing both on the water’s surface and above it, the theoretical computations look very similar to the leaves found in nature. Wanting to take it a step further, though, Xu decided to test his solutions experimentally.
After looking around for a while, they found water-swelling rubber. Commonly used in civil engineering, this material can swell to over 300 percent of its original volume in water, making it a workable proxy of plant growth. “The deformation of this material is entirely elastic-like in our model and in nature,” he adds.
Rolling out the rubber into thin sheets and precisely cutting it to the leaf shapes they studied, Xu’s group produced a series of young leaf mimics. They then either placed them directly in water or suspended them on three-dimensional support, feeding the growing suspended “leaves” with water. As they grew, the shape of rubber sheets changed, much like actual growing leaves!
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| Figure 2. Xu’s theoretical models of leaves (top and fourth rows) come very close to leaves found in nature. The water-swelling rubber mimics also align with both the theoretical and natural models. (In this image, a blue background indicates that the leaf is grown on water, while a white background denotes a suspended leaf.) Image credit: Fan Xu |
While this research may seem purely curiosity-driven, Xu says that it could have important applications in materials science down the line. “[The growth pattern] is very universal, so it is possible that in the nanoworld, with 2-dimensional materials, this wrinkling phenomenon could be used to change some physical property of the material. In addition, military camouflaging and environment adaption could also be relevant,” he says.
Looking forward, Xu is considering collaborating with biologists to quantitatively measure the long-term growth of lotuses, or potentially pushing the study into the application—proving that sometimes a seemingly short detour can have long-reaching implications.
*The curious reader can follow the solution in the supplemental materials included at the end of the paper.
– Eleanor Hook