CAREER: Ultrathin sheets on curved liquid surfaces: Stress focusing and interfacial assembly

两个表面之间曲率的不匹配是自然界和工业中常见的问题：扁平绷带不能很好地粘在弯曲的指关节或肘部上，地球地图夸大了两极附近的区域，汽车金属必须冲压或锻造才能制成弯曲的挡泥板。该项目研究了一类极其可弯曲但难以拉伸的材料中的这种“几何挫折”，包括聚合物薄膜，纺织品和轻质充气结构。这项研究调查了液体表面的曲率如何推动薄聚合物薄膜，以及它如何使它们起皱和起皱。研究结果将揭示使用柔性片材控制液体界面的新方法，超越目前使用肥皂或固体颗粒的方法。这项研究与一系列针对广泛受众的教育和外联项目相结合。该项目将培养两名博士生，他们将在实验室与高中生和本科生一起工作。高中教师也将进行研究实习。一个实验室的YouTube频道将被创建，一个安装在装饰上的装置将被开发为科学和技术博物馆在市中心的锡拉丘兹，NY.技术摘要该项目调查的机械和几何行为的极端弯曲但几乎不可伸展的片材，一类材料，包括可弯曲聚合物薄膜，纺织品，和轻质充气结构。首先，曲率驱动的液体表面上的聚合物薄膜的组装进行了研究。利用新开发的几何框架进行模拟，可以量化弯曲地形上的能量地形，该框架允许人们避开高度非线性的片方程，以利于简单的几何最小化。实验研究重力的附加作用，并探测由曲率梯度推动的片材的动力学。研究结果将揭示用薄膜控制和修饰液体表面的新方法，超越颗粒和分子表面活性剂所能实现的。第二，研究了浮置聚合物膜的应力集中转变。通常不知道曲率、张力和限制是如何在光滑的皱纹中产生尖锐的应力集中特征的。研究了聚合物膜在几种控制良好的设置中的“挣扎到起皱”过渡，包括：（i）压痕到液体浴中，（ii）轴向压缩圆柱形弯曲的弯月面，和（iii）各向同性压缩。这项工作将阐明图案的形成和对称性破缺的非线性设置。

Nontechnical AbstractA mismatch in curvature between two surfaces is a common problem in nature and industry: flat bandages don't stick as well to curved knuckles or elbows, maps of the earth exaggerate areas near the poles, and automotive metal must be stamped or forged to make a curved fender. The project investigates such "geometric frustration" in a class of extremely bendable materials that are nonetheless hard to stretch, including ultrathin polymer films, textiles, and lightweight inflatable structures. The research investigates how the curvature of a liquid surface can propel thin polymer films, and how it can also wrinkle and crease them. The results will uncover new ways for controlling liquid interfaces by using flexible sheets, going beyond current methods using soap or solid particles. The research is coupled to a set of education and outreach projects that target a wide range of audiences. The project will train two PhD students, who will work with high school students and undergraduates in the lab. High-school teachers will also conduct research internships. A laboratory YouTube channel will be created, and an installation on wrinkling will be developed for the Museum of Science and Technology in downtown Syracuse, NY.Technical AbstractThe project investigates the mechanical and geometrical behaviors of extremely bendable yet nearly inextensible sheets, a class of materials that includes ultrathin polymer films, textiles, and lightweight inflatable structures. First, curvature-driven assembly of thin polymer films on liquid surfaces is investigated. The energy landscape of an ultrathin sheet on a curved topography can be quantified using simulations that harness a newly-developed geometric framework, which allows one to side-step the highly nonlinear sheet equations in favor of a simple geometric minimization. Experiments study the additional role of gravity and probe the dynamics of a sheet that is propelled by a curvature gradient. The results will uncover new methods for controlling and modifying liquid surfaces with thin films, going beyond what can be accomplished with particle and molecular surfactants. Second, stress-focusing transitions are studied for floating polymer films. It is generally unknown how curvature, tension, and confinement conspire to create sharp stress-focusing features out of smooth wrinkles. A "wrinkle-to-crumple" transition is studied for polymer films in several well-controlled setups including: (i) indentation into a liquid bath, (ii) axial compression on a cylindrically-curved meniscus, and (iii) isotropic compression. The work will shed light on pattern formation and symmetry breaking in nonlinear settings.