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

两个表面之间曲率不匹配是自然界和工业中常见的问题：扁平的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，汽车金属必须通过冲压或锻造才能制成弯曲的护舷。该项目研究了一类极可弯曲材料的“几何挫折”，这些材料虽然难以拉伸，但包括超薄聚合物薄膜、纺织品和轻质充气结构。这项研究调查了液体表面的曲率是如何推动聚合物薄膜的，以及它是如何使它们起皱和折痕的。研究结果将揭示使用柔性薄片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展项目相结合。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。他们将在YouTube上创建一个实验室频道，并为纽约州锡拉丘兹市中心的科学技术博物馆（Museum of Science and Technology）开发一个有关皱纹的装置。技术摘要：该项目研究了极度可弯曲但几乎不可扩展的薄片的机械和几何行为，这类材料包括超薄聚合物薄膜、纺织品和轻质充气结构。首先，研究了液体表面上聚合物薄膜的曲率驱动组装。利用新开发的几何框架进行模拟，可以量化弯曲地形上超薄薄片的能量景观，该框架允许人们避开高度非线性的薄片方程，以支持简单的几何最小化。实验研究了重力的附加作用，并探测了由曲率梯度推动的薄片的动力学。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完成的。其次，研究了浮动聚合物薄膜的应力聚焦转变。通常不知道曲率、张力和约束如何共同作用，在光滑的皱纹上产生尖锐的应力聚焦特征。在几种控制良好的设置下，研究了聚合物薄膜的“褶皱到皱褶”转变，包括：(i)压痕进入液体浴，（ii）圆柱形弯曲半月板上的轴向压缩，以及（iii）各向同性压缩。这项工作将阐明非线性环境下的图案形成和对称破缺。

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.