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

非技术摘要两个表面之间的曲率不匹配在自然界和工业中是一个常见的问题：扁平的绷带不能很好地粘在弯曲的指节或肘部上，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造出弯曲的挡泥板。该项目研究了一类极易弯曲但很难拉伸的材料中的“几何挫折感”，包括超薄聚合物薄膜、纺织品和轻型充气结构。这项研究调查了液体表面的曲率如何推动薄的聚合物薄膜，以及它如何也会使它们起皱和起皱。研究结果将发现使用柔性薄片控制液体界面的新方法，超越了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，他们将与高中生和本科生一起在实验室工作。高中教师也将进行研究实习。将创建一个实验室YouTube频道，并将为纽约州锡拉丘兹市中心的科学和技术博物馆开发起皱装置。技术摘要该项目研究极可弯曲但几乎不可伸展的薄板的机械和几何行为，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，研究了曲率驱动的聚合物薄膜在液体表面的组装。利用一种新开发的几何框架，可以通过模拟来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，而倾向于简单的几何最小化。实验研究了重力的附加作用，并探索了由曲率梯度推动的薄片的动力学。这些结果将揭示出用薄膜控制和修饰液体表面的新方法，超越了粒子和分子表面活性剂所能完成的任务。其次，研究了漂浮聚合物薄膜的应力聚焦转变。人们通常不知道曲率、张力和约束是如何在光滑的皱纹中创造出尖锐的应力集中特征的。研究了聚合物薄膜在几种控制良好的装置中的“皱折”转变，包括：(I)在液浴中的压痕，(Ii)圆柱形弯曲半月面上的轴向压缩，和(Iii)各向同性压缩。这项工作将有助于揭示非线性背景下的图案形成和对称性破缺。

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.